Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets (2020)

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Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) INTRODUCTION Version 1.0 Page 47 CHAPTER 38 SYSTEM ANALYSES (DRAFT) CONTENTS 1. INTRODUCTION ..................................................................................................... 56 Overview ................................................................................................................. 56 Chapter Organization ............................................................................................ 56 Related HCM Content ............................................................................................ 56 2. CONCEPTS ................................................................................................................ 58 Overview ................................................................................................................. 58 Spillback Impact on Freeways .............................................................................. 58 Spillback Impact on Urban streets ........................................................................ 62 Lane-by-Lane Analysis .......................................................................................... 63 Performance Measurement for Systems and O-D .............................................. 63 3. METHODOLOGY .................................................................................................... 64 Scope of the Methodology ..................................................................................... 64 Required Data and Sources ................................................................................... 66 Computational Steps .............................................................................................. 67 4. EXAMPLE PROBLEMS............................................................................................ 84 Example Problem 1: O-D Based Travel Time Estimation for I-75 NB Freeway in Gainesville, Florida ..................................................................................... 84 Example Problem 2: I-10 On-Ramp Spillback analysis in Baton Rouge, Louisiana .......................................................................................................... 95 Example Problem 2, Part 1: Signalized Intersection Ramp Terminal .............. 97 Example Problem 2, Part 2: TWSC Ramp Terminal ......................................... 118 Example Problem 2, Part 3: AWSC Intersection Ramp Terminal .................. 123 Example Problem 3: Off-Ramp Queue Spillback Analysis for a Freeway-to- Freeway Ramp in Miami, Florida. .............................................................. 127 Example Problem 4: On-Ramp Queue Spillback Analysis into a Single-Lane Roundabout in Los Angeles, California ..................................................... 137 5. REFERENCES .......................................................................................................... 143 APPENDIX A: OFF-RAMP QUEUE SPILLBACK ANALYSIS .......................... 144 Capacity Checks .................................................................................................... 144 Queue Length Estimation .................................................................................... 146

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis INTRODUCTION Chapter 38 System Analyses (Draft) Page 48 Version 1.0 Evaluation of Off-Ramp Queue Spillback Impacts .......................................... 152 APPENDIX B: ON-RAMP QUEUE SPILLBACK ANALYSIS ............................ 188 Demand Estimation .............................................................................................. 189 Capacity Estimation ............................................................................................. 195 Evaluation of On-Ramp Queue Spillback Impacts .......................................... 196 All-Way Stop-Controlled (AWSC) Intersections .............................................. 208 Roundabout ramp terminals ............................................................................... 208 APPENDIX C: LANE-BY-LANE ANALYSIS FOR FREEWAY FACILITIES ................................................................................................................. 214 Lane-by-Lane Flow Models by Segment Type ................................................. 214 Speed Flow Curves by Lane and by Segment Type ......................................... 220 Application Examples .......................................................................................... 224

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) INTRODUCTION Version 1.0 Page 49 LIST OF EXHIBITS Exhibit 38-1 Off-Ramp Components ........................................................................... 59 Exhibit 38-2 Definition of Spillback Regimes ............................................................. 60 Exhibit 38-3 Capacity Adjustment Factors (CAFBL) for Through Lanes Adjacent to Blocked Lanes during Queue Spillback.......................................... 60 Exhibit 38-4 Queue Influence Area with Increased Turbulence .............................. 61 Exhibit 38-5 Length of Queue Influence Area as a Function of the Segment Free-Flow Speed (FFS) ........................................................................... 61 Exhibit 38-6 Queue Spillback from an On-Ramp into Urban Street Intersections ............................................................................................................ 62 Exhibit 38-7 Required Input Data, Potential Data Sources, and Default Values for the Systems Analysis Methodology .................................................. 66 Exhibit 38- 8 Default spillback regimes as a function of ramp geometry and driver aggressiveness ..................................................................................... 67 Exhibit 38-9 Systems Analysis Methodology Flowchart .......................................... 68 Exhibit 38-10 Sample Study Network, with Multiple Origins and Destinations ............................................................................................................. 69 Exhibit 38-11 Potential Bottlenecks Constraining the Ramp Terminal Demand .................................................................................................................... 70 Exhibit 38-12 Potential Bottlenecks Constraining the On-Ramp Demand ............ 71 Exhibit 38-13 Spillback Check Procedure for Off-Ramps ......................................... 72 Exhibit 38-14 Spillback Check Procedure for On-Ramps ......................................... 74 Exhibit 38-15 Probability of Lane Choice for Entry/Exit Segments on Freeway Facilities ................................................................................................... 76 Exhibit 38-16 Illustration of Lane Choice Probabilities Along a Freeway Facility ...................................................................................................................... 76 Exhibit 38-17 Speed-flow Curves for Freeway Ramps ............................................. 78 Exhibit 38-18 Sample Calculation of Total Travel Time Using Multi- Period Analysis ....................................................................................................... 80 Exhibit 38-19 Reference Input Values for O-D Analysis at Free-Flow Conditions ............................................................................................................... 81 Exhibit 38-20 List of Example Problems ..................................................................... 84 Exhibit 38-21 Example Problem 1 Network Interchanges, with indication of origins and destinations: ................................................................................... 85 (a) Williston Rd.(b) Archer Rd.(c) Newberry Rd.(d) NW 39th Ave. ........................ 85 Exhibit 38-22 Freeway Origins and Destinations for Example Problem 1 ............. 85 Exhibit 38-23 O-D Matrix for Example Problem 1..................................................... 86 Exhibit 38-24 Urban Street Facilities Evaluated for Example Problem 1 ............... 86 Exhibit 38-25 List of Segments Included Within D-H ............................................... 86

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis INTRODUCTION Chapter 38 System Analyses (Draft) Page 50 Version 1.0 Exhibit 38-26 Input Data for Freeway Facility Analysis ........................................... 87 Exhibit 38-27 Input Data for Intersection Analysis – Archer Rd. WB ..................... 88 Exhibit 38-28 Input Data for Segment Analysis – Archer Rd. WB .......................... 88 Exhibit 38-29 Input Data for Intersection Analysis – NW 39th Ave. EB .................. 88 Exhibit 38-30 Input Data for Segment Analysis – NW 39th Ave. EB ....................... 88 Exhibit 38-31 Demands at the On-Ramps Along the Freeway Facility for Example Problem 1 ................................................................................................. 89 Exhibit 38-32 LOS for the Freeway Segments of Example Problem 1 .................... 89 Exhibit 38-33 Demands at the Off-Ramps Along the Freeway Facility for Example Problem 1 ................................................................................................. 90 Exhibit 38-34 Queue Length Estimation and Queue Storage Checks for Off-Ramps ................................................................................................................ 91 Exhibit 38-35 Flow Distribution and Speeds for Freeway Segments ...................... 92 Exhibit 38-36 Estimated Speeds by Segment Based on Lane Choice Probability and Speeds .......................................................................................... 92 Exhibit 38-37 Speeds for Urban Streets Segments ..................................................... 92 Exhibit 38-38 Travel Times for Urban Streets Segments ........................................... 93 Exhibit 38-39 Travel Times for Freeway Segments ................................................... 93 Exhibit 38-40 Estimated Travel Times for Ramps Entering or Exiting the Freeway Facility ...................................................................................................... 93 Exhibit 38-41 Estimated Travel Times for Ramps Entering or Exiting the Freeway Facility ...................................................................................................... 94 Exhibit 38-42 Example Problem 2 Network Intersections: ....................................... 96 (a) Perkins Rd.; (b) Acadian Center; (c) I-10 EB;(d) I-10 WB .................................... 96 Exhibit 38-43 Origins and Destinations for the freeway facility (I-10 EB) in Baton Rouge, LA................................................................................................. 97 Exhibit 38-44 Acadian Thruway Urban Street Facility ............................................. 97 Exhibit 38-45 Signalized Intersection Geometry – Acadian Thruway @ I- 10 EB ......................................................................................................................... 98 Exhibit 38-46 Phasing Sequence – I-10 EB Intersection ............................................. 98 Exhibit 38-47 Demand Flow Rates (veh/h) – I-10 EB Intersection ........................... 98 Exhibit 38-48 Input Data – I-10 EB Intersection ......................................................... 99 Exhibit 38-49 Freeway Facility Segmentation– I-10 EB ............................................. 99 Exhibit 38-50 Freeway facility (I-10 EB) - Geometric Features ............................... 100 Exhibit 38-51 Calculation of NBR Capacity for a Single Cycle – Time Period 2 .................................................................................................................. 102 Exhibit 38-52 NBR Capacity, Computed for Each Time Period ............................ 102 Exhibit 38-53 Calculation of the On-Ramp Demand (vR) Based on the Intersection Operation. ........................................................................................ 103

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) INTRODUCTION Version 1.0 Page 51 Exhibit 38-54 Freeway Facility (I-10 EB) – Demand Inputs ................................... 103 Exhibit 38-55 Performance Measures for the Freeway Facility (I-10 EB) ............. 104 Exhibit 38-56 Spillback Check – I-10 EB on-Ramp .................................................. 104 Exhibit 38-57 Freeway Facility, Segment 5 (merge) Performance: a) Merge Capacities and b) Queue Lengths .......................................................... 106 Exhibit 38-58 Freeway Performance During Time Period 4 – with and without the Queue Storage Constraint .............................................................. 106 Exhibit 38-59 Estimated Queue Lengths And Merge Capacities – Time Period 2 .................................................................................................................. 107 Exhibit 38-60 Discharge Flow Rates into the On-Ramp for each Phase Throughout the Cycle – Time Period 2 .............................................................. 110 Exhibit 38-61 Estimated Queue Lengths and Merge Capacities – Time Period 3 .................................................................................................................. 111 Exhibit 38-62 Discharge Flow Rates Into the On-Ramp for Each Phase Throughout the Cycle – Time Period 3 .............................................................. 113 Exhibit 38-63 Calculation of Spillback Capacity Reduction Factor for the SBL Movement for Time Period 3 ...................................................................... 114 Exhibit 38-64 Estimated Queue Lengths and Merge Capacities – Time Period 4 .................................................................................................................. 115 Exhibit 38-65 Calculation of Spillback Capacity Reduction Factor for the SBL Movement During Time Period 4 ............................................................... 116 Exhibit 38-66 Comparison of Performance Measures – with and without Consideration of Spillback Effects ...................................................................... 117 Exhibit 38-67 TWSC Intersection Geometry – Acadian Thruway @ I-10 EB. ........................................................................................................................... 118 Exhibit 38-68 Calculation of the On-Ramp Demand (vR) Based on the TWSC Intersection Operation. ............................................................................ 119 Exhibit 38-69 Queue Accumulation Plot Calculations for On-Ramp – TWSC Intersection ................................................................................................ 120 Exhibit 38-70 Queue Accumulation Polygon for the On-Ramp – TWSC Intersection ............................................................................................................ 121 Exhibit 38-71 Comparison of Performance Measures in a TWSC Intersection – Time Period 3 - with and without Spillback Effects ................ 122 Exhibit 38-72 AWSC Intersection Geometry – Acadian Thruway @ I-10 EB ............................................................................................................................ 123 Exhibit 38-73 Calculation of the On-Ramp Demand (vR) Based on the AWSC Intersection Operation ............................................................................ 124 Exhibit 38-74 Check for Spillback Occurrence – AWSC Intersection ................... 124 Exhibit 38-75 Queue Accumulation Plot Calculations for On-Ramp – AWSC Intersection ............................................................................................... 125

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis INTRODUCTION Chapter 38 System Analyses (Draft) Page 52 Version 1.0 Exhibit 38-76 Queue Accumulation Polygon for the On-Ramp – AWSC Intersection ............................................................................................................ 125 Exhibit 38-77 Equivalent Capacities and Headways for on-ramp – Time Period 3 – AWSC Intersection ............................................................................. 126 Exhibit 38-78 Comparison of Performance Measures – Time Period 3 - with and without Spillback Effects .................................................................... 126 Exhibit 38-79 Study Site for Freeway-to-Freeway Queue Spillback Check, Miami, FL ............................................................................................................... 127 Exhibit 38-80 Individual Freeway Facilities: (a) I-75 SB and (b) SR-826 SB ......... 128 Exhibit 38-81 Traffic Demands for the Subject Freeway Facilities ........................ 128 Exhibit 38-82 Performance Measures for I-75 (Freeway Facility 1) ....................... 129 Exhibit 38-83 Performance Measures for SR-826 (Freeway Facility 2) ................. 129 Exhibit 38-84 Estimation of Queue Length and Storage Ratio at the SR- 826 On-Ramp ......................................................................................................... 130 Exhibit 38-85 Link-node Structure for Spillback Analysis – I-75 SB ..................... 131 Exhibit 38-86 Queued Vehicles and Total Number of Vehicles in the Ramp – Time Period 2 .......................................................................................... 132 Exhibit 38-87 Ramp Capacity and Ramp Inputs – Time Period 2 ........................ 133 Exhibit 38-88 Ramp Capacities and Ramp Inputs – Time Period 3 ..................... 134 Exhibit 38-89 Spillback Queue Length – Segment 3 (Diverge) – I-75 SB .............. 134 Exhibit 38-90 Available Queue Storage – Segment 3 (Diverge) – I-75 SB ............. 135 Exhibit 38-91 ................................................................................................................. 135 Back of Queue Length, Including QIA, at the End of Time Period 3 .................... 135 Exhibit 38-92 Schematic of the Study Interchange for Example Problem 4 ......... 137 Exhibit 38-93 Flows and Queues at the Roundabout of Example Problem 4 ............................................................................................................................... 139 Exhibit 38-94 Priority Order for the Roundabout of Example Problem 4 ............ 139 Exhibit 38-A1 Off-Ramp Queue Spillback Check Flowchart ................................. 144 Exhibit 38-A2 Capacity of Ramp Roadways (veh/h)............................................... 145 Exhibit 38-A3 Examples of Unbalanced Ramp Lane Usage: (a) Norfolk/VA and (b) Tampa/FL ........................................................................... 147 Exhibit 38-A4 Spillback Occurrence by Lane at an Off-Ramp / Weaving Segment .................................................................................................................. 148 Exhibit 38-A5 Expanded Link-Node Structure to Evaluate the Off-Ramp Segment .................................................................................................................. 153 Exhibit 38-A6 Sample Geometry of an off-Ramp Considering the Arterial Intersection with Heavy Demanded Left-Turn ................................................ 153 Exhibit 38-A7 Off-Ramp Queue Spillback Regimes ................................................ 155 Exhibit 38-A8 Freeway Facilities Oversaturated Segment Evaluation Procedure, Adapted for Off-Ramp Queue Spillback Evaluation ................... 159

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) INTRODUCTION Version 1.0 Page 53 Exhibit 38-A9 Freeway Facilities Oversaturated Segment Evaluation Procedure, Adapted for Off-Ramp Queue Spillback Evaluation - Continued .............................................................................................................. 160 Exhibit 38-A10 Freeway Facilities Oversaturated Segment Evaluation Procedure, Adapted for Off-Ramp Queue Spillback Evaluation - Continued .............................................................................................................. 161 Exhibit 38-A11 Freeway Facilities Oversaturated Segment Evaluation Procedure, Adapted for Off-Ramp Queue Spillback Evaluation - Continued .............................................................................................................. 162 Exhibit 38-A12 Capacity Adjustment Factors for Lane Blockage (CAFBL) as a Function of the Number of Directional Lanes and the Number of Blocked Lanes ....................................................................................................... 163 Exhibit 38-A13 Equivalent Segment Capacity for Unblocked Lanes When Lane Blockage Occurs .......................................................................................... 163 Exhibit 38-A14 Maximum Off-Ramp Queue Storage Length at Diverge Segments with Occurrence of (a) Regime 3 Queue Spillback And (b) Regime 4 Queue Spillback, when no Shoulder is Available ........................... 165 Exhibit 38-A15 Maximum Off-Ramp Queue Storage Length at Diverge Segments with Occurrence of (A) Regime 3a Queue Spillback and (B) Regime 4a Queue Spillback, when Shoulder is Available .............................. 165 Exhibit 38-A16 Node Structure for Example 1 ......................................................... 166 Exhibit 38-A17 Node Structure for Example 2 ......................................................... 167 Exhibit 38-A18 Node Structure for Example 3 ......................................................... 167 Exhibit 38-A19 Default Spillback Regimes as a Function of Ramp Geometry and Driver Aggressiveness ............................................................... 168 Exhibit 38-A20 Queue Influence Area with Increased Turbulence....................... 168 Exhibit 38-A21 Queue Influence Area as Function of the Segment FFS ............... 169 Exhibit 38-A22 Capacity of Ramp Proper for Off-Ramps ...................................... 169 Exhibit 38-A23 Speed-flow Curves for Freeway Ramps ........................................ 170 Exhibit 38-A24 Ramp Density at Capacity as a Function of Ramp FFS ............... 170 Exhibit 38-A25 Reference HCM Equations for Back-of-Queue Length Estimation .............................................................................................................. 171 Exhibit 38-A26 Selection of a Cycle Reference Point to Determine the Initial Number of Vehicles Within the Approach ............................................ 172 Exhibit 38-A27 Sample Signalized Intersection Approach from an Off- Ramp ...................................................................................................................... 173 Exhibit 38-A28 Conversion of Green Times to Time Steps .................................... 174 Exhibit 38-A29 Illustration of Mainline Flow Rate Split into Blocked and Unblocked Lanes .................................................................................................. 175

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis INTRODUCTION Chapter 38 System Analyses (Draft) Page 54 Version 1.0 Exhibit 38-A30 Procedure for Evaluating the Impact of Queue Spillback on Upstream Nodes and Determination of the Queue Length within Upstream Segments .............................................................................................. 179 Exhibit 38-A31 Illustration of Different Impacts of an off-Ramp Queue at Node i: (a) Lane Blockage, (b) Increased Turbulence and (c) No Effect ........ 180 Exhibit 38-A32 Distribution of pi as Function of Distance from the Off- Ramp Exit, for a 3-Lane Segment ....................................................................... 182 Exhibit 38-A33 Illustration of Lane Change Maneuvers Within the Queue Influence Area in a 4-Lane Segment With Regime 3 ....................................... 182 Exhibit 38-A34 Illustration of Lane Change Maneuvers Within the Queue Influence Area in a 4-Lane Segment With Regime 4 ....................................... 182 Exhibit 38-A35 Impact of a queue spillback on the discharge capacity of an upstream on-ramp ........................................................................................... 184 Exhibit 38-A36 Illustration of Different Density Values Within One Diverge Segment ................................................................................................... 184 Exhibit 38-B1 Procedure for Detecting Spillback Occurrence at an On- Ramp ...................................................................................................................... 188 Exhibit 38-B2 Schematic of Movements Turning to an On-Ramp from a TWSC Intersection ................................................................................................ 191 Exhibit 38-B3 Schematic of Movements Turning to an On-Ramp from an AWSC Intersection ............................................................................................... 192 Exhibit 38-B4 Schematic of Movements Turning to an On-Ramp from a Roundabout ........................................................................................................... 193 Exhibit 38-B5 Signalized Intersections Methodology With Adjustments to Address On-Ramp Queue Spillback .................................................................. 197 Exhibit 38-B6 Typical Signalized Intersection Ramp Terminal in a Diamond Interchange .......................................................................................... 198 Exhibit 38-B7 Step 7B - Estimation of Merging Capacity in a Freeway Ramp ...................................................................................................................... 200 Exhibit 38-B8 Sample Intersection for Calculation of a QAP for the On- Ramp ...................................................................................................................... 201 Exhibit 38-B9 On-Ramp Queue Accumulation Polygon During Queue Spillback ................................................................................................................. 202 Exhibit 38-B10 Illustration of Cooperative Behavior in Unsignalized Intersections With Queue Spillback ................................................................... 203 Exhibit 38-B11 TWSC intersections Core Methodology With Adjustments to Address On-Ramp Queue Spillback .............................................................. 204 Exhibit 38-B12 On-ramp Queue Accumulation Polygon – TWSC Intersection ............................................................................................................ 205 Exhibit 38-B13 AWSC Intersections Core Methodology With Adjustments to Address On-Ramp Queue Spillback ...................................... 208

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) INTRODUCTION Version 1.0 Page 55 Exhibit 38-B14 Roundabouts Methodology With Adjustments to Address On-Ramp Queue Spillback .................................................................................. 209 Exhibit 38-B15 Required Data and Potential Data Sources – Roundabout Spillback Evaluation ............................................................................................. 210 Exhibit 38-B16 Priority Order for a Roundabout Upstream of an On- Ramp ...................................................................................................................... 210 Exhibit 38-C1 Adjustment Factors for Lane Flow Distribution on Basic, Merge and Diverge Segments ............................................................................. 216 Exhibit 38-C2 Adjustment Factors for Lane Flow Distribution on Weaving Segments ............................................................................................... 217 Exhibit 38-C3 LFR Distribution for a Sample 2-Lane Segment (Minneapolis/MN) ................................................................................................ 218 Exhibit 38-C4 LFR Distribution for a Sample 3-Lane Segment (Tampa/FL) ........ 218 Exhibit 38-C5 LFR Distribution for a Sample 4-Lane Segment (Tampa/FL) ........ 218 Exhibit 38-C6 Check for Negative Lane Flows ........................................................ 219 Exhibit 38-C7 Check for Lane Capacity .................................................................... 220 Exhibit 38-C8 Multipliers to Estimate Lane FFS from Segment FFS ..................... 221 Exhibit 38-C9 Capacity of Individual Lanes as a Percentage of Segment Capacity, by Segment Type and Number of Lanes ......................................... 222 Exhibit 38-C10 Comparison of Speed-Flow Curves for Each Lane and for the Segment ........................................................................................................... 226 Exhibit 38-C11 Example of LFR Calculation for a Weaving Segment .................. 226 Exhibit 38-C12 Field × Predicted Speed-Flow Curve for (a) Lane 1 and (b) Lane 2 (CA-1 NB – Santa Cruz/CA) ................................................................... 231

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis INTRODUCTION Chapter 38 System Analyses (Draft) Page 56 Version 1.0 1. INTRODUCTION OVERVIEW This chapter provides methodologies for evaluating the interactions between freeways and urban streets and the effects of spillback from one facility to another. The methodology of this chapter can be applied to a system of interconnected freeways and to freeway-to-arterial connections. It can also be applied when the freeway-arterial interchange consists of signalized intersections, stop-controlled intersections, and roundabouts. The analysis tools of this chapter provide travel times and speeds for networks and for origin- destination pairs (O-D) within these facilities. The methodology builds on the analysis methods of individual points and segments and points and extends them in several ways in order to consider spillback effects from the downstream facility. First, because spillback affects each lane differently, the analysis is conducted on a lane-by-lane basis. Second, supplemental performance measures are provided at the network level and at the O-D level for undersaturated and oversaturated conditions. Travel time measures are also provided for segments and facilities, and their values are consistent with the analysis methods described in other parts of the manual. CHAPTER ORGANIZATION Section 2 provides the performance measures used at the systems level and includes example calculations of O-D travel time and network travel time. Section 3 describes the procedures to evaluate the spillback impact on the freeway due to congestion on the ramp or urban street. Section 4 describes the procedures to evaluate the spillback impact on the urban street due to congestion on the freeway or on- ramp. Section 5 provides case studies to illustrate the application of the methods described in this chapter. A series of appendices provide detailed information on specific models and analysis steps. RELATED HCM CONTENT Other HCM content related to this chapter includes: • Chapters 10 and 25, which present the freeway systems analysis methodology, • Chapters 12, 13, and 14, which present the freeway segment methodologies for basic freeway segments, freeway weaving segments, and freeway merge and diverge segments, respectively, • Chapter 26, which provides additional details for basic freeway segments capacity measurement and driver population factors, VOLUME 4: APPLICATIONS GUIDE 25. Freeway Facilities: Supplemental 26. Freeway and Highway Segments: Supplemental 27. Freeway Weaving: Supplemental 28. Freeway Merges and Diverges: Supplemental 29. Urban Street Facilities: Supplemental 30. Urban Street Segments: Supplemental 31. Signalized Intersections: Supplemental 32. STOP-Controlled Intersections: Supplemental 33. Roundabouts: Supplemental 34. Interchange Ramp Terminals: Supplemental 35. Pedestrians and Bicycles: Supplemental 36. Concepts: Supplemental 37. ATDM: Supplemental 38. System Analyses An origin - destination pair (O- D) represents the route between two specific points in the analysis network. The definition of “point” is provided in the HCM Chapter 2 - Applications

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) INTRODUCTION Version 1.0 Page 57 • Chapters 16 and 18, which provide methodologies for evaluating urban street facilities and urban street segments, respectively, • Chapters 19, 20, 21, and 22, which provide analysis tools for signalized intersections, two-way stop-controlled intersections, all-way stop- controlled intersections, and roundabouts, respectively, and • Chapter 23, which provides methods for evaluating ramp terminals and alternative intersections.

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Concepts Chapter 38 System Analyses (Draft) Page 58 Version 1.0 2. CONCEPTS OVERVIEW This section discusses concepts related to spillback on the freeway, spillback on the urban street, lane-by-lane analysis, and performance measurement for systems and O-Ds. Concepts related to freeway analysis and urban street analysis are described in the respective chapters of this manual. SPILLBACK IMPACT ON FREEWAYS Spillback on the freeway may occur either due to inadequate capacity of the ramp roadway, or due to inadequate capacity at the ramp terminal (typically the intersection at the downstream interchange). The capacity of the ramp roadway is defined as the off-ramp’s maximum allowable hourly flow rate based on its geometric characteristics (mainly number of lanes and free-flow speed). The capacity of the ramp terminal is defined as the capacity of the signalized or unsignalized approach to the surface street. The methodology compares demand and capacity at the off-ramp and at the ramp terminal to determine whether oversaturation conditions will occur. If demand exceeds capacity at either of those two locations, then the queue length is estimated and compared to the available storage on the ramp and along the deceleration lane. When the queue extends beyond the ramp roadway, blockage may occur on one or more mainline freeway lanes. In that case, the methodology estimates the impact of this queue spillback along the freeway by reducing the segment capacity dependent on the number of blocked lanes and the effects of that blockage on adjacent lanes. Off-ramp elements A freeway off-ramp typically consists of three components (Exhibit 38-1): • Deceleration lane(s): its distance is measured from the beginning of the taper of the auxiliary lane to the gore • Ramp roadway: the road section connecting the deceleration lane and the downstream ramp terminal; its distance is measured from the gore to the taper of the ramp terminal; • Ramp terminal: ramp terminals connecting to urban street facilities can be uncontrolled, stop-controlled or signalized intersections; its distance is measured from the point where additional lanes are added to the intersection approaches to the stop bar of the approach. The length of this section should be at least as long as the turn bay lengths of the approach. When the ramp connects two freeway facilities, the downstream ramp terminal is replaced by the merge section of the on-ramp, with no storage length.

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Concepts Version 1.0 Page 59 Queue spillback regimes The impact of queue spillback on the freeway mainline varies as a function of the queue length and the lanes blocked. Four spillback regimes are defined: a) Regime 1 Under this regime, the queue ends within the deceleration lane and does not spill back into the mainline freeway (Exhibit 38-2 (a)) Deceleration lanes typically serve as a transition zone between speeds on the mainline (typically 55 – 75 mi/h) and advisory speeds posted along the off-ramp roadway (typically 20 – 50 mi/h). When queues begin to form on the deceleration lane, the available deceleration distance is reduced, and speeds begin to be affected in the rightmost lane. b) Regime 2 Under this regime, the queue of vehicles extends upstream beyond the deceleration lane, but sufficient lateral clearance on the right-hand shoulder allows for additional queue storage. In this case the deceleration lane does not serve as a transition zone and drivers decelerate and join the back of the queue more abruptly, resulting in turbulence and reduced speeds in the rightmost lane (Exhibit 38-2 (b)). If no lateral clearance exists immediately upstream of the deceleration lane, Regime 2 conditions are not possible. In some cases, this regime does not occur even if storage is available; this depends on local driver behavior and is site-specific. c) Regime 3 Under this regime, the queue extends to the rightmost lane of the freeway mainline (Exhibit 38-2 (c)). This may occur either when there is no shoulder available for additional queue storage, or when drivers choose to queue in the rightmost lane once the deceleration lane is entirely occupied. Non-exiting vehicles on the rightmost lane are delayed or change lanes, which causes increased turbulence and reduced speeds in the two rightmost lanes. d) Regime 4 Exhibit 38-1 Off-Ramp Components

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Concepts Chapter 38 System Analyses (Draft) Page 60 Version 1.0 Under this regime, the queue blocks the rightmost lane, and drivers occasionally or often use the adjacent freeway mainline lane next to the rightmost freeway mainline lane to force their way into the queue, blocking thus an additional lane (Exhibit 38-2 (d)). During this regime, mainline speed and capacity are significantly reduced. The effects of spillback vary from site to site and from time period to time period due to driver behavior and site geometry. Data collection has shown that at some sites, drivers block the adjacent lane, while at other sites they do not, regardless of the queue spillback length at the site. For unblocked lanes adjacent to those completely or temporarily blocked, the methodology uses a “friction factor” in the form of a Capacity Adjustment Factor (CAFBL). This adjustment factor is applied only to segments where Regime 3 or Regime 4 occur. The values for this factor are equal to the Incident Capacity Adjustment Factors of Chapter 11, Freeway Reliability Analysis (Exhibit 11-23), as there are currently no data available to accurately assess the impacts on capacity for this case. However, these values may be conservative, as capacities during incidents may be further reduced due to rubbernecking and the presence of police vehicles. Exhibit 38-3 presents the adjustment factors to be applied in order to obtain the capacity of through lanes adjacent to blocked lanes during queue spillback. This adjustment factor is not applicable for 2-lane segments with Regime 4, as there are no unblocked lanes. Directional Lanes 1 Queued Lane 2 Queued Lanes Exhibit 38-2 Definition of Spillback Regimes Exhibit 38-3 Capacity Adjustment Factors (CAFBL) for Through Lanes Adjacent to Blocked Lanes during Queue Spillback (a) Regime 1 – Queue within the deceleration lane (b) Regime 2 – Queue along the shoulder (c) Regime 3 – Queue in the rightmost lane (d) Regime 4 - Queue blockage of the adjacent lane

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Concepts Version 1.0 Page 61 2 0.70 N/A 3 0.74 0.51 4 0.77 0.50 5 0.81 0.67 6 0.85 0.75 7 0.88 0.8 8 0.89 0.84 A Capacity Adjustment Factor (𝐶𝐴𝐹 ) is also applied to the Queue Influence Area (QIA) upstream of the back of the queue (Exhibit 38-4). Along this area, there is additional turbulence due to increased lane changing, which results in a reduction of capacity. The length of the QIA is estimated as function of the segment free-flow speed (FFS), as shown in Exhibit 38-5. During undersaturated operations, drivers have adequate warnings regarding the presence of a ramp through signage and navigation aids and can position themselves according to their destination. However, when queue spillback occurs drivers can only detect a downstream queue visually and therefore have shorter times to react, resulting in more aggressive lane changes and additional turbulence. Segment Free-Flow Speed (mi/h) Queue Influence Area (ft) 50 810 55 900 60 980 65 1060 70 1140 75 1220 Exhibit 38-4 Queue Influence Area with Increased Turbulence Additional discussion on the determination of the Queue Influence Area (QIA) is presented in Appendix A Exhibit 38-5 Length of Queue Influence Area as a Function of the Segment Free-Flow Speed (FFS)

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Concepts Chapter 38 System Analyses (Draft) Page 62 Version 1.0 SPILLBACK IMPACT ON URBAN STREETS Similar to spillback on freeways, spillback on urban streets may occur due to oversaturated conditions on freeways. Exhibit 38-6(a) illustrates spillback at a signalized intersection, while Exhibit 38-6(b) illustrates spillback at a roundabout. Using the Chapter 13, Freeway Merge and Diverge Segments or Chapter 12, Freeway Weaving Segments procedures, the analyst can determine whether oversaturated conditions will prevail for a single freeway segment and analysis period. The methodology of this chapter provides an estimate of the discharge rate from the intersection to the on-ramp during congested conditions, while also considering any effects from ramp-metering. Estimating this discharge rate is necessary in order to estimate the resulting queue length along the on- ramp. If the ramp is metered, the metering rate should be used instead. (a) Signalized Intersection Spillback (b) Roundabout Spillback The queue length along the on-ramp also depends on the upstream demands. In the example shown in Exhibit 38-6(a), there are three possible movements contributing to this demand: NB right, SB left, and EB through. If the NB right movement is very heavy and/or has the right-of-way for a significant amount of time, the SB left movement may not have as much of an opportunity to contribute to the demand and may spill back upstream, affecting the adjacent SB through movement, as well as the upstream intersection. Thus, in the case of signalized intersections, the relative contribution of demands to the queue length will depend on the relative demands of these movements and the respective signal timings and right-of-way allocation. The discharge rate of these upstream intersection movements will depend on the storage availability on the on-ramp during the respective phase. The analysis estimates the additional lost time due to the presence of the downstream queue and adjusts the effective green of these movements. In the roundabout example shown in Exhibit 38-6(b), the same three movements contribute to the on-ramp demand. However, in this case the movements have priority in the following order: (1) SB left, (2) EB through and (3) NB right. A high-priority movement with a heavy demand may constrain the entry capacity of lower priority movements, resulting in total throughput that is lower than the sum of the three contributing movement demands. Exhibit 38-6 Queue Spillback from an On- Ramp into Urban Street Intersections

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Concepts Version 1.0 Page 63 LANE-BY-LANE ANALYSIS Spillback affects each lane of a facility differently. For example, when spillback occurs at a freeway off-ramp, the right-most lanes of the freeway may be blocked, while the left-most lanes operate in free-flow conditions. Therefore, the methodology estimates operating conditions by lane as well as by segment. The lane-by-lane performance metrics are also used to obtain O-D based travel times. The lane-by-lane analysis provides lane flow ratios (LFR) which represent the percentage of the entering demand by lane. LFR is a function of the segment-wide v/c ratio and values are provided for each segment type (basic, merge, diverge and weaving). In addition, FFS, speeds, and capacities are estimated by lane. When the facility reaches oversaturated conditions, the speeds are estimated based on the Chapter 10, Freeway Systems method, which is based on interactions between successive segments. PERFORMANCE MEASUREMENT FOR SYSTEMS AND O-D In order to evaluate network and O-D performance, it is necessary to have a common performance measure across different types of facilities. Therefore, the methodology estimates travel time by segment and lane, and aggregates these for O-Ds and for the network. For urban streets, Chapter 16 provides tools for obtaining speeds for all segments, and these are used in the systems analysis methodology. For freeway systems, operational performance is determined based on the density and speed at each segment along the network. The average travel time for each segment can be derived based on the respective average speeds. The average travel time for the entire facility can be obtained as a sum of the segments’ average travel times. However, the travel time of some O-D’s cannot be accurately obtained, as they may predominantly or exclusively use specific lanes. The speeds in these lanes could differ substantially from the average segment speed. Generally, speed varies widely between lanes, especially during congested conditions around off- ramp bottlenecks, which may lead to significantly different travel times. For example, travelers exiting at a congested off-ramp will experience a much different travel time than those using the left most lanes of the same segment. Therefore, the O-D based analysis along a freeway network is based on: • Prevailing speeds by individual lanes: A set of models have been developed for estimating the speeds and capacities of each lane for each type of freeway segment. • Selected travel lanes for each O-D: The set of lanes used by an O-D in every segment of the freeway facility is also necessary to calculate the corresponding travel times at each segment. For every feasible O-D, the set of lanes that may be selected are obtained and considered in the estimation. The demand flow rates by lane are estimated as a percentage of the segment demand.

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis METHODOLOGY Chapter 38 System Analyses (Draft) Page 64 Version 1.0 3. METHODOLOGY The methodology of this chapter provides tools for evaluating the performance of networks consisting of freeway and urban street facilities. It also provides methods to evaluate the interactions between freeway and urban street facilities and assess the impact of queue spillback if it occurs. The methodology is based on lane-by-lane analysis for freeway facilities. For signalized and unsignalized intersections the methodology relies on lane group analysis, while for urban street segments there is no differentiation between travel lanes. The methodology provides travel times and speeds for the network, each segment, and by O-D. SCOPE OF THE METHODOLOGY The methodology of this chapter builds on the freeway systems and urban streets analysis methods, and therefore incorporates the scope and all aspects of these chapters’ methodologies. The method of this chapter can evaluate interconnected freeway facilities, and interconnected freeway and urban street facilities. It can consider signalized intersections, stop-controlled intersections, all-way stop-controlled intersections, and roundabouts, as well as a wide range of interchange ramp terminal configurations. Spatial and Temporal Limits The spatial scope of the analysis is a function of the network to be studied, the extent of congestion, and the specific O-D pairs of interest. The external links to the network should remain uncongested throughout the study period. The definition of analysis boundaries, in practical terms, follow the guidance provided by the Freeway Facilities Core Methodology. The temporal and spatial extent of the analysis should be sufficiently long to fully contain the formation and dissipation of all queues within the corridor. Similar to the spatial scope, the temporal scope of the analysis must be compatible with the selected O-D pairs, the study period, and the duration of congestion. The first and last analysis periods should be free of congestion. The methodology can perform multi-period analysis when the travel time is longer than 15 minutes. Performance Measures The methodology of this chapter generates the following performance measures: Freeway Facilities: • Flow, free-flow speed, operating speed, and capacity for individual lanes • Expected travel speed along each segment Urban Streets Facilities: • Travel time along each segment HCM Chapters that address segments and facilities are: 10. Freeway Facilities Core Methodology 12. Basic Freeway and Multilane Highway Segments 13. Freeway Weaving Segments 14. Freeway Merge and Diverge Segments 16. Urban Street Facilities 18. Urban Street Segments 19. Signalized Intersections 20. TWSC Intersections 21. All-Way Stop-Controlled Intersections 22. Roundabouts 23. Ramp Terminals and Alternative Intersections

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) METHODOLOGY Version 1.0 Page 65 • Expected travel speed along each segment System Analysis: • Total and free-flow travel times • Travel time index • Average speed Strengths of the Methodology The strengths of the methodology include: 1. The methodology evaluates the effects of spillback from one facility to another and considers the interactions between urban streets and freeways. 2. The methodology evaluates oversaturated and undersaturated conditions by lane, by segment, and for the entire network. 3. The methodology produces travel times and other performance measures by O-D within the network. 4. The methodology tracks the formation and dissipation of queues across lanes, segments, and facilities. 5. The methodology can be used to evaluate the impacts of modifications in one facility to an adjacent one. Limitations The methodology has the following limitations: 1. Multiple overlapping breakdowns or bottlenecks cannot be fully evaluated by this methodology. Consult Chapter 6, HCM and Alternative Analysis Tools for a discussion of simulation and other models. 2. Demand is an input into the process, and the methodology does not address any changes in demand that are due to traffic operational conditions. 3. Managed lanes can be analyzed as part of the freeway system. However, the interaction of managed lanes operations with spillback conditions are not addressed. 4. The methodology does not explicitly consider alternative intersection and interchange designs, such as DDI and SPUI. However, it can be extended to consider these, assuming turning movements, demands, and queues can be accurately estimated for the movements of interest. 5. The methodology does not consider two-lane roundabouts and their interaction with freeway on-ramps. 6. The reliability method cannot be applied for systems analysis because the process for developing reliability scenarios is different for freeways and arterials.

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis METHODOLOGY Chapter 38 System Analyses (Draft) Page 66 Version 1.0 REQUIRED DATA AND SOURCES The system analysis requires details concerning each freeway and urban street segment’s geometric characteristics, as well as each segment’s demand characteristics during each analysis time period. Exhibit 38-7 shows the data inputs that are required for an operational analysis of a system, potential sources of these data, and suggested default values. Required Input Potential Data Source Suggested Default Value Trajectory Parameters by O-D Origin and destination points Set by analyst Must be provided Route between origin and destination points Set by analyst Must be provided Freeway Facilities Input data for current methods As recommended by HCM (Chapters 10, 12, 13 and 14) As recommended by HCM (Chapters 10, 12, 13 and 14) Ramp access density (number of ramps within 1 mile) Road geometry Must be provided Grade (%) Road geometry Must be provided Urban Street Facilities Input data for current methods As recommended by HCM (Chapters 16 and 18–23) As recommended by HCM (Chapters 16 and 18–23) Urban street segments - corresponding movement at downstream intersection Set by analyst, according to the selected route Must be provided Off-Ramp Queue Spillback Off-ramp queue spillback – expected number of queued lanes Road geometry, field observations Function of the diverge geometry and driver aggressiveness Length of available shoulder (ft) Road geometry Must be provided Off-ramp detailed geometry Road geometry Must be provided On-ramp Queue Spillback On-ramp metering rate (veh/h) (if applicable) Field data Must be provided On-ramp detailed geometry Road geometry Must be provided Roundabouts - exit capacity (pc/h) Field data, past counts 1,300 pc/h Off-ramp queue spillback – expected number of queued lanes If queue spillback from the off-ramp is expected to be extended beyond the length of the deceleration lane, the expected prevailing spillback regime (3 or 4) must be provided by the analyst. Field observations [1] have shown that locations that experience recurring queue spillback always have the same type of spillback regime when the queue extends beyond the deceleration lane (Regime 3 or 4). Regime 4 occurs often at Exhibit 38-7 Required Input Data, Potential Data Sources, and Default Values for the Systems Analysis Methodology

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) METHODOLOGY Version 1.0 Page 67 ramp junctions with a lane drop. At these locations, the exiting traffic can access the off-ramp with a single lane change. Therefore, drivers are more likely to wait until they are closer to the exit to change lanes, blocking the adjacent through lane. However, not all lane drop exits experience a Regime 4 queue spillback. Generally, Regime 4 occurs more frequently in locations with more aggressive driver behavior. Local information and driver behavior should be taken into consideration in determining the prevailing regime at a given site. For operational analyses of existing locations, it is recommended that the analyst provides the expected spillback regime based on observed field conditions. For planning level purposes where no field data is available, Exhibit 38- 8 provides the expected queue spillback regime as a function of the number of exiting lanes and driver aggressiveness. Ramp Geometry Driver Aggressiveness Low Medium High Diverge with deceleration lane Regime 3 Regime 3 Regime 3 Diverge with lane drop Regime 3 Regime 4 Regime 4 COMPUTATIONAL STEPS This section describes the methodology’s computational steps. Exhibit 38-9 illustrates the process used to evaluate systems operations. Exhibit 38- 8 Default spillback regimes as a function of ramp geometry and driver aggressiveness

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis METHODOLOGY Chapter 38 System Analyses (Draft) Page 68 Version 1.0 Step 1: Define Spatial and Temporal Analysis Scope The first step in the analysis requires identification of the spatial and temporal extent of the network to be evaluated. For accurate evaluation of traffic operations, it is essential that the spatial and temporal extent of congestion is contained within the network. If initial analysis determines that queues extend beyond the limits of the network, the analysis area should be modified accordingly in order to contain all congestion effects. The analyst should also select any O-D pairs to be evaluated, along with the respective set of links to be traveled for each selected O-D. Exhibit 38-10 illustrates a sample network with 6 possible origin/destination nodes. Exhibit 38-9 Systems Analysis Methodology Flowchart

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) METHODOLOGY Version 1.0 Page 69 Step 2: Provide Input Parameters for Freeway and Urban Street Analysis The urban street and freeway facilities are first modeled separately using the methodologies from the respective chapters. If multiple facilities of the same type are to be analyzed (for example, two distinct urban street facilities), each facility must first be modeled separately. The performance measures for each of these facilities must also be computed at this step, as they are used next to analyze the freeway-arterial interactions. Step 3: Balance Demands at Freeway-Urban Street Interface When urban street and freeway facilities are modeled independently, the analyst is required to provide demand flow rate values for both facilities. In the case of an interface between a freeway and an urban street, the demand flows traveling through a freeway ramp and the demands at the ramp terminal should be the same in order to conduct systems analysis. The presence of any bottlenecks upstream of the freeway exit may reduce the demand to the ramp junction. If the total off-ramp demand is greater than the ramp roadway capacity, the intersection demand will be reduced accordingly. Similarly, any movements operating above capacity at the ramp/surface street junction would constrain the demand to the downstream freeway on-ramp. This process must be performed for every time period in the analysis and starting from the upstream end of the facility. When demand exceeds capacity at any given location, the downstream demands must be recalculated considering the throughput from the bottleneck. Off-Ramp Demand vs. Downstream Ramp Terminal Demand The demand for the turning movements at the ramp terminal downstream of an off-ramp can be metered by insufficient capacity of the ramp roadway, as shown in Exhibit 38-11. If this bottleneck is not active, the sum of intersection demands vLT and vRT are equal to the off-ramp demand vR. Exhibit 38-10 Sample Study Network, with Multiple Origins and Destinations

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis METHODOLOGY Chapter 38 System Analyses (Draft) Page 70 Version 1.0 However, if the demand at the off-ramp exceeds its capacity, the flow that will reach the ramp terminal will be lower than the off-ramp demand vR. In this case, the following adjustments are performed: a) Insufficient Capacity at a Bottleneck Freeway Segment In order to balance demands, the OFRF is first aggregated for a 15-minute time period as follows: 𝑣 , 𝑇𝑆 𝑂𝐹𝑅𝐹 𝑖, 𝑡,𝑝 where 𝑣 , = adjusted demand at the subject off-ramp (pc/h); 𝑂𝐹𝑅𝐹 𝑖, 𝑡,𝑝 = actual flow that can exit at off-ramp 𝑖 during time step 𝑡 in time interval 𝑝; 𝑇 = number of time steps in 1 h; and 𝑆 = number of computational time steps in an analysis period (typically S=240 for time steps of 15s) If the freeway facility operates at undersaturated conditions, the value of 𝑣 , is equal to the off-ramp demand 𝑣 . If the subject freeway facility operates at oversaturated conditions, the total demand of the off-ramp may be metered at an upstream bottleneck segment. The Oversaturated Segment Evaluation methodology (HCM Chapter 25) provides equations to estimate the off-ramp flow parameter OFRF (Equations 25-23 through 25-25) at every 15-second time step. b) Insufficient Capacity at the Ramp Roadway If the total demand at a freeway exit is greater than the capacity of the ramp roadway (cR ), the flow that will reach the downstream ramp terminal will be constrained by the ramp roadway capacity. For each movement 𝑖 at the intersection, the adjusted demand is calculated as follows: 𝑣 , 𝑣 𝑣∑ 𝑣 𝑚𝑖𝑛 𝑐𝑣 , , 1 where 𝑣 , = adjusted demand for movement 𝑖 at the downstream intersection (pc/h); 𝑣 = demand for movement 𝑖 at the downstream intersection (pc/h); 𝑣 = off-ramp demand (pc/h); Exhibit 38-11 Potential Bottlenecks Constraining the Ramp Terminal Demand Equation 38- 1 The parameter OFRF(i, t, p) is defined as the “actual flow that can exit at off- ramp i during time step t in time interval p” (Chapter 25). It can account for the effects of bottlenecks upstream of the off-ramp that can meter the traffic that arrives to the ramp. Equation 38-2

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) METHODOLOGY Version 1.0 Page 71 𝑣 , = adjusted off-ramp demand (Equation 38- 1) and 𝑐 = capacity of ramp roadway (Exhibit 14-12). On-Ramp Demand vs. Upstream Ramp Terminal Demand At a freeway merge segment the on-ramp demand flow rate vR can be constrained by the following bottlenecks: 1. Insufficient capacity of one or more movements in the ramp terminal 2. Insufficient capacity at the ramp roadway These potential bottlenecks are illustrated in Exhibit 38-12. If capacity is not exceeded at any of those locations, the on-ramp demand vR is equal to the sum of intersection demands that contribute to the on-ramp (vNBR, vEBT and vSBL). However, if capacity is exceeded at any of those locations, the flow that will reach the freeway merge will be lower than the on-ramp demand vR and adjustments should be made to the respective volumes. If any of the ramp terminal movements that discharge into the on-ramp operates over capacity, the total throughput to the on-ramp will be: 𝑣 , 𝑚𝑖𝑛 𝑣 , 𝑐 where 𝑣 , = adjusted on-ramp demand (veh/h); 𝑣 = demand for movement 𝑖 at the intersection (veh/h); 𝑐 = demand for movement 𝑖 at the intersection (veh/h); 𝑁 = number of intersection movements that discharge into the on-ramp If the total on-ramp demand vR is greater than the ramp roadway capacity cR, the adjusted on-ramp demand is: 𝑣 , 𝑚𝑖𝑛 𝑣 , 𝑐 where 𝑣 , = adjusted on-ramp demand (veh/h); Exhibit 38-12 Potential Bottlenecks Constraining the On-Ramp Demand Equation 38-3 Equation 38-4

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis METHODOLOGY Chapter 38 System Analyses (Draft) Page 72 Version 1.0 𝑣 = on-ramp demand (veh/h) 𝑐 = ramp roadway capacity (veh/h), as provided in Exhibit 14-12. Step 4A: Check for Queue Spillback (Off-Ramp) During this step, the methodology evaluates the network to determine whether there is queue spillback from a freeway off-ramp. The analysis is first conducted using 15-minute time periods (single period or multi-period) to determine whether queue spillback is expected to occur. If spillback is expected, Step 5 will perform an analysis based on 15-second time steps. If spillback is not expected, Step 5 will evaluate the performance of the freeway segments in 15- minute intervals. Exhibit 38-13 summarizes the process for conducting a spillback check at off- ramps. The process evaluates whether the spillback originates from the demand to the ramp roadway, or from the demand to the ramp junction at the surface street, or from the downstream freeway on-ramp. Based on this determination, the procedure uses the demand and the capacity for the analysis interval, as well as the previous queue length, to calculate the anticipated queue length for this Exhibit 38-13 Spillback Check Procedure for Off-Ramps

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) METHODOLOGY Version 1.0 Page 73 interval. The detailed calculations for off-ramp spillback check are presented in Appendix A. Step 4B: Check for Queue Spillback (On-Ramp) Queue spillback into a surface street intersection (or upstream freeway facility) can occur when the freeway merge segment has insufficient capacity to process the ramp demand. During this step, the methodology evaluates the network to determine whether there is queue spillback from a freeway on-ramp onto upstream facilities. Exhibit 38-14 illustrates the process for conducting a queue spillback analysis at on-ramps. When the freeway facility operates at oversaturated conditions (at least one segment with LOS F), on-ramp queues are computed using the Freeway Facility Oversaturated Segment evaluation procedure (HCM Chapter 25), through the parameter ONRQ (Equation 25-21). The parameter ONRQ(i, t, p) is defined as the “unmet demand that is stored as a queue on the on-ramp roadway at node i during time step t in time interval p (veh)”

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis METHODOLOGY Chapter 38 System Analyses (Draft) Page 74 Version 1.0 Appendix B details the calculations used to estimate the on-ramp demand based on the intersection operation as well as the procedures for conducting the on-ramp spillback check. Exhibit 38-14 Spillback Check Procedure for On-Ramps

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) METHODOLOGY Version 1.0 Page 75 Step 5A: Compute Operating Speeds for Individual Lanes Along the Freeway Facility Along freeway facilities, operational performance is determined based on the density and speed at each segment along the network. The average travel time for each segment can be derived based on the respective average speeds. For a system analysis, the speed along a segment is function of: • Estimated speeds for individual lanes; • Probability that a lane will be selected by the subject O-D. To estimate the speeds and capacities for individual lanes, a set of models have been developed for each type of freeway segment considering the total number of mainline freeway lanes. These models are valid only for undersaturated conditions, and they predict the Lane Flow Ratio (LFR) for each lane. They are of the form: 𝐿𝐹𝑅 = 𝑎 × 𝑙𝑛 𝑣/𝑐 + 𝑏 𝐿𝐹𝑅 = 1 − 𝐿𝐹𝑅 where 𝑎 = multiplicative calibration parameter (Equation 38-C3, Equation 38-C5, and Equation 38-C7); 𝑏 = additive calibration parameter (Equation 38-C4, Equation 38-C6, and Equation 38-C8); 𝐿𝐹𝑅 = share of the total flow on lane 𝑖, where 𝑖 ranges from 1 to n-1 (n = total number of segment lanes); 𝐿𝐹𝑅 = share of the total flow on the leftmost lane (lane n); and 𝑣/𝑐 = volume/capacity ratio 0 < 𝑣/𝑐 ≤ 1 . Using these LFR values, the methodology next estimates the lane-by-lane free-flow speeds and capacities. These are used to obtain the speeds of each lane using the speed-flow models defined in HCM Equation 12-1. The LFR models and their coefficients, along with the procedures for estimating lane-by-lane free-flow speeds, capacities, and speeds are provided in Appendix C. These models can be used to analyze basic, merge, diverge and weaving segments and mainline freeways with two to four lanes. Freeway segments with 5 or more lanes were not modeled due to insufficient data. Limited field observations for these facilities indicate that flow distributions become more homogenous at wider segments. Therefore, the flow distribution for these segments can be estimated as: 𝐿𝐹𝑅 = 𝑣𝑛 where 𝑣 = segment entering demand (pc/h) and 𝐿𝐹𝑅 = share of the total flow on lane 𝑖, where 𝑖 ranges from 1 to n (n = total number of segment lanes). Equation 38-5 Equation 38-6 The full methodology to predict lane by lane speeds on freeway facilities is discussed in Appendix C. Equation 38-7

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis METHODOLOGY Chapter 38 System Analyses (Draft) Page 76 Version 1.0 For all segment types the share of flow is estimated on the mainline upstream of the segment. The oversaturated portion of the speed-flow curve (when density is greater than density at capacity) cannot be addressed by the speed flow models, as this is a limitation of the existing methods. The lane-by- lane flows for oversaturated conditions are estimated using the procedures of Chapter 25, adjusted to determine the incoming and outgoing flow on a lane-by- lane basis. If off-ramp queue spillback occurs in the freeway facility, then the methodology in Appendix A provides a procedure to determine the lane-by-lane flow distribution. The probability that a given lane is selected depends on the type of O-D. For segments where a driver enters (merge segment) or leaves a freeway facility (diverge segment), the probability of lane selection is shown in Exhibit 38-15 (assuming right-side ramps). Lane choice probability for lane i Number of lanes in the segment 2 3 4+ p1 0.90 0.90 0.90 p2 0.10 0.05 0.05 p3 - 0.05 0.05 p4+ - - 0 For other segments within a freeway facility the probability of choice for a given lane i is equal to the Lane Flow Ratio of lane i (LFRi), defined as the percentage of the total flow assigned to lane i: 𝑝 = 𝐿𝐹𝑅 This concept is illustrated in Exhibit 38-16 for a 3-lane freeway facility with 9 segments. The exhibit shows the lane choice probabilities for the O-D where the traveler enters the freeway facility on segment 2 (merge) and leaves the freeway on segment 8 (diverge). For segments 2 and 8, the choice probabilities for lanes 1, 2 and 3 are 0.90, 0.05 and 0,05 respectively (Exhibit 38-15). For segments 3 through 8, the probabilities of lane choice are equal to LFR (Equation 38-3), calculated for each lane of each segment. The speed for each segment is then computed as the sum of products of speeds for each lane and the corresponding probability of lane choice: 𝑆 = 𝑝 × 𝑠 Exhibit 38-15 Probability of Lane Choice for Entry/Exit Segments on Freeway Facilities Equation 38-8 Exhibit 38-16 Illustration of Lane Choice Probabilities Along a Freeway Facility Equation 38-9

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) METHODOLOGY Version 1.0 Page 77 where 𝑆 = expected speed for the segment (mi/h) 𝑝 = probability that lane i is selected 𝑁 = number of lanes in the segment 𝑆 = speed at lane i (mi/h) (Equation 38-C14) Step 5B: Compute Speeds for Urban Street Segments For urban street facilities, the speeds along each segment are calculated using the Chapter 18, Urban Streets Segments procedures. However, for the intersection at the ramp junction, the control delay value for the corresponding movement (typically right- or left-turn movement into the on-ramp) must be used in the analysis. If there is queue spillback from the on-ramp into the urban street intersection, the increased control delay of the movement towards the on- ramp is obtained using the methodology used in Appendix B. Step 6: Compute Travel Times for Each Segment This step calculates the travel times for each segment using the speeds obtained in Steps 5A and 5B by dividing each segment’s length by its respective speed: 𝑇𝑇 = 𝐿1.47 × 𝑆 where 𝑇𝑇 = travel time for segment i (s) 𝐿 = length of segment i (mi) 𝑆 = speed for segment I, depending on the facility: If a freeway facility: S = Se (expected speed), from Equation 38-9 If a urban street facility: S = St,seg (travel speed), from Equation 18-15 Step 7: Compute Travel Time for Freeway Ramps Ramp speeds can be obtained through the following equation: 𝑆 = 1 − 0.109 × 𝑣1000 × 𝑆 where 𝑆 = ramp speed (mi/h) 𝑣 = ramp demand flow rate (pc/h) 𝑆 = ramp free-flow speed (mi/h) The speed-flow relationship for ramps is linear and speed decreases with higher ramp flows, as shown in Exhibit 38-17. The maximum allowed values of vR are bounded by ramp capacity, consistent with guidance provided by Chapter 14 – Merge and Diverge segments (Exhibit 14-12). Equation 38-10 Equation 38-11

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis METHODOLOGY Chapter 38 System Analyses (Draft) Page 78 Version 1.0 The travel time along freeway ramps is calculated by dividing the ramp length by its respective speed. When an O-D includes an off-ramp, the control delay for the corresponding movement at the at-grade intersection must also be added to the off-ramp travel time. This calculation is consistent with the Urban Streets Facilities methods, where each segment’s travel time includes the control delay of the corresponding movement at the downstream intersection. For off-ramps: 𝑇𝑇 = 𝐿1.47 × 𝑆 + 𝑑 + 𝑎 For on-ramps: 𝑇𝑇 = 𝐿1.47 × 𝑆 + 𝑎 where 𝑇𝑇 = ramp travel time (s) 𝑆 = ramp speed (mi/h) 𝐿 = ramp length (ft) 𝑑 = control delay of the corresponding movement in the downstream ramp terminal (s); applicable for off-ramps only 𝑎 = delay due to acceleration or deceleration, assumed to be 5s In the case of queue spillback, Appendix A describes the procedure for estimating the speed at the ramp, which uses a procedure similar to the Oversaturated Segment Evaluation method described in HCM Chapter 25. Off-ramp Queue Spillback If the ramp roadway is the bottleneck, the off-ramp flow will be constant (equal to the ramp roadway capacity), with the prevailing density equal to the ramp density at capacity. The ramp speed is then computed as equal to the ramp free-flow speed; If the downstream intersection is the bottleneck, queues will build at the intersection and limit the number of vehicles that can exit the ramp roadway and enter the intersection. As a result, the number of vehicles (NV) stored inside the For ramps with lower values of free-flow speed, the threshold value of 45 pc/h/ln for density at capacity is not feasible as it would result in ramp capacity values inconsistent with Exhibit 14-12. The values of density at capacity increases as free-flow speed goes down. These values are used to estimate ramp queue lengths in case of off-ramp queue spillback, as discussed in Appendix A. Exhibit 38-17 Speed-flow Curves for Freeway Ramps Equation 38-12 Equation 38-13

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) METHODOLOGY Version 1.0 Page 79 ramp roadway will increase until the limit value of jam density. The NV parameter for the ramp roadway is computed every time step (15 seconds) and then aggregated to the 15-minute period to compute the average density at the ramp roadway. Similarly, the flow through the ramp roadway is aggregated to 15-minutes and then the speed at the off-ramp is obtained through Equation 12-1, which is repeated here for convenience: below: 𝑆 = 𝐹𝐹𝑆 , 𝑖𝑓 𝑣 ≤ 𝐵𝑃 𝑆 = 𝐹𝐹𝑆 − 𝑖𝑓 𝐵𝑃 < 𝑣 < 𝑐 where 𝑆 = mean speed of a basic segment (mi/h) 𝐹𝐹𝑆 = adjusted free-flow speed (mi/h) 𝑐 = adjusted segment capacity (pc/h/ln) 𝐵𝑃 = breakpoint (pc/h/ln) 𝐷 = density at capacity, typically 45 pc/mi/ln 𝑣 = adjusted 15-min demand flow rate (pc/h/ln) On-ramp Queue Spillback If the on-ramp demand is greater than the merge capacity or any active ramp metering, the number of vehicles (NV) stored in the on-ramp will be increased at every time step by the difference between vehicles that are discharged from the upstream intersection and the number of vehicles that are discharged into the freeway. Similar to off-ramp bottlenecks that form due constraints at a downstream intersection, flows and density values at the on-ramp are computed at every time step (15 seconds) and then aggregated to a 15-minute time period. Next, the speed is computed through Equation 12-1. Step 8: Compute Travel Times for the Network and Each O-D This step computes the total travel time TTO-D for the network as the sum of travel times over all segments along the route. For multi-period analysis, it is important that the travel time for the correct time period at each segment is selected, as a long O-D may encompass several time periods. Exhibit 38-18 presents a sample calculation for a facility with two time periods (15 minutes each). The first segment in the O-D is traversed during Time Period 1, and the Cumulative Travel Time column is updated with the respective value. Subsequent segments follow the same procedure until the cumulative travel time exceeds the length of the first time period (900 seconds). For the next segment in the network, travel times from Time Period 2 are added to the Cumulative Travel Time. This procedure is then repeated until the final segment is reached. The total travel time is obtained as the last value of the Cumulative Travel Time column

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis METHODOLOGY Chapter 38 System Analyses (Draft) Page 80 Version 1.0 Segment ID Segment Travel Time (s) Selected Travel Time (s) Active Time Period Cumulative Travel Time (s) Time Period 1 Time Period 2 1 34 28 34 TP 1 34 2 26 29 26 TP1 60 3 73 86 73 TP1 133 4 345 390 345 TP1 478 5 185 195 185 TP1 663 6 310 359 310 TP1 973 7 240 240 240 TP2 1213 8 120 122 122 TP2 1335 9 20 18 18 TP2 1353 10 45 53 53 TP2 1406 Total travel time (s): 1406 * Cells shaded in gray highlight the selected Time Period applicable to each segment within the O-D Step 9: Compute Performance Measures for Segments The last step in the methodology computes performance measures for each of the segments in the network, using the methods of the respective chapters. Also, the mean travel time index (TTImean,O-D) for a specific O-D can be calculated for each segment and for the network by dividing the O-D total time TTO-D by the respective free-flow total time (Equation 38-14). The free-flow travel time TTFF can be obtained by repeating Steps 1 through 8 for free-flow conditions. 𝑇𝑇𝐼 , = 𝑇𝑇𝑇𝑇 , where 𝑇𝑇 = total travel time for a specific O-D (s) 𝑇𝑇 , = free-flow travel time for a specific O-D during (s) The free-flow travel time 𝑇𝑇 , can be obtained by applying the methodology steps for the subject O-D assuming free-flow conditions. Exhibit 38- 19 provides guidance on key input parameters to be considered for such analysis. Exhibit 38-18 Sample Calculation of Total Travel Time Using Multi- Period Analysis Equation 38-14

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) METHODOLOGY Version 1.0 Page 81 Performance measure Reference parameter Input value Freeway Facilities Lane flow ratio (LFR) v/c 0.1 Speed by lane Free-flow speed by lane (FFSi) Equation 38-C9 Urban Street Segments Travel speed Running time Equation 18-7 Urban Street Intersections Control delay - Signalized Intersections Demand-to-capacity ratio (X) 0 Control delay - TWSC Intersections Movement demand (vx) 0 Control delay - AWSC Intersections Demand-to-capacity ratio (x) 0 Control delay - Roundabouts Demand-to-capacity ratio (x) 0 Freeway ramps Ramp speed Ramp free-flow speed Analyst input The computation of free-flow performance measurements for different facility types is discussed next. Freeway Facilities At free-flow, the speed at freeway segments is computed as equal to their free-flow speed. When a lane-by-lane analysis is applied, the methodology computes the free-flow speed for each lane (Equation 38-C9). Next, the probabilities of lane choice on each segment are calculated for each segment. If the subject segment is a entry/exit segment (segments where the driver enters or leaves the freeway facility, as illustrated in Exhibit 38-16), the lane choice probabilities are obtained from Exhibit 38-15. For other segments, the lane choice probability is equal to its LFR (Equation 38-5). For the calculations of LFR under free-flow conditions, a value of v/c = 0.1 is recommended to provide results consistent with field data for free-flow conditions. Due to the log form of the LFR equation (Equation 38-5), using v/c = 0 is mathematically unfeasible, and very low values of v/c would yield unrealistic results Urban Street Segments The travel speed along urban street segments (Equation 18-15) is calculated as a function of the segment running time (18-7), as shown: 𝑆 , = 3,600𝐿5,280 𝑡 + 𝑑 𝑡 = 6.0 − 𝑙0.0025𝐿 𝑓 + 3,600𝐿5,280 𝑆 𝑓 + 𝑑 , + 𝑑 where 𝑆 , = travel speed of through vehicles for the segment (mi/h) (s) 𝑡 = segment running time (s) 𝑙 = start-up lost time (2s if signalized, 2.5s if stop or yield-controlled) 𝐿 = segment length (ft) Exhibit 38-19 Reference Input Values for O-D Analysis at Free-Flow Conditions

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis METHODOLOGY Chapter 38 System Analyses (Draft) Page 82 Version 1.0 𝑑 = control delay at the downstream intersection (s) 𝑆 = segment free-flow speed (mi/h) 𝑓 = control-type adjustment factor 𝑓 = segment length (ft) 𝑑 , = delay due to left and right turns into intersection i (s/veh) 𝑑 = delay due to other sources along the segment (e.g., curb parking or pedestrians) (s/veh) As shown by Equation 18-7, the running time along an urban street segment is not directly affected by variations in demand. Therefore, free-flow running time is calculated according to Equation 18-7. The only parameter in the segment travel speed that accounts for congestion is the control delay at specific O-D related movement at the downstream intersection, which is discussed next. Urban Street Intersections When intersections are analyzed as part of an urban street facility, the computed control delay is taken into account when estimating the travel speed of the upstream segment. Even at free-flow, intersections still experience a small amount of delay intrinsic to their operation. The control delay for a given lane at a signalized intersection is provided by Equation 19-18: 𝑑 = 𝑑 + 𝑑 + 𝑑 where 𝑑 = control delay (s/veh) 𝑑 = uniform delay (s/veh) 𝑑 = incremental delay (s/veh) 𝑑 = initial queue delay (s/veh) At free-flow conditions, the values of 𝑑 and 𝑑 are equal to zero. Therefore, the free-flow control delay is equal to the value of uniform delay (𝑑 ) computed for a demand-to-capacity ratio 𝑋 = 0. TWSC Intersections The control delay d for TWSC intersections (Rank 2 through Rank 4 movements) is computed through Equation 20-64: 𝑑 = 3,600𝑐 , + 900𝑇 ⎣⎢⎢ ⎢⎡ 𝑣𝑐 , − 1 + 𝑣𝑐 , − 1 + 3,600𝑐 , 𝑣𝑐 ,450𝑇 ⎦⎥⎥ ⎥⎤ + 5 where 𝑐 , = capacity of movement x (veh/h) 𝑣 = flow rate for movement x (veh/h) 𝑇 = analysis time period (0.25 h for a 15-min period) (h)

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) METHODOLOGY Version 1.0 Page 83 At free-flow conditions, the demand 𝑣 is set at zero, which allows Equation 20-64 to be reduced to the following form: 𝑑 = 3,600𝑐 , + 5 AWSC Intersections The control delay d for AWSC intersections is computed through Equation 21-30: 𝑑 = 𝑡 + 900𝑇 𝑥 − 1 + 𝑥 − 1 + ℎ 𝑥450𝑇 + 5 where 𝑡 = service time (s) 𝑥 = volume-to-capacity ratio of the subject lane ℎ = departure headway (s) 𝑇 = analysis time period (0.25 h for a 15-min period) (h) At free-flow conditions, the demand-to-capacity ratio 𝑥 is set at zero, which allows Equation 21-30 to be reduced to the following form: 𝑑 = 𝑡 + 5 The estimation of service time 𝑡 requires an iterative and computationally intensive procedure described in the AWSC Intersections methodology (Chapter 21). It must be performed setting x = 0. Roundabouts The control delay d for roundabouts is computed through Equation 22-17: 𝑑 = 3,600𝑐 + 900𝑇 𝑥 − 1 + 𝑥 − 1 + 3,600𝑐 𝑥450𝑇 + 5 × 𝑚𝑖𝑛 𝑥, 1 where 𝑥 = volume-to-capacity ratio of the subject lane 𝑐 = capacity of the subject lane (veh/h) 𝑇 = analysis time period (0.25 h for a 15-min period) (h) Similar to TWSC intersections, setting the demand-to-capacity ratio x=0 reduces Equation 22-17 to a simpler form: 𝑑 = 3,600𝑐 , + 5 Freeway Ramps Freeway ramp speeds at free-flow are equal to the ramp free-flow speed 𝑆 , as provided by the analyst, and do not require additional adjustments. Equation 38-15 Equation 38-16 Equation 38-17

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Example Problems Chapter 38 System Analyses (Draft) Page 84 Version 1.0 4. EXAMPLE PROBLEMS This section presents four example problems illustrating the evaluation of networks and addressing several cases of spillback into freeways and into urban street facilities. Example Problem Description Application 1 O-D Based Travel Time Estimation For I-75 NB Freeway in Gainesville, FL Operational Analysis 2 I-10 On-Ramp Spillback Check in Baton Rouge, LA on different ramp terminal intersections Operational Analysis 2a Signalized intersection ramp terminal Operational Analysis 2b TWSC ramp terminal Operational Analysis 2c AWSC ramp terminal Operational Analysis 3 Queue Spillback Analysis for a Freeway-to-Freeway Ramp in Miami, FL. Operational Analysis 4 On-Ramp Queue Spillback Analysis into a Single-Lane Roundabout in Los Angeles, CA Operational Analysis EXAMPLE PROBLEM 1: O-D BASED TRAVEL TIME ESTIMATION FOR I-75 NB FREEWAY IN GAINESVILLE, FLORIDA A freeway section of I-75 NB, with length of 8.72 miles in Gainesville, Florida is evaluated to obtain selected O-D travel times. Four consecutive interchanges are evaluated: (a) Williston Rd., (b) Archer Rd., (c) Newberry Rd., and (d) NW 39th Ave., shown in Exhibit 38-21. Exhibit 38-20 List of Example Problems

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Example Problems Version 1.0 Page 85 When a freeway facility is analyzed in isolation, each on-ramp is a unique origin and each off-ramp is a unique destination. However, for a systems analysis approach, these must be expanded to include turning movements at the urban street intersections. Each turning movement is a different origin / destination with a distinct travel time. The subject network has three freeway lanes throughout its entire length. Four on-ramps and four off-ramps are connected to surface streets. Exhibit 38-22 provides the schematic representation of the freeway network, with five possible origins (A, C, E, G and I) and five possible destinations (B, D, F, H and J). The analysis steps for evaluating this network are discussed below. Step 1: Define Spatial and Temporal Analysis Scope The first step in the methodology is the selection of origin and destination nodes in the network. For each selected O-D pair, the methodology lists the segments traversed and their travel times are estimated. Exhibit 38-21 Example Problem 1 Network Interchanges, with indication of origins and destinations: (a) Williston Rd.(b) Archer Rd.(c) Newberry Rd.(d) NW 39th Ave. Exhibit 38-22 Freeway Origins and Destinations for Example Problem 1

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Example Problems Chapter 38 System Analyses (Draft) Page 86 Version 1.0 As shown in Exhibit 38-21, the system has 9 nodes and 72 O-Ds, shown in Exhibit 38-23. This case study estimates the travel time for the O-D from Archer Rd. East (D) to NW 39th Ave (H), as depicted in red in Exhibit 38-21. Origins Destinations A B C D E F G H J A - A-B A-C A-D A-E A-F A-G A-H A-J B B-A - B-C B-D B-E B-F B-G B-H B-J C C-A C-B - C-D C-E C-F C-G C-H C-J D D-A D-B D-C - D-E D-F D-G D-H D-J E E-A E-B E-C E-D - E-F E-G E-H E-J F F-A F-B F-C F-D F-E - F-G F-H F-J G G-A G-B G-C G-D G-E G-F - G-H G-J H H-A H-B H-C H-D H-E H-F H-G - J J-A J-B J-C J-D J-E J-F J-G J-H - The total average travel time for each O-D can be obtained by adding the travel times on each segment plus any delay experienced at all intersections traversed. Travel time for each ramp traversed is also computed. The O-D from node D to node H will traverse two urban street facilities, as shown in Exhibit 38-24: • Archer Rd. Westbound, comprised of two urban street segments and two signalized intersections (SW 40th Blvd. and I-75 NB on-ramp); • NW 39th Ave. Eastbound, comprised of one urban street segment and two signalized intersections (I-75 NB off-ramp and NW 95th Blvd). (a) Urban Street Facility 1: Archer Rd. WB (b) Urban Street Facility 2: NW 39th Ave. EB The O-D also includes the freeway facility (I-75 NB), starting at segment 8 and ending at segment 16 (Exhibit 38-22). The on-ramp and off-ramp at the boundary ends of the facility are also included in the travel time evaluation. Exhibit 38-25 summarizes the list of segments, ramps and intersections traversed for this O-D. Facility 1 - Archer Rd WB Facility 2 - I-75 NB Facility 3 - NW 39th Ave. Intersections Segments Ramp Junctions Segments Intersections Segments SW 40th Blvd. (WB-Through) SW 37th Blvd - SW 40th Blvd Archer Rd. On- Ramp 8, 9, 10, 11, 12, 13, 14, 15, 16 I-75 NB (NB- Right) I-75 NB - NW 95th Blvd. I-75 NB (WB- Right) SW 40th Blvd. - I-75 WB NW 39th Ave Off-Ramp - NW 95th Blvd. (EB-Through ) - The temporal scope of the analysis must also be defined. Given the short length of the subject network, a single-period analysis will be performed. When Exhibit 38-23 O-D Matrix for Example Problem 1 Exhibit 38-24 Urban Street Facilities Evaluated for Example Problem 1 The movements that must be accounted for their control delay in the traversed intersections are specified in parentheses in Exhibit 38-24 Exhibit 38-25 List of Segments Included Within D-H

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Example Problems Version 1.0 Page 87 the final travel time is obtained, its value will be checked and if it exceeds the 15- minute study period the temporal scope of the study will be reevaluated. Step 2: Provide Input Parameters for Freeway and Urban Street Analysis For this step, the facilities within the subject O-D must be modeled individually using the respective HCM methods. Freeway Facility – I-75 NB The freeway facility was divided into 19 segments for capacity analysis and modeled according to the methodology described in Chapter 10, Freeway Facilities Core Methodology. The detailed input data for each segment are presented in Exhibit 38-26. Segment ID Type Length (ft) Mainline Flow Rate (veh/h) Grade (%) Ramp Flow Rate (veh/h) Accel/ Decel Lane Length (ft) Ramp Length (ft) 1 Basic 2220 4800 0 - - - 2 Diverge 1500 4800 -2 480 800 900 3 Basic 990 4320 0 - - - 4 Merge 1500 4240 0.5 580 1124 1000 5 Basic 1600 4900 3 - - - 6 Diverge 1500 4900 0 364 541 1650 7 Basic 1800 4536 0 - 8 Merge 1500 4536 1.7 868 438 2250 9 Basic 6300 5404 0 - - - 10 Basic 5385 5404 0 - - - 11 Diverge 1500 5404 -1 936 490 660 12 Basic 2014 4468 0 - 13 Merge 1500 4468 1.8 380 1443 1850 14 Basic 6494 4848 0 - - - 15 Basic 2480 4848 0 - - - 16 Diverge 1500 4848 1 960 377 2380 17 Basic 1000 3888 0 - - - 18 Merge 1500 3888 -2.2 148 747 2200 19 Basic 3760 4036 0 - - - Additional input parameters for the urban street facility are as follows: • Urban area, 3 lanes in each direction; • Base FFS: 75.4 mi/h; • Ramp FFS: 35 mi/h; • Ramp side: Right; • Lane width: 12 ft; • Right side clearance: 10 ft; • Traffic composition: 2% trucks on both freeway and ramps; and • Familiar facility users. Urban Street Facility 1 – Archer Rd Westbound This facility contains two signalized intersections and two segments (Exhibit 38-24(a)). The corresponding input data are presented in Exhibit 38-27 and Exhibit 38-28. Exhibit 38-26 Input Data for Freeway Facility Analysis

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Example Problems Chapter 38 System Analyses (Draft) Page 88 Version 1.0 Intersection Parameter Eastbound Westbound Northbound Southbound L T R L T R L T R L T R Archer Rd. @ I-75 NB Demand (veh/h) 320 2064 - - 524 548 104 - 260 - - - Phase Split (s) 20 80 - 70 20 30 - - - - - - Archer Rd. @ SW 40th Blvd. Demand (veh/h) 120 2348 88 36 864 548 60 208 96 36 480 304 Phase Split (s) 20 50 - 20 50 - 20 30 - 20 30 - Input Parameter SW 40th Blvd - I-75 WB SW 37th Blvd - SW 40th Blvd Segment length (ft) 530 1288 Speed limit 45 45 Through lanes 3 3 Restrictive median length (ft) 0 0 Upstream Intersection width (ft) 50 50 Curb proportion (%) 70 70 Base FFS (mi/h) 46.42 46.42 Running Speed (mi/h) 32.24 41.37 Running time (s) 11.21 21.23 Percent of base FFS 50.84 52.04 Urban Street Facility 2 – NW 39th Ave. Eastbound This facility contains two signalized intersections and one segment (Exhibit 38-24(b)). The corresponding input data are presented in Exhibit 38-29 and Exhibit 38-30. Intersection Parameter Eastbound Westbound Northbound Southbound L T R L T R L T R L T R NW 39th @ I- 75 NB Demand (veh/h) 72 1416 - - 872 76 336 - 624 - - - Phase Split (s) 20 80 - - 70 - 20 30 - - - - NW 39th @ NW 95th Blvd. Demand (veh/h) 180 1772 68 96 640 128 84 160 76 60 228 120 Phase Split (s) 20 50 - 20 50 - 20 30 - 20 30 - Input Parameter I-75 NB - NW 95th Blvd Segment length (ft) 510 Speed limit 45 Through lanes 2 Restrictive median length (ft) 0 Upstream Intersection width (ft) 50 Curb proportion (%) 70 Base FFS (mi/h) 46.42 Running Speed (mi/h) 31.53 Running time (s) 11.03 Percent of base FFS 58.38 Additional input parameters for this facility are as follows: • Base saturation flow rate: 1,900 veh/h/ln; • Traffic composition: 0% heavy vehicles; • Cycle length: 120s; • Grade: 0%; • Arrival type: 3; • Speed limit: 45 mi/h; Exhibit 38-27 Input Data for Intersection Analysis – Archer Rd. WB Exhibit 38-28 Input Data for Segment Analysis – Archer Rd. WB Exhibit 38-29 Input Data for Intersection Analysis – NW 39th Ave. EB Exhibit 38-30 Input Data for Segment Analysis – NW 39th Ave. EB

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Example Problems Version 1.0 Page 89 • Yellow change interval: 4s; • Red clearance interval: 0s; and • No pedestrians. Step 3: Balance Demands at Freeway-Urban Street Interface After each facility along the O-D is modeled individually, this step checks the consistency of traffic flows in the interfaces between urban streets and freeway facilities. For each of the four on-ramps along the freeway facility, there are two movements at the corresponding urban street intersection that contribute to the on-ramp demand: eastbound left-turn (EBL) and westbound right-turn (WBR). Exhibit 38-31 compares the demand volumes at the intersection (𝑣) with their respective movement capacities (c), and the minimum of each is added to the total on-ramp demand 𝑣 . As observed, no movement operates with 𝑣/𝑐 > 1.0, therefore no adjustments are required, and the on-ramp demands 𝑣 are equal to the sum of the turning movement demands at the intersection. Intersection Movement Parameter Demand (v), veh/h v/c c (veh/h) min(v, c) Merge demand vR Williston Rd. @ I-75 NB EBL 160 0.15 1055 160 580 WBR 420 0.43 985 420 Archer Rd. @ I-75 NB EBL 320 0.34 935 320 868 WBR 548 0.53 1037 548 Newberry Rd. @ I-75 NB EBL 216 0.25 862 216 380 WBR 164 0.14 1163 164 NW 39th Ave. @ I-75 NB EBL 72 0.14 501 72 148 WBR 76 0.075 1012 76 Next, the off-ramp volumes are checked against the intersection turning movement demands. The first check determines whether there are bottlenecks along the freeway facility that may meter off-ramp demands. Exhibit 38-32 shows the estimated LOS for all 19 segments in the freeway facility. Since no segment is oversaturated, the off-ramp demand is not metered, and no adjustments are necessary. Segment Number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Type B D B M B D B M B B D B M B B D B M B LOS D D D D D D D E E E D D C D D D C C C Segment types: Basic (B), Merge (M), Diverge (D) The second check compares the off-ramp demands to the respective ramp roadway capacity, as shown in Exhibit 38-33. The demand does not exceed capacity for any of the ramps, therefore no adjustments to the intersection volumes are performed. Exhibit 38-31 Demands at the On-Ramps Along the Freeway Facility for Example Problem 1 Exhibit 38-32 LOS for the Freeway Segments of Example Problem 1

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Example Problems Chapter 38 System Analyses (Draft) Page 90 Version 1.0 Segment Off-Ramp Demand (pc/h) Ramp Lanes Ramp Roadway Capacity (pc/h) Ramp v/c 2 480 1 2000 0.24 6 364 1 2000 0.18 11 936 1 2000 0.47 16 960 2 4000 0.24 Step 4: Check for Queue Spillback The next step determines whether there are bottlenecks at the on-ramps and off-ramps. Off-ramp spillback check The procedure presented in Exhibit 38-10 is applied to each of the four off- ramps in the freeway facility: • Capacity of ramp roadway: The off-ramp demand was previously compared to ramp roadway capacity (Exhibit 38-33), and no capacity constraint was detected. • Queue length estimation: The back-of-queue length (95th percentile) in the downstream terminals (signalized intersections) are obtained through the HCM methodology (Chapter 31) and are presented in Exhibit 38-34. The resulting 95th percentile queues are expected to be within the available turn bay lengths at the intersection, except for the left-turn movement at Williston Rd. (freeway segment 2). The queue length will spillback into the ramp roadway, and the next check will evaluate if it its storage is adequate. • Queue storage ratio: Any queues exceeding the available turn bay length at the intersection must be checked against the available storage along the ramp roadway. For single-lane off-ramps, any queues upstream of the intersection will share the same storage and must then be aggregated. If a ramp has two or more lanes, the analyst must determine how ramp lanes are channelized relative to intersection approaches, based on the off-ramp geometry. As shown in Exhibit 38-33, only the off-ramp at segment 16 (NW 39th) has two lanes - the ramp leftmost lane L2 is connected to left- turn movement, while the ramp rightmost lane L1 is connected to the right turn movement. For this step, the only movement that must be evaluated is the left turn at Williston Rd. The queue length upstream of the intersection is compared to the available ramp length, with a resulting queue storage ratio RQ = 436/900 = 0.48 < 1.0. Therefore, spillback is not expected to occur along the off-ramps. Exhibit 38-33 Demands at the Off-Ramps Along the Freeway Facility for Example Problem 1

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Example Problems Version 1.0 Page 91 Parameter 2 (Williston Rd.) 6 (Archer Rd.) 11 (Newberry Rd.) 16 (NW 39th Ave.) LT RT LT RT LT RT LT RT Ramp length (ft) 900 1650 660 2380 Number of Ramp Lanes 1 1 1 2 Upstream Ramp Lane L1 L1 L1 L2 L2 L1 Turn Bay Length (ft) 250 210 480 480 800 800 1260 1200 Back of Queue Length Q95 (ft/ln) 689 21 120 363 223 363 193 482 Exceeding Turn Bay Queue Length (ft) 439 - - - - - - Queue Storage Ratio (RQ) 0.49 - - - - - - - On-ramp Spillback Check On-ramp queue spillback is expected to occur when a freeway merge segment operates above capacity or when there is active ramp metering with a rate lower than demand. As shown in Exhibit 38-32, no merge segments operate at LOS F and no ramp metering is present, therefore spillback is not expected to occur. Step 5A: Obtain Speeds for Individual Lanes in the Freeway Facility First, the flow distribution among freeway lanes must be determined for the segments in the freeway facility. Using the estimated flow rates, lane speeds are computed as shown in Exhibit 38-35. The highlighted rows (8 through 16) represent the segments included in the O-D and used to compute the overall travel time. The rightmost lane is labeled Lane 1. The expected speed for each segment is then computed as the sum of products of speeds for each lane and the corresponding probability of lane choice, as provided in Equation 38-9. (Exhibit 38-36). Even though the travel times of the remaining segments are not directly used in calculating the O-D travel time, the entire facility must be analyzed, as any existing bottleneck would affect the performance of other segments in the facility. For this example, no segment operates under LOS F, and no queues are developed at the ramps connecting nearby urban street streets. Exhibit 38-34 Queue Length Estimation and Queue Storage Checks for Off-Ramps The step by step calculations to determine lane-by-lane flows and speeds on segment 16 (diverge) are presented in an example problem under Appendix C

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Example Problems Chapter 38 System Analyses (Draft) Page 92 Version 1.0 Segment ID Segment LOS Lane Flow Ratio (LFR) Lane Speed (mi/h) Lane 1 Lane 2 Lane 3 Lane 1 Lane 2 Lane 3 1 C 0.286 0.351 0.362 66.5 71.3 77.7 2 C 0.338 0.319 0.343 56.7 73.1 77.5 3 C 0.279 0.356 0.365 68.3 71.6 77.2 4 C 0.259 0.388 0.353 72.0 72.4 77.3 5 C 0.281 0.348 0.371 66.4 69.9 75.6 6 C 0.336 0.326 0.337 55.3 72.2 77.4 7 C 0.286 0.354 0.36 67.7 70.6 76.5 8 C 0.253 0.387 0.359 71.7 71.5 76.8 9 C 0.294 0.346 0.36 56.3 67.3 74.0 10 C 0.288 0.344 0.368 58.2 67.7 73.9 11 D 0.358 0.290 0.352 41.6 71.7 75.2 12 C 0.286 0.355 0.359 67.8 70.8 76.6 13 B 0.253 0.382 0.365 71.9 72.1 76.8 14 C 0.281 0.349 0.37 66.8 70.0 75.7 15 C 0.281 0.349 0.37 66.8 70.0 75.7 16 C 0.350 0.296 0.354 50.6 74.1 76.8 17 B 0.278 0.362 0.361 68.3 72.6 78.1 18 B 0.252 0.383 0.365 72.0 74.2 77.7 19 B 0.272 0.358 0.37 68.7 72.7 78.1 Bold rows represent the segments included in the O-D that are used to compute the total travel time Segment ID Lane Choice Probability for the Subject O-D Lane Speeds (mi/h) Expected Speed (mi/h) L1 L2 L3 L1 L2 L3 8* 90.0% 5.0% 5.0% 71.7 71.5 76.8 68.4 9 29.4% 34.6% 36.0% 55.2 68.7 75.8 67.3 10 28.8% 34.4% 36.8% 57.3 68.8 75.4 67.9 11 35.8% 29.0% 35.2% 41.6 71.7 75.2 62.2 12 28.6% 35.5% 35.9% 69.3 72.5 78.7 73.8 13 25.3% 38.2% 36.5% 71.9 72.1 76.8 73.8 14 28.1% 34.9% 37.0% 67.0 71.3 77.2 72.3 15 28.1% 34.9% 37.0% 67.0 71.3 77.2 72.3 16* 90.0% 5.0% 5.0% 50.6 74.1 76.8 53.1 (*): Entry/exit segments: require mandatory use of the rightmost lane Step 5B: Compute Travel Speeds for Urban Street Segments The travel speeds for urban streets segments are calculated using the core methodology of HCM Chapter 16, Urban Streets Segments, adjusted to consider the relevant turning movements. Exhibit 38-37 shows the three urban streets segments analyzed, with their associated movements at the intersection. Facility Segment Input parameters Segment length (ft) Base FFS (mi/h) Running Speed (mi/h) Segment Running time (s) Downstream Intersection movement Control delay d (s) Travel speed (mi/h) Facility 1 (Archer Rd. WB) SW 40th Blvd - I-75 WB 530 46.42 32.24 11.21 Right 7.6 19.21 SW 37th Blvd - SW 40th Blvd 1288 46.42 41.37 21.23 Through 15.12 24.16 Facility 2 (NW 39th St. EB) I-75 NB - NW 95th Blvd 510 46.42 31.53 11.03 Through 26.2 9.34 Exhibit 38-35 Flow Distribution and Speeds for Freeway Segments Exhibit 38-36 Estimated Speeds by Segment Based on Lane Choice Probability and Speeds Exhibit 38-37 Speeds for Urban Streets Segments

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Example Problems Version 1.0 Page 93 Step 6 – Compute Travel Times for Each Segment The travel times for each segment in the freeway and urban street facilities are computed by dividing the segment length by the travel speed (Exhibit 38-39 and Exhibit 38-38). Facility Segment Travel Speed (mi/h) Length (ft) Travel Time (s) Archer Rd. WB SW 40 th Blvd. @ I-75 BB 19.21 530 18.8 SW 37th Blvd. @ SW 40th Blvd. 24.16 1288 36.4 NW 39th Ave. EB I-75 NB @ NW 95th Blvd. 9.34 1040 75.9 Segment ID Expected Speed (mi/h) Segment Length (ft) Travel Time (s) 8 68.4 1500 15.0 9 66.5 6300 64.6 10 67.2 5385 54.6 11 64.4 1500 15.9 12 72.0 2014 19.1 13 73.8 1500 13.9 14 71.2 6494 62.2 15 71.2 2480 23.7 16 53.1 1500 19.3 Step 7: Obtain Travel Times for Freeway Ramps As shown, the ramps at the freeway facility operate at undersaturated conditions. Therefore, ramp roadway speeds can be estimated using Equation 38- 11, as shown in Exhibit 38-40. For the off-ramp at segment 16, the control delay at the downstream ramp terminal is included on the computation of the ramp total travel time. Segment ID Ramp Flow (pc/h) Ramp FFS (mi/h) Speed (mi/h) Ramp Length (ft) Ramp Roadway Travel time (s) Control Delay - Ramp Terminal (s) Ramp Total Travel Time (s) 8 886 35 31.6 2250 48.5 - 48.5 16 980 35 31.3 1200 26.2 96.6 122.8 Step 8: Compute Travel Times for the Network and Each O-D All segments within the subject O-D (E1-H1) are sorted according to the travel sequence and their respective travel times are listed, as shown in Exhibit 38-41. The cumulative travel time for the O-D must also be computed to evaluate if the network analysis is correctly contained within the temporal scope defined in Step 1. For this example, a single 15-min analysis period was considered, for a total time of 900s. Since the cumulative travel time does not exceed this boundary value, all travel times obtained from time period 1 are valid for the analysis. Exhibit 38-38 Travel Times for Urban Streets Segments Exhibit 38-39 Travel Times for Freeway Segments Exhibit 38-40 Estimated Travel Times for Ramps Entering or Exiting the Freeway Facility

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Example Problems Chapter 38 System Analyses (Draft) Page 94 Version 1.0 Facility Segment ID Travel time (s) Cumulative travel time (s) Time Period Type Name Urban Street 1 Archer Rd. WB SW 37th Blvd @ SW 40th Blvd 18.8 40.5 1 SW 40th Blvd @ I-75 WB 36.4 76.8 1 Freeway I-75 NB On-ramp to I-75 NB 48.5 125.3 1 8* 15.0 140.3 1 9 63.8 204.1 1 10 54.1 258.2 1 11 16.5 274.6 1 12 18.6 293.2 1 13 13.9 307.1 1 14 61.3 368.4 1 15 23.4 391.8 1 16* 19.3 411.0 1 Off-ramp to NW 39th Ave. 122.8 533.8 1 Urban Street 2 NW 39th Ave. EB I-75 NB - NW 95th Blvd 75.9 609.7 1 Total travel time (s): 609.7 Step 9: Compute Performance Measures for Segments Since no spillback occurred in the subject study period, the performance measures obtained by the respective HCM methods for each type of segment are valid. Exhibit 38-41 Estimated Travel Times for Ramps Entering or Exiting the Freeway Facility

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Example Problems Version 1.0 Page 95 EXAMPLE PROBLEM 2: I-10 ON-RAMP SPILLBACK ANALYSIS IN BATON ROUGE, LOUISIANA This case study illustrates the application of the on-ramp spillback methodology by evaluating operations at an interchange when there is queue spillback originating from the on-ramp. There are three parts to the case study with each one analyzing a different intersection type at the ramp terminal: signalized, TWSC and AWSC. The main objective in each analyzed scenario is to determine the new control delay for the movements affected by queue spillback. All other parameters in the network (freeway design and traffic demand, and intersection demand) are kept the same. An urban network in Baton Rouge, LA is comprised of the following facilities: • One freeway facility (I-10) • One urban street facility (Acadian Thruway), with four signalized intersections: o Perkins Rd. o Acadian Center Rd. o I-10 WB o I-10 EB The subject network has three freeway lanes throughout its entire length. One interchange connects the freeway to an urban street network (Acadian Thruway), as illustrated in Exhibit 38-42. The selected origin and destination points for analysis are H and F, respectively, with the traveled segments highlighted in red.

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Example Problems Chapter 38 System Analyses (Draft) Page 96 Version 1.0 The freeway facility (I-10 EB) is modeled according to the Freeway Facilities methodology (Chapter 10), while the ramp terminal is modeled according to its respective intersection methodology. First a check is performed to confirm the occurrence of queue spillback. Next, the respective spillback analysis is applied to evaluate the impacts of queue spillback in the capacity of each movement at the intersection. With the estimated reduced capacities at the intersection, the control delay values considering queue spillback are computed and compared to the delay values without consideration of queue spillback. Exhibit 38-43 illustrates the schematic representation of the freeway network in the eastbound direction. Segments 3 (merge) and 5 (diverge) connect the freeway to the urban street facility (Acadian Thruway). Exhibit 38-42 Example Problem 2 Network Intersections: (a) Perkins Rd.; (b) Acadian Center; (c) I-10 EB;(d) I-10 WB

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Example Problems Version 1.0 Page 97 The analyzed urban street facility comprises four signalized intersections and three segments, as shown in Exhibit 38-44. The on-ramp terminal subject to analysis is the I-10 EB intersection. EXAMPLE PROBLEM 2, PART 1: SIGNALIZED INTERSECTION RAMP TERMINAL Part 1 of the example problem evaluates the impacts of queue spillback originating from the I-10 EB on-ramp when the upstream ramp terminal is signalized. Input data Signalized Intersection The geometry of the intersection connected to the I-10 EB on-ramp (I-10 EB) is shown in Exhibit 38-45. There are three movements leading into the on-ramp: • NBR: One channelized, unsignalized right-turn lane; • SBL: One exclusive left turn lane with a protected phase; and • EBT: One through lane. Exhibit 38-43 Origins and Destinations for the freeway facility (I-10 EB) in Baton Rouge, LA Exhibit 38-44 Acadian Thruway Urban Street Facility

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Example Problems Chapter 38 System Analyses (Draft) Page 98 Version 1.0 The phasing sequence of the subject intersection is presented in Exhibit 38- 46. The north-south direction corresponds to the major street, while the minor streets correspond to the freeway off-ramp and on-ramp. The intersection has a leading left turn phase with a protected left turn movement (SBL). The demand volumes for each time period are presented in Exhibit 38-47. Additional input data are summarized in Exhibit 38-48. Eastbound Northbound Southbound L T R T R L T Time Period 1 8 48 87 362 315 652 804 Time Period 2 16 96 20 1812 521 586 1759 Time Period 3 16 96 20 271 630 1071 717 Time Period 4 8 24 28 845 80 463 201 Exhibit 38-45 Signalized Intersection Geometry – Acadian Thruway @ I-10 EB Exhibit 38-46 Phasing Sequence – I-10 EB Intersection Exhibit 38-47 Demand Flow Rates (veh/h) – I-10 EB Intersection

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Example Problems Version 1.0 Page 99 Eastbound Northbound Southbound L T R T R L T General Information Base Sat. Flow Rate (s0), veh/h 1900 1900 1900 1900 1900 1900 1900 Arrival Type (AT) 3 3 3 3 3 3 3 Lane Width (W), ft 11 11 11 11 11 11 11 Heavy Vehicles % 5 5 5 5 5 5 5 Grade (Pg), % 0 0 0 Speed Limit, mi/h 35 35 35 35 35 35 35 Phase Information Maximum Green (Gmax), s 20 20 - 53 - 47 100 Yellow Change Interval (Y), s 4.7 4.7 - 4.7 - 4.7 4.7 Red Clearance Interval (Rc), s 1 1 - 1 - 1 1 Minimum Green (Gmin), s 5 5 - 15 - 5 15 Start-Up Lost Time (lt), s 2 2 - 2 - 2 2 Green Extension (e), s 2 2 - 2 - 2 2 Passage (PT), s 2 2 - 2 - 2 2 Recall Mode Off Off - Off - Off Off Dual Entry No No - Yes - No Yes Freeway Facility (I-10 EB) The freeway facility (I-10 EB) is divided in seven segments (Exhibit 38-49), where segment 3 (diverge) and segment 5 (merge) connect to the subject signalized intersection (Acadian Thruway). The geometric features of the freeway facility are summarized in Exhibit 38- 50. Exhibit 38-48 Input Data – I-10 EB Intersection Exhibit 38-49 Freeway Facility Segmentation– I-10 EB

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Example Problems Chapter 38 System Analyses (Draft) Page 100 Version 1.0 Segment ID Type Length (ft) Grade (%) Acceleration / deceleration lane length (ft) Ramp length (ft) 1 Basic 5280 0 - - 2 Diverge 1500 0 800 1139 3 Diverge 720 0 0 965 4 Basic 732 0 - - 5 Merge 1000 0 1000 924 6 Basic 1200 0 - - 7 Basic 900 0 - - Spillback check – on-ramp The first step in the spillback check analysis is to determine the on-ramp demand flow rates for each time period, based on the demands at the signalized intersection. For each time period, the demand (v) and capacities (c) are compared for each movement that flows into the on-ramp (EBT, NBR and SBL). The minimum value between demand and capacity for each movement is computed and the merge demand vR is then computed as the sum of the three movements. The capacities for protected movements (EBT and SBL) are computed for each time period. Due to the actuated control operation, the green times for these movements vary by time period; therefore the method uses the average green time for each phase and for each time period. The NBR movement is unsignalized and therefore no capacity estimation is provided by HCM methods. The capacity for this movement is computed by calculating the maximum throughput through one cycle and then aggregating to an hourly flow rate. During the phases when there are no conflicting movements discharging into the on-ramp, the NBR maximum throughput is computed as its respective saturation flow rate, considering the applicable adjustment factors fRT (for right- turn movements) and fHV (for the presence of heavy vehicles). During the transition time between consecutive phases, the throughput of the unsignalized turning movement is also assumed to be equal to its saturation flow rate. Therefore: 𝑠 , = 𝑠 , × 𝑓 × 𝑓 where sNBR,FF = saturation flow rate of NBR movement during the phases with no conflicting flows (veh/h/ln) s0,NBR = base saturation flow rate (1,900 pc/h/ln) fRT = adjustment factor for right-turn vehicle presence in a lane group fHVg = adjustment factor for heavy vehicles and grade The adjustment factor for right-turn vehicle presence is computed using Equation 19-13: 𝑓 = 1𝐸 = 11.18 where Exhibit 38-50 Freeway facility (I-10 EB) - Geometric Features

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Example Problems Version 1.0 Page 101 ET = equivalent number of through cars for a protected right-turning vehicle (1.18) The adjustment factor for heavy vehicles and grade is computed using Equation 19-10: 𝑓 = 100 − 0.78𝑃 − 0.31𝑃100 𝑓 = 100 − 0.78 × 5 − 0.31 × 0100 = 0.961 where PHV = percentage heavy vehicles in the corresponding movement group (5%) PHV = approach grade for the corresponding movement group (0%) Therefore, the saturation flow rate is computed as: 𝑠 , = 1,900 × 11.18 × 0.961 = 1,547 𝑣𝑒ℎ/ℎ Since there are conflicting movements discharging into the on-ramp (for example, a protected left-turn), the NBR capacity is constrained as drivers yield to the higher priority movement. The estimated discharge flow rate for the NBR movement with a conflicting protected flow vprot can be obtained by the following equation, based on HCM equation 31-100: 𝑠 = 𝑣 𝑒 ,1 − 𝑒 , where sp = saturation flow rate of a permitted movement (veh/h/ln) v0 = opposing demand flow rate (veh/h); tcg = critical headway = 4.5 (s); and tfh = follow-up headway = 2.5 (s); The computation of the permitted saturation flow rates must take into consideration that the conflicting phase may have two distinct flow rates on signalized intersection operation, as discussed in Chapter 31 (Signalized Intersections Supplemental): • During the queue service time (gs) portion of the conflicting phase green, the opposing movement flow rate is equal to its saturation flow rate; • During the green extension time (ge), the opposing movement flow rate is equal to its arrival flow rate during the effective green (qg); Exhibit 38-51 illustrates the calculation of the NBR capacity for a single cycle during time period 1. For each active phase, the procedure identifies the respective conflicting flow to the on-ramp along with its duration and flow rate. The NBR saturation flow rate is then computed using HCM Equation 31-100. The last column computes the maximum number of vehicles that can be discharged

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Example Problems Chapter 38 System Analyses (Draft) Page 102 Version 1.0 during each phase as the product of the NBR saturation flow rate and the phase duration. Clearance times between consecutive phases are also taken into consideration assuming that they have no conflicting flow rate to the on-ramp. Active phase Conflicting flow Duration (s) Conflicting flow rate (veh/h) NBR saturation flow rate sNBR (veh/h) NBR discharge volume (veh) φ1 (SBL) - gs,SBL sSBL 40.2 1739 282 3.1 φ1 (SBL) -ge,SBL qg,SBL 3.7 128 1282 1.3 Clearance time 1 - 5.7 - 1547 2.5 φ2 (NBT) - 50.7 - 1547 21.8 Clearance time 2 - 5.7 - 1547 2.5 φ7 (EBT) - gs,EBT sEBT 6.3 1811 263 0.5 φ7 (EBT) - ge,EBT qg,EBT 2 97.2 1319 0.8 Clearance time 7 - 5.7 - 1547 2.5 Total 120 34.8 gs: queue service time; ge: green extension time; qg: arrival flow rate during effective green; s: saturation flow rate As shown, for a 120s cycle the capacity of the unsignalized NBR movement is 34.8 vehicles. Aggregated to an hourly flow rate: 𝑐 = 34.8 × 3600120 = 1045 𝑣𝑒ℎ/ℎ Because of the actuated control operation, the discharging rates to the on- ramp are different during each time cycle, and during each period. Therefore, this procedure must be repeated for every time period to compute the capacity of the NBR unsignalized movement cNBR (Exhibit 38-52). Time Period NBR capacity (veh/h) 1 1213 2 1045 3 978 4 1182 Exhibit 38-53 summarizes the calculations for this step. During time period 3, the SBL movement operates at demand over capacity (v/c = 1.56), therefore its throughput to the ramp is constrained by its capacity value (685 veh/h). For all other movements and time periods the throughput to the on-ramp is equal to its demand because v/c < 1. Exhibit 38-51 Calculation of NBR Capacity for a Single Cycle – Time Period 2 Exhibit 38-52 NBR Capacity, Computed for Each Time Period

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Example Problems Version 1.0 Page 103 Time Period Parameter Movements EBT NBR SBL 1 Demand (veh/h) 8 315 652 v/c 0.064 - 0.96 c (veh/h) 125 1213 677 min (v, c) 8 315 652 Merge demand vR (veh/h) 975 2 Demand (veh/h) 96 521 586 v/c 0.768 - 0.93 c (veh/h) 125 1045 630 min (v, c) 96 521 586 Merge demand vR (veh/h) 1203 3 Demand (veh/h) 96 630 1071 v/c 0.77 - 1.56 c (veh/h) 125 978 685 min (v, c) 96 630 685 Merge demand vR (veh/h) 1411 4 Demand (veh/h) 24 80 463 v/c 0.39 - 0.62 c (veh/h) 62 1182 746 min (v, c) 24 80 463 Merge demand vR (veh/h) 567 The calculated on-ramp demand is then provided as input into the freeway facility analysis (Exhibit 38-54). As shown, the ramp flow rates for the merge segment (segment 5) are obtained from Exhibit 38-53 and highlighted in bold. Segment ID Time Period 1 Time Period 2 Time Period 3 Time Period 4 ML flow rate (veh/h) Ramp flow rate (veh/h) ML flow rate (veh/h) Ramp flow rate (veh/h) ML flow rate (veh/h) Ramp flow rate (veh/h) ML flow rate (veh/h) Ramp flow rate (veh/h) 1 5209 - 6300 - 5300 - 5000 - 2 5209 348 6300 450 5300 1200 5000 50 3 4861 135 5850 116 4100 1000 4950 96 4 4726 - 5734 - 3100 - 4854 - 5 4726 975 5734 1203 3100 1411 4854 567 6 5701 - 6937 - 4511 - 5421 - 7 5701 - 6937 - 4511 - 5421 - The results of the freeway facility analysis are provided in Exhibit 38-55. Oversaturated conditions occur during time periods 2 and 3, therefore queueing may occur along the on-ramp. Exhibit 38-53 Calculation of the On-Ramp Demand (vR) Based on the Intersection Operation. Exhibit 38-54 Freeway Facility (I-10 EB) – Demand Inputs

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Example Problems Chapter 38 System Analyses (Draft) Page 104 Version 1.0 Time period Seg 1 Seg 2 Seg 3 Seg 4 Seg 5 Seg 6 Seg 7 B D D B M B B 1 D C D C D D D 2 E F F F F F E 3 D D F F F E E 4 D C C B C C C Segment type: B: basic; D: diverge; M: merge The next step will estimate the on-ramp queue length compared to the available queue storage length to determine whether spillback is expected to occur. Exhibit 38-56 shows the expected on-ramp queues from the freeway facility analysis. For each time period, the ramp storage ratio (RQ) is computed by dividing the ramp queue by the available storage length (924 ft). During time period 2, a queue is expected on the ramp, but it is not long enough to cause queue spillback (RQ < 1). During time period 3, however, the on-ramp is expected to have RQ = 2.31, which indicates that spillback will occur at the intersection during this time period. Time period vR (veh/h) Ramp queue (veh) Ramp queue (ft) Ramp storage ratio (RQ) Spillback expected? 1 975 0.0 0.0 0.00 No 2 1,203 15.0 388.6 0.42 No 3 1,411 82.1 2,133.6 2.31 Yes 4 567 0.0 0.0 0.00 No Since spillback will occur for at least one time period, the impacts on the operation of the signalized intersection must be evaluated. The next section illustrates the application of the methodology to evaluate spillback effects at a signalized intersection. Evaluation of queue spillback impacts The evaluation of queue spillback impacts on the signalized intersection follows the procedure detailed in the methodology (Exhibit 38-B5). Since this is a multiperiod analysis, the procedure must be applied for every time period. In this example, time periods 2, 3 and 4 will be evaluated. Time period 1 is not analyzed here since it does not have oversaturated conditions. Time Period 2 The procedure to evaluate queue spillback into intersections is applied for time period 2, even though spillback is not expected to occur during this time period. The application of the methodology is presented for this time period to facilitate the understanding of the calculations. Step 7A – Determine intersection throughput to on-ramp The throughput of movements into the on-ramp have been previously determined as part of the queue spillback check, as shown in Exhibit 38-53. Exhibit 38-55 Performance Measures for the Freeway Facility (I-10 EB) Exhibit 38-56 Spillback Check – I-10 EB on- Ramp

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Example Problems Version 1.0 Page 105 Step 7B – Obtain merging capacity with Freeway Facilities method When the freeway facility operates in oversaturated conditions, the capacity of the subject merge section may be constrained by the presence of queues along the mainline. The Oversaturated Segment Evaluation procedure (Chapter 25) computes the on-ramp queue (ONRQ) and on-ramp capacity (ONRO) every 15 seconds. The merge capacity cmerge is then obtained by aggregating the ONRO parameter into an hourly flow rate for each time period. Exhibit 38-57 shows the values of ONRQ and ONRO over the analysis period (60 minutes), converted to hourly flow rates. Exhibit 38-57(a) compares the on-ramp capacity ONRO to the on-ramp demand. During the first time period there are no oversaturated conditions along the freeway, thus the on-ramp capacity ONRO equals 2,000 pc/h (corresponding to the ramp roadway capacity as provided by HCM Exhibit 14-12), or 1,903 veh/h. During time periods 2 and 3, oversaturated conditions occur and the on- ramp capacity drops to 5 pc per time step, corresponding to 1,142 veh/h. During the last time period, the lower demand along the freeway allows the mainline queue to clear within 4 time steps (60 seconds). Therefore, during the first 60 seconds the on-ramp capacity remains at 1,142 veh/h. From the fifth time step to the end of the time period, there is no congestion at the merge and thus the on- ramp capacity is again 1,903 veh/h. Exhibit 38-57(b) provides the on-ramp queue as estimated by the Oversaturated Segment Evaluation procedure. Since spillback is expected to occur, an adjustment to the Freeway Facility Oversaturated Segment evaluation procedure is necessary to account for the maximum ramp storage (35.5 vehicles). This value is the upper boundary of the on-ramp queue length. At the end of time period 3, the predicted on-ramp queue length would be 82 vehicles if there were no storage constraints (black curve). The red curve represents the adjusted queue profile for the on-ramp considering the maximum storage capacity. At the start of time period 4, having an on-ramp queue of 35.5 vehicles instead of 82 results in a shorter queue clearance time, with a slight positive impact on the freeway performance. In other words, the intersection has a metering effect, which may improve operations along the freeway. Exhibit 38-58 compares the performance results of the freeway segments downstream of the merge (see Figure E-15) with and without consideration of the maximum storage constraint.

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Example Problems Chapter 38 System Analyses (Draft) Page 106 Version 1.0 Seg 5 (Merge) Seg 6 (Basic) Seg 7 (Basic) Without storage constraint With storage constraint Without storage constraint With storage constraint Without storage constraint With storage constraint Speed (mi/h) 67.2 67.4 67.7 67.8 72.2 72.5 Density (pc/mi/ln) 20.9 19.9 20.8 19.7 19.5 18.4 Step 7C – Plot queue accumulation polygon for the on-ramp and unsignalized movements In this step, a queue accumulation polygon is plotted for the on-ramp as a function of all protected and permitted movements entering the on-ramp, on a cycle-by-cycle basis. Since an unsignalized movement (NBR) also discharges into the on-ramp, a queue accumulation polygon must be developed for this movement as well. This is required to: (a) determine the discharge pattern of the unsignalized movement throughout the cycle and (b) allow the estimation of control delay for this movement. Exhibit 38-59 presents the queue accumulation profiles for (a) the on-ramp and (b) for the NBR movement. Exhibit 38-57 Freeway Facility, Segment 5 (merge) Performance: a) Merge Capacities and b) Queue Lengths Exhibit 38-58 Freeway Performance During Time Period 4 – with and without the Queue Storage Constraint

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Example Problems Version 1.0 Page 107 The cycle starts with a permitted left-turn movement (Φ1: SBL) discharging into the on-ramp with a green time g1 = 43.9s, divided in a queue service time gs1 = 40.2s and a queue extension time ge1 = 3.7s (as defined in Chapter 31 – Signalized Intersections Supplemental). During the green interval for SBL, the capacity of the NBR movement is constrained since drivers must yield to the protected left-turn vehicles. The estimated saturation flow rate for the NBR movement with a conflicting flow vSBL can be obtained by the following equation, based on HCM equation 31-100: 𝑠 , = 𝜆 𝑒 ,1 − 𝑒 , where sNBR,perm = saturation flow rate of the NBR movement (veh/h/ln) λSBL = throughput of the opposing SBL movement(veh/h) tcg = critical headway = 4.5 (s) tfh = follow-up headway = 2.5 (s) The saturation flow rates of the NBR movement during Φ1 are determined next. During the SBL queue service time is: 𝜆 = 𝑠 = 1,739 veh/h/ln → 𝑠 , = 282 veh/h/ln Exhibit 38-59 Estimated Queue Lengths And Merge Capacities – Time Period 2

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Example Problems Chapter 38 System Analyses (Draft) Page 108 Version 1.0 where sSBL = saturation flow rate of the SBL movement (veh/h/ln) sNBR,perm1 = saturation flow rate of the NBR movement during the SBL queue service time (veh/h/ln) The throughput for the NBR movement is obtained as the minimum of the demand and saturation flow rate. Since the demand flow rate is greater than the saturation flow rate, a queue will develop for the NBR movement: 𝜆 , = 𝑚𝑖𝑛 𝑠 , ,𝑣 = 𝑚𝑖𝑛 282, 521 𝜆 , = 282 𝑣𝑒ℎ/ℎ where λNBR,1 = throughput for the NBR movement during the SBL queue service time (veh/h/ln) vNBR = demand flow rate of the NBR movement (veh/h) During the SBL green extension time ge, the SBL throughput λSBL is equal to the arrival flow rate during the effective green (qg,SBL, from Equation 19-32): 𝜆 = 𝑞 , = 𝑃 × 𝑣3600 × 𝐶𝑔 𝜆 = 0.08 × 5863600 × 12043.9 = 0.0356 𝑣𝑒ℎ/𝑠/𝑙𝑛 = 128 𝑣𝑒ℎ/ℎ/𝑙𝑛 where P = proportion of vehicles arriving during the green indication (decimal); VSBL = SBL demand flow rate (veh/h); C = cycle time (s); and gSBL = SBL effective green time (s) For this conflicting flow, therefore, the NBR saturation flow rate sNBR,perm2 is obtained using Equation 31-100: 𝑠 , = 𝜆 𝑒 ,1 − 𝑒 , 𝜆 = 0.08 × 5863600 × 12043.9 = 0.0356 𝑣𝑒ℎ/𝑠/𝑙𝑛 = 128 𝑣𝑒ℎ/ℎ/𝑙𝑛 with all variables previously defined. Since a queue is present in the NBR movement, the throughput for the NBR movement is equal to its saturation flow rate: 𝜆 , = 𝑠 , = 1282 𝑣𝑒ℎ/ℎ where λNBR,2 = throughput for the NBR movement during the SBL green

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Example Problems Version 1.0 Page 109 extension(veh/h/ln) sNBR,perm2 = saturation flow rate of the NBR movement during the SBL green extension time (veh/h/ln) With the discharge patterns for the NBR determined, the queue profile in the on-ramp during Φ1 can be determined. During the SBL queue service time (cycle time t = 0 to t = 40.2s), the throughput to the on-ramp is given by: 𝜆 = 𝜆 + 𝜆 , = 1,739 + 282 = 2,021𝑣𝑒ℎ/ℎ 𝑜𝑟 0.561𝑣𝑒ℎ/𝑠 Given the merge capacity cmerge = 1,142 veh/h for the current time period, the on-ramp queue will grow at the following rate during the SBL queue service time: 𝜆 − 𝑐 = 2,021 − 1,142 𝜆 − 𝑐 = 879𝑣𝑒ℎ/ℎ 𝑜𝑟 0.244 𝑣𝑒ℎ/𝑠 Therefore, at the end of the SBL queue service time (t = 40.2s), the queue at the on-ramp will be 0.244 x 40.2 = 9.8 vehicles (Exhibit 38-59a). This process is then repeated for all phases throughout the cycle. The results for a single cycle (120 sec) are presented in Exhibit 38-60, where the maximum on-ramp queue occurs at t = 50.48s, with 10.82 vehicles (t = 50.48s). The expected on-ramp queue at the end of the cycle is 2.02 vehicles. The remaining cycles within time period 2 show the same pattern, where the on-ramp queue at the end of each cycle becomes the initial queue at the start of the next cycle. Each row in Exhibit 38-60 describes a portion of the cycle, as follows: • gs1: queue service time for SBL (Φ1), as previously discussed • ge1: green extension time for SBL (Φ1). The NBR movement discharges at the permitted saturation flow rate due to the queue that has developed during gs1, and the on-ramp queue grows at a rate of 0.07 veh/s • r1: effective red time for SBL (Φ1). There is no throughput from protected movements and the NBR movement discharges freely at the saturation flow rate. The on-ramp queue grows at a rate of 0.11 veh/s • g2*: effective green for NBT (Φ2), with no throughput from protected movements. The duration of 0.88s is calculated based on the queue service time of the NBR approach. The on-ramp queue grows at a rate of 0.11 veh/s • g2**: remaining effective green for NBT (Φ2). For this portion, no queue remains on the NBR approach, therefore the NBR throughput is equal to its demand flow rate (vNBR). The on-ramp queue discharges at a rate of 0.17 veh/s • r2: effective red time for NBT (Φ2). There is no throughput from protected movements and the NBR throughput is equal to its demand flow rate (vNBR). The on-ramp queue discharges at a rate of 0.17 veh/s • gs7: queue service time for EBT (Φ7). The EBT discharges into the on-ramp at the saturation flow rate. The throughput of the NBR movement is

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Example Problems Chapter 38 System Analyses (Draft) Page 110 Version 1.0 restricted to the permitted saturation flow rate, causing queues to develop in the NBR approach. The on-ramp queue grows at a rate of 0.26 veh/s • ge7*: green extension time for EBT (Φ7). The duration of 0.03s is calculated based on the queue service time of the NBR approach. The NBR movement discharges at the permitted saturation flow rate. The on-ramp queue grows at a rate of 0.08 veh/s • ge7**: remaining extension time for EBT (Φ7). The EBT movement discharges at a rate equal to its arrival flow rate during the effective green. For this portion, no queue remains on the NBR approach, therefore the NBR throughput is equal to its demand flow rate (vNBR). The on-ramp queue discharges at a rate of 0.15 veh/s • r7: effective red time for EBT (Φ7). No throughput from protected movements and the NBR throughput is equal to its demand flow rate (vNBR). The on-ramp queue discharges at a rate of 0.17 veh/s. Active phase t (s) Duration (s) Protected movement Permitted movement On-ramp analysis λprot (veh/s) vNBR (veh/s) λNBR (veh/s) NBR queue (veh) λONR (veh/s) λONR - cmerge (veh/s) On- ramp queue (veh) gs1 0 40.16 0.483 0.145 0.078 0 0.56 0.24 0 ge1 40.16 3.74 0.036 0.145 0.356 2.66 0.39 0.07 9.8 r1 43.9 5.7 0 0.145 0.43 1.87 0.43 0.11 10.08 g2* 49.6 0.88 0 0.145 0.43 0.25 0.43 0.11 10.72 g2** 50.48 49.82 0 0.145 0.145 0 0.14 -0.17 10.82 r2 100.3 5.7 0 0.145 0.145 0 0.14 -0.17 2.22 gs7 106 6.25 0.503 0.145 0.073 0 0.58 0.26 1.24 ge7* 112.25 2.02 0.027 0.145 0.366 0.45 0.39 0.08 2.85 ge7** 114.27 0.03 0.027 0.145 0.145 0 0.17 -0.15 3.01 r7 114.3 5.7 0 0.145 0.145 0 0.14 -0.17 3.01 Cycle end 120 2.02 At the end of the time period, a residual queue of 23.32 vehicles is expected along the on-ramp, and this value is carried to the start of the next time period. The time period length of 900s does not correspond to an exact number of signal cycles, and the last cycle is interrupted at t = 60s. Therefore, the next time period will start the analysis from the same timestamp to maintain consistency. Step 7D – Calculate equivalent capacities for the affected movements Since spillback does not occur during time period 2, no adjustment to the intersection capacity is necessary. Exhibit 38-60 Discharge Flow Rates into the On-Ramp for each Phase Throughout the Cycle – Time Period 2

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Example Problems Version 1.0 Page 111 Time Period 3 The same steps performed for the analysis of time period 2 are applied again for the analysis of time period 3. Step 7A – Determine intersection throughput to on-ramp The throughput for movements that discharge into the on-ramp have been previously determined as part of the queue spillback check, and are shown in Exhibit 38-53. Step 7B – Obtain merging capacity with Freeway Facilities method As in the analysis of the previous time period, the merging capacity cmerge is obtained as an output from the Freeway Facilities method (Exhibit 38-57a). The merging capacity for time period 3 is 1,142 veh/h. Step 7C – Plot queue accumulation polygon for the on-ramp and unsignalized movements The procedure described earlier is applied but with an initial on-ramp queue of 23.32 vehicles, which is the estimated queue at the end of time period 2. The analysis begins at the middle of the cycle (t= 60s), which is the end of the previous time period. Exhibit 38-61 illustrates the queue accumulation polygon for both the on-ramp and the NBR movement. Exhibit 38-61 Estimated Queue Lengths and Merge Capacities – Time Period 3

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Example Problems Chapter 38 System Analyses (Draft) Page 112 Version 1.0 Queue spillback occurs during the third cycle (SBL queue service time), when the on-ramp queue reaches the maximum storage LONR = 35.5 vehicles. At this time, the maximum flow rate that can enter the on-ramp is constrained by the merge capacity cmerge. In other words, the maximum number of vehicles allowed to enter the ramp is equal to the number of vehicles that are able to merge to the freeway mainline. Also, the queues developed in the NBR are longer during cycles 3 through 8, causing an increased delay on this movement due to the queue spillback conditions at the on-ramp. The on-ramp queue at the start of cycle 3 is 27.9 vehicles. The cycle starts with the SBL movement, with an effective green time g1 = 47.3s. Since this movement already operates with v/c > 1, the queue service time gs1 is equal to g1, and no green extension time is available (ge1 = 0). The protected movement then discharges at saturation flow rate sSBL = 0.483 veh/s, while the NBR movement discharges at a permitted saturation flow rate sNBR = 0.078 veh/s. At the same time, the on-ramp discharges to the freeway at a rate cmerge = 1,142 veh/h = 0.317 veh/s. Therefore, the on-ramp queue grows at the following rate: 𝜆 − 𝑐 = 0.483 + 0.078 − 0.317 = 0.244 𝑣𝑒ℎ/𝑠 At this rate, the time remaining until spillback occurs is calculated by dividing the remaining on-ramp queue storage by the growth rate: 𝑇𝑖𝑚𝑒 𝑡𝑜 𝑠𝑝𝑖𝑙𝑙𝑏𝑎𝑐𝑘 = 35.5 − 27.90.244 = 31.2𝑠 Spillback is then expected to occur within 31.2 seconds of the onset of g1. The total effective green g1 value of 47.3s is then divided in two portions: • gs1* (31.2s): discharging at saturation flow rate • gs1,sp (16.1s): the remainder of g1 will be affected by queue spillback, limiting the maximum discharge to the on-ramp to the merge capacity cmerge = 0.317 veh/s. Note that this constraint is shared by two movements entering the on-ramp (SBL and NBR). The effect of queue spillback on the intersection capacity during gs1,sp is then measured by the capacity reduction factor β1,sp, defined as the ratio between the maximum on-ramp capacity during queue spillback and the throughput from the intersection movements (SBL and NBR): 𝛽 , = 𝑐𝜆 + 𝜆 = 0.3170.483 + 0.078 = 𝟎.𝟓𝟔𝟓 A capacity reduction factor β1,sp= 0.565 means that only 56.5% of the expected intersection throughput is able to enter the on-ramp when queue spillback occurs during phase gs1,sp. This capacity adjustment factor is applied to each movement to obtain their adjusted throughputs for this time period: 𝜆 , = 𝜆 × 𝛽 , = 0.483 × 0.565 = 0.273 𝑣𝑒ℎ/𝑠 𝜆 , = 𝜆 × 𝛽 , = 0.078 × 0.565 = 0.044 𝑣𝑒ℎ/𝑠

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Example Problems Version 1.0 Page 113 The procedure is then repeated for the remaining movements of the cycle, as shown in Exhibit 38-62. As shown, at time t = 31.2 s the maximum storage length of the on-ramp is reached and spillback occurs. From this time through t = 83.3s, the throughput from intersection movements to the on-ramp λONR is greater than the merge capacity cmerge. Therefore, the maximum allowed throughput λONR,ajd is constrained by the on-ramp discharge capacity cmerge = 0.137 veh/s. For these cases, the spillback capacity reduction factor fsp is computed as the ratio of λONR,ajd and λONR. Note that for this time range the on-ramp queue is kept constant at the maximum storage of 35.54 vehicles. From t = 83.3s, the on-ramp queue begins to discharge at a rate of 0.142 veh/s, followed by a small increase during the green time of phase 7 (EBT), but it is not sufficient to cause spillback. At the end of the cycle, the residual on-ramp queue is 33.51 vehicles. The subsequent cycles follow a recurring pattern, with the on-ramp reaching maximum storage early in the cycle and slightly diminishing at the end of the cycle. Active phase t (s) Duration (s) QONR (veh) Protected movement Permitted movement On-ramp analysis βsp λprot (veh/s) vNBR (veh/s) λNBR (veh/s) Q(NBR) (veh) λONR (veh/s) λONR,adj (veh/s) λONR,adj - cmerge (veh/s) gs1* 0.0 31.2 27.9 0.483 0.175 0.078 0 0.561 0.561 0.244 1 gs1,sp 31.2 16.1 35.5 0.483 0.175 0.078 3.01 0.561 0.317 0 0.565 r1 47.3 5.7 35.5 0 0.175 0.43 5.12 0.43 0.317 0 0.739 g2* 53.0 30.3 35.5 0 0.175 0.43 4.31 0.43 0.317 0 0.739 g2** 83.3 17 35.4 0 0.175 0.175 0 0.175 0.175 -0.142 1 r2 100.3 5.7 33.1 0 0.175 0.175 0 0.175 0.175 -0.142 1 gs7 106.0 6.3 32.3 0.503 0.175 0.073 0 0.576 0.576 0.259 1 ge7 112.3 2 33.9 0.027 0.175 0.366 0.64 0.393 0.393 0.076 1 r7* 114.3 1 34.1 0 0.175 0.43 0.25 0.43 0.43 0.113 1 r7** 115.3 4.7 34.2 0 0.175 0.175 0 0.175 0.175 -0.142 1 Cycle end 120 0 33.5 - - - - - - Step 7D – Calculate adjusted capacities for the affected movements The adjusted capacities of the affected movements are estimated based on the volume of vehicles that can actually be discharged during each time period. Exhibit 38-63 provides the calculation of the adjusted capacity of the SBL movement during time period 3. The table lists all occurrences of green times for the SBL movement during the analysis time period and their respective durations. For each row, the expected throughput from the intersection λONR and the actual throughput λONR,adj are computed. Next, the capacity reduction factor βsp is computed as the ratio of λONR and λONR,adj. A value of βsp < 1.0 indicates the occurrence of queue spillback in the subject phase. The expected and actual discharge volumes are obtained by multiplying the values of λONR and λONR,adj, Exhibit 38-62 Discharge Flow Rates Into the On-Ramp for Each Phase Throughout the Cycle – Time Period 3

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Example Problems Chapter 38 System Analyses (Draft) Page 114 Version 1.0 respectively, by their duration. At the end of the table, the expected and actual volumes are aggregated and a capacity reduction factor βsp,SBL = 0.704 is obtained as the ratio of these values. The capacity of the SBL movement without consideration of queue spillback is 685 veh/h (Exhibit 38-53). The adjusted capacity is calculated by applying the spillback capacity reduction factor βsp, calculated in Exhibit 38-63 𝑐 , = 𝑐 × 𝛽 , = 685 × 0.704 = 482.2 𝑣𝑒ℎ/ℎ In this example, this step is not required for the EBT movement, since this movement does not experience effects of queue spillback. As shown in Exhibit 38-61, the on-ramp queue during the EBT green does not reach the maximum storage length of 35.5 veh. Cycle Active phase Duration (s) On-ramp analysis Spillback adjustment λONR (veh/s) λONR,adj (veh/s) βsp On-ramp expected discharge volume (veh) On-ramp actual discharge volume (veh) 2 gs1 47.3 0.561 0.561 1 26.56 26.56 3 gs1* 31.2 0.561 0.561 1 17.51 17.51 3 gs1,sp 16.1 0.561 0.317 0.565 9.04 5.11 4 gs1 8.3 0.561 0.561 1 4.67 4.67 4 gs1,sp 39 0.561 0.317 0.565 21.89 12.37 5 gs1 5.1 0.561 0.561 1 2.87 2.87 5 gs1,sp 42.2 0.561 0.317 0.565 23.68 13.39 6 gs1 4.7 0.561 0.561 1 2.62 2.62 6 gs1,sp 42.6 0.561 0.317 0.565 23.93 13.53 7 gs1 4.6 0.561 0.561 1 2.59 2.59 7 gs1,sp 42.7 0.561 0.317 0.565 23.97 13.55 8 gs1 4.6 0.561 0.561 1 2.58 2.58 8 gs1,sp 42.7 0.561 0.317 0.565 23.97 13.55 Total: 185.89 130.89 Capacity reduction factor (βsp,SBL): 0.704 Time Period 4 The same steps performed for time periods 2 and 3 are applied again in time period 4. Step 7A – Determine intersection throughput to on-ramp The throughput for movements that enter the on-ramp has been previously determined as part of the queue spillback check, and shown in Exhibit 38-53 Step 7B – Obtain merging capacity with Freeway Facilities method Exhibit 38-63 Calculation of Spillback Capacity Reduction Factor for the SBL Movement for Time Period 3

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Example Problems Version 1.0 Page 115 The merge capacity for time period 4 has been previously determined, as shown in Exhibit 38-57a. Since the congestion along the freeway mainline is dissipating during this time period, the merge capacity is not constant: from time steps 1 through 4, the merge capacity is 1,142 veh/h, consistent with oversaturated conditions from previous time periods. After time step 5, the merge capacity is set equal to the ramp roadway capacity (1,904 veh/h) Step 7C – Plot queue accumulation polygon for the on-ramp and unsignalized movements The procedure described earlier is applied to plot the queue accumulation polygons, shown in Exhibit 38-64. Queue spillback occurs during the first cycle, due to the residual queue from the previous time period. However, due to low volumes at the intersection and improvement of performance along the freeway mainline, the on-ramp clears quickly. The queue has cleared by the end of the second cycle. Step 7D – Calculate adjusted capacities for the affected movements The procedure described earlier is used to calculate the capacity reduction factor for the SBL movement, as shown in Exhibit 38-65. The estimated capacity reduction is minor, as spillback only occurs during the first cycle. The EBT movement does not experience queue spillback, therefore no adjustment is necessary. Exhibit 38-64 Estimated Queue Lengths and Merge Capacities – Time Period 4

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Example Problems Chapter 38 System Analyses (Draft) Page 116 Version 1.0 Cycle Active phase Duration (s) QONR (veh) On-ramp analysis Spillback adjustment λONR (veh/s) λONR,adj (veh/s) βsp On-ramp expected throughput (veh) On-ramp actual throughput (veh) 1 gs1 6 34.4 0.505 0.505 1 3.02 3.02 1 gs1,sp 29.9 35.5 0.505 0.317 0.628 15.12 9.5 1 ge1 0 35.5 0.388 0.317 0.818 0 0 2 gs1 31.2 13.2 0.505 0.505 1 15.79 15.79 2 ge1 4.7 19.1 0.095 0.095 1 0.44 0.44 3 gs1 31.2 0.0 0.505 0.505 1 15.79 15.79 3 ge1 4.7 5.9 0.058 0.058 1 0.27 0.27 4 gs1 40.2 0.0 0.561 0.561 1 22.55 22.55 4 ge1 3.7 9.8 0.392 0.392 1 1.46 1.46 5 gs1 40.2 0.0 0.561 0.561 1 22.55 22.55 5 ge1 3.7 1.3 0.392 0.392 1 1.46 1.46 6 gs1 40.2 0.0 0.561 0.561 1 22.55 22.55 6 ge1 3.7 1.3 0.392 0.392 1 1.46 1.46 7 gs1 40.2 0.0 0.561 0.561 1 22.55 22.55 7 ge1 3.7 1.3 0.392 0.392 1 1.46 1.46 8 gs1 40.2 0.0 0.561 0.561 1 22.55 22.55 8 ge1 3.7 1.3 0.392 0.392 1 1.46 1.46 Total: 170.49 164.86 Spillback capacity reduction factor: 0.967 The adjusted capacity of the SBL movement is calculated by applying the spillback capacity reduction factor βsp: 𝑐 , = 𝑐 × 𝛽 , = 746 × 0.967 = 721.4 𝑣𝑒ℎ/ℎ With the adjusted capacity values obtained, the performance measures for the intersection can be computed using the remaining steps from the Signalized Intersections methodology (Chapter 19): compute the adjusted demand-to- capacity ratio (Step 8) and compute control delay (Step 9). Exhibit 38-66 compares the performance measures for the affected movement (SBL) for the cases with and without accounting for spillback effects. There is no change in the performance measures in time period 2 even though the on-ramp demand is greater than the merge capacity, as the queue can be stored in the on-ramp. Time period 3 yields a significant increase in the SBL control delay due to the queue spillback: 589.2 s/veh, while the intersection analysis without consideration of the spillback effects would return a control delay of 293.5 s/veh. Time period 4 shows a small increase in control delay, from 575.2 s/veh to 609.5 s/veh. Even though spillback occurs for only a short time during this time period, the high value of control delay obtained is due to the initial queue delay (d3), as a result of the unmet demand at the end of time period 3. Exhibit 38-65 Calculation of Spillback Capacity Reduction Factor for the SBL Movement During Time Period 4

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Example Problems Version 1.0 Page 117 Time Period Movement capacity (veh/h) Control delay (s/veh) Without spillback With spillback Without spillback With spillback 1 652 652 60.3 60.3 2 586 586 55.9 55.9 3 685 482 293.5 589.2 Exhibit 38-66 Comparison of Performance Measures – with and without Consideration of Spillback Effects

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Example Problems Chapter 38 System Analyses (Draft) Page 118 Version 1.0 EXAMPLE PROBLEM 2, PART 2: TWSC RAMP TERMINAL This scenario study will replace the signalized intersection from Part 1 with a TWSC intersection, while keeping the freeway facility characteristics unchanged. Similar to Part 1, the control delay for the intersection movements with the occurrence of queue spillback will be evaluated and compared to the Exhibit 38-67 shows the geometry of the study intersection. Spillback check – on-ramp The first step in the spillback check analysis is to determine the on-ramp demand flow rates for each time period, based on the demand inputs of the TWSC intersection. For each time period, the demand (v) and capacities (c) are compared for each movement that enters the on-ramp (EBT, NBR and SBL). The minimum value between demand and capacity for each movement is computed and the merge demand vR is then computed as the sum of the three movements. The capacities for minor rank movements (EBT and SBL) are computed for each time period, since they change as a function of the conflicting demand. The NBR movement is unsignalized and therefore its capacity is computed by its respective saturation flow rate, considering the applicable adjustment factors fRT (for right-turn movements) and fHV (for the presence of heavy vehicles): 𝑠 = 𝑠 , × 𝑓 × 𝑓 𝑠 = 1,900 × 11.18 × 0.961 = 1,547 𝑣𝑒ℎ/ℎ Exhibit 38-67 TWSC Intersection Geometry – Acadian Thruway @ I-10 EB.

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Example Problems Version 1.0 Page 119 Different from the signalized intersection scenario, there are no conflicting flows to the unsignalized right turn since it is a Rank 1 movement (highest priority). Therefore, the capacity for the NBR movement is equal to its saturation flow rate. Exhibit 38-68 summarizes the calculations for this step. Time Period Parameter Movements EBT NBR SBL 1 Demand (veh/h) 8 315 652 v/c 0.064 - 0.96 c (veh/h) 125 1547 677 min (v, c) 8 315 652 Merge demand vR (veh/h) 975 2 Demand (veh/h) 96 521 586 v/c 0.768 - 0.93 c (veh/h) 125 1547 630 min (v, c) 96 521 586 Merge demand vR (veh/h) 1203 3 Demand (veh/h) 96 630 1071 v/c 0.77 - 1.56 c (veh/h) 125 1547 685 min (v, c) 96 630 685 Merge demand vR (veh/h) 1411 4 Demand (veh/h) 24 80 463 v/c 0.39 - 0.62 c (veh/h) 62 1547 746 min (v, c) 24 80 463 Merge demand vR (veh/h) 567 The on-ramp demand estimates are then used as inputs for the freeway facility analysis. Since the input demands for the freeway are identical to the example provided in Part 1, it is already known that spillback will occur during time period 3 (Exhibit 38-56). Evaluation of queue spillback impacts The evaluation of queue spillback impacts on the TWSC intersection follows the procedure detailed in Exhibit 38-B11. Since this is a multiperiod analysis, the procedure must be applied for each time period. In this example, time periods 2, 3 and 4 will be evaluated. Time period 1 will be excluded since no oversaturated conditions occur in the freeway. Step 9A - Determine intersection throughput to on-ramp The throughput for movements that enter the on-ramp has been previously determined as part of the queue spillback check, and these values are shown in Exhibit 38-57. Step 9B. Obtain merging capacity using the freeway facilities methodology This step computes the merging capacity into the freeway cmerge. Since the inputs of the freeway facility remain unchanged, the same values from the previous case study are used: Exhibit 38-68 Calculation of the On-Ramp Demand (vR) Based on the TWSC Intersection Operation.

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Example Problems Chapter 38 System Analyses (Draft) Page 120 Version 1.0 • Time periods 2 and 3: 1,142 veh • Time period 4: 1,142 veh/h during 4 time steps (60 seconds), then 1,903 veh/h. This time period considers a lower merge capacity while a mainline queue is present at the first 60 seconds. For the remainder of the time period, the merge capacity is constrained only by the on-ramp capacity, similar to the scenario presented in the signalized intersection example. Step 9C. Determine proportion of time period with queue spillback In order to determine the spillback time TSB, a queue accumulation polygon is developed for the on-ramp. Exhibit 38-69 shows the calculations for plotting the on-ramp queue. For each time period, the difference between the on-ramp throughput λΟΝR and the merge capacity cmerge is calculated. Then, the time to spillback is obtained considering the queue growth and the available queue storage. Time period 4 is split into two rows (4a and 4b), since the merge capacity changes within this time period. For the first minute of the time period (4a), the merge capacity remains at 1,142 veh/h due to existing oversaturated conditions along the freeway mainline. For the remaining of the time period (4b), the merge capacity is equal to the ramp roadway capacity (1,903 veh/h). The results show that queue spillback occurs only during time period 3. The initial queue of time period 2 is 15.2 vehicles, and it takes 4.55 minutes for the on- ramp to reach maximum storage capacity. Therefore, the spillback time TSB is computed as 15 – 4.55 = 10.45 minutes. Time Period Duration (min) On- ramp demand (vR) (veh/h) On-ramp queue growth rate (λONR - cmerge) (veh/s) Initial ONR queue (veh) Time to spillback (min) Spillback time (TsB) (min) Final ONR queue (veh) 2 15 1203 0.017 0.0 - - 15.2 3 15 1411 0.075 15.2 4.55 10.45 35.5 4a 1 567 -0.160 35.5 - - 26.0 4b 14 567 -0.371 26.0 - - - Exhibit 38-70 illustrates the queue accumulation polygon for the on-ramp, based on the table results. Exhibit 38-69 Queue Accumulation Plot Calculations for On-Ramp – TWSC Intersection

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Example Problems Version 1.0 Page 121 Step 10. Final capacity adjustments When queue spillback occurs at a TWSC intersection, movements discharging towards the on-ramp tend to follow a cooperative approach instead of the priority-based regular operation. Therefore, the merge capacity cmerge is shared among the three movements that enter the on-ramp: 𝑐 , + 𝑐 , + 𝑐 , = 𝑐 = 1,142 𝑣𝑒ℎ/ℎ The capacities during spillback conditions are then obtained proportionally to their demand flow rates (Equation 38-B22): 𝑐 , = 𝑐 × 𝑣𝑣 + 𝑣 + 𝑣 = 1,142 × 685685 + 708 + 18 = 554.4 𝑣𝑒ℎ/ℎ 𝑐 , = 𝑐 × 𝑣𝑣 + 𝑣 + 𝑣 = 1,142 × 708685 + 708 + 18 = 573.0 𝑣𝑒ℎ/ℎ 𝑐 , = 𝑐 × 𝑣𝑣 + 𝑣 + 𝑣 = 1,142 × 18685 + 708 + 18 = 14.6 𝑣𝑒ℎ/ℎ The equivalent capacities cEQ,i for each movement i, aggregated for the 15- min time period, are obtained proportionately to the spillback time TSB (Finally, the adjusted capacity of each affected movement ci,EQ is obtained as a function of the amount of time within the time period when spillback was present. The adjusted capacity considers the): 𝑐 , = , × × = . × . × . = 757 𝑣𝑒ℎ/ℎ 𝑐 , = , × × = × . × . = 869 𝑣𝑒ℎ/ℎ 𝑐 , = , × × = × . . × . = 24 𝑣𝑒ℎ/ℎ Exhibit 38-70 Queue Accumulation Polygon for the On-Ramp – TWSC Intersection

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Example Problems Chapter 38 System Analyses (Draft) Page 122 Version 1.0 With the adjusted capacity values obtained, the performance measures for the intersection can be computed using the next step from the TWSC methodology (Chapter 20): compute movement control delay (Step 11). Exhibit 38-71 compares the performance measures of the affected intersection movements for the cases with and without spillback effects during time period 3. All three movements discharging to the on-ramp experienced significant increase in the control delay. Movement Demand (veh/h) Capacity (veh/h) Control delay (s/veh) Without spillback With spillback Without spillback With spillback EBT 18 28 18.7 166.5 479.8 NBR 708 1547 868.9 0 24.5 SBL 685 1222 757.2 9.4 37.2 Exhibit 38-71 Comparison of Performance Measures in a TWSC Intersection – Time Period 3 - with and without Spillback Effects

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Example Problems Version 1.0 Page 123 EXAMPLE PROBLEM 2, PART 3: AWSC INTERSECTION RAMP TERMINAL This scenario will replace the signalized intersection from Part 1 with an AWSC intersection, while keeping the freeway facility characteristics unchanged. A ramp meter is active at the freeway on-ramp, with a constant metering rate of 900 veh/h (4 s/veh). Additionally, the NBR movement is not channelized as presented in the previous scenarios and now conflicts with the other movements in the intersection. Exhibit 38-72 shows the geometry of the study intersection. Spillback check – on-ramp The first step in the spillback check analysis is to determine the on-ramp demand flow rates for each time period, based on the demand inputs of the AWSC intersection. For each time period, the demand (v) and capacities (c) are compared for each movement that feeds the on-ramp (EBT, NBR and SBL). The minimum value between demand and capacity for each movement is computed and the merge demand vR is then computed as the sum of three movements. Exhibit 38-73 summarizes the calculations for this step. Exhibit 38-72 AWSC Intersection Geometry – Acadian Thruway @ I-10 EB

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Example Problems Chapter 38 System Analyses (Draft) Page 124 Version 1.0 Time Period Parameter Movements EBT NBR SBL 1 Demand (veh/h) 54 467 313 v/c 0.14 - 0.67 c (veh/h) 377 539 466 min (v, c) 54 467 313 Merge demand vR (veh/h) 834 2 Demand (veh/h) 40 512 432 v/c 0.11 - 0.98 c (veh/h) 350 521 439 min (v, c) 40 512 432 Merge demand vR (veh/h) 984 3 Demand (veh/h) 19 539 546 v/c 0.05 - 1.18 c (veh/h) 396 550 462 min (v, c) 19 539 462 Merge demand vR (veh/h) 1020 4 Demand (veh/h) 28 160 316 v/c 0.06 - 0.62 c (veh/h) 455 619 511 min (v, c) 28 160 316 Merge demand vR (veh/h) 504 The estimated on-ramp demand values are provided as inputs for the freeway facility analysis. The freeway facility is then analyzed and the expected on-ramp queues are provided in Exhibit 38-74. Time period vR (veh/h) Ramp queue (veh) Ramp queue (ft) Ramp storage ratio (RQ) Spillback expected? 1 834 0 0 0 No 2 984 14.9 21.9 0.62 No 3 1020 82.1 53.4 1.5 Yes 4 504 0 0 0 No Since spillback will occur, the impacts on the operation of the intersection must be evaluated. The next section illustrates the application of the evaluation methodology at the AWSC intersection. Evaluation of queue spillback impacts The evaluation of queue spillback impacts on the AWSC intersection follows the procedure detailed in Exhibit 38-B13. Since this is a multiperiod analysis, the procedure must be applied for each time period. In this example, time periods 2, 3 and 4 will be evaluated. Time period 1 will be excluded since no oversaturated conditions occur along the freeway. Step 13A - Determine intersection throughput to on-ramp The intersection throughput to the on-ramp was previously determined at the spillback check (Exhibit 38-92). Exhibit 38-73 Calculation of the On-Ramp Demand (vR) Based on the AWSC Intersection Operation Exhibit 38-74 Check for Spillback Occurrence – AWSC Intersection

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Example Problems Version 1.0 Page 125 Step 13B - Obtain merging capacity with Freeway Facilities method For this example, the ramp metering rate (900 veh/h) is an additional input to the freeway facility analysis and is considered as a potential constraint of the merge capacity. Therefore, the merge capacity for this analysis is kept constant at 900 veh/h. Step 13C - Determine fraction of time period with queue spillback The procedure to evaluate the spillback time (TSB) is similar to the TWSC procedure, and the calculations are provided in Exhibit 38-75. Time Period Duration (min) On-ramp demand (vR) (veh/h) On-ramp queue growth rate (λONR - cmerge) (veh/s) Initial ONR queue (veh) Time to spillback (min) Spillback time (TsB) (min) Final ONR queue (veh) 2 15 984 0.023 0 - - 21 3 15 1020 0.033 15.2 7.25 7.75 35.5 4 15 504 -0.11 35.5 - - 0 Exhibit 38-94 illustrates the queue accumulation polygon for the on-ramp, based on the table results. Step 13D - Compute spillback departure headway This step is similar to the calculation of adjusted capacities in the TWSC procedure. The same calculations are performed, and adjusted capacity values are converted into headways (hsp), as shown in Exhibit 38-77. Exhibit 38-75 Queue Accumulation Plot Calculations for On-Ramp – AWSC Intersection Exhibit 38-76 Queue Accumulation Polygon for the On-Ramp – AWSC Intersection

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Example Problems Chapter 38 System Analyses (Draft) Page 126 Version 1.0 Movement Capacity during spillback (csp) (veh/h) Regular Capacity (c) (veh/h) Equivalent Capacity (cEQ) (veh/h) Spillback departure headway (hsp) (s) EBT 15 396 212.1 17 NBR 439 550 496.5 7.3 SBL 445 462 453.7 7.9 With the adjusted capacity values obtained, the performance measures for the intersection can be computed using the remaining steps from the AWSC methodology (Chapter 21): compute the service times (Step 13) and compute control delay (Step 14). Exhibit 38-78 compares the performance measures of the intersection movements for the cases with and without spillback effects during time period 3. The three movements that discharge into the on-ramp (EBT, NBR and SBL) experience increased delay, while the remaining movements have their performance measures unchanged. Movement Demand (veh/h) Capacity (veh/h) Control delay (s/veh) Departure headway (s) Without spillback With spillback Without spillback With spillback Without spillback With spillback EBL 75 359 359 15.6 15.6 10 10 EBT 19 396 212 12.6 21.7 9.1 17 NBT 229 497 497 16.3 16.3 7.2 7.2 NBR 539 550 497 58.9 92.3 6.5 7.3 SBL 546 462 454 128 136.5 7.8 7.9 SBT 220 494 494 16 16 7.3 7.3 Exhibit 38-77 Equivalent Capacities and Headways for on-ramp – Time Period 3 – AWSC Intersection Exhibit 38-78 Comparison of Performance Measures – Time Period 3 - with and without Spillback Effects

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Example Problems Version 1.0 Page 127 EXAMPLE PROBLEM 3: OFF-RAMP QUEUE SPILLBACK ANALYSIS FOR A FREEWAY-TO-FREEWAY RAMP IN MIAMI, FLORIDA. This case study illustrates the application of the off-ramp spillback methodology to evaluate a network comprised of two freeway facilities (I-75 SB to SR-826 SB, Miami, Florida), as shown in Exhibit 38-79. Due to congested conditions at the downstream merge segment (SR-826), spillback is expected to affect the operations of the upstream freeway facility (I-75). Vehicles traveling from node A to D are likely to have their travel time severely affected if spillback occurs. This freeway-to-freeway connector is modeled as two separate freeway facilities. The upstream freeway (Facility 1: I-75) is modeled as a diverge section that is connected to the downstream freeway (Facility 2: SR-826). The system’s detailed geometry is shown in Exhibit 38-80. Exhibit 38-79 Study Site for Freeway-to- Freeway Queue Spillback Check, Miami, FL

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Example Problems Chapter 38 System Analyses (Draft) Page 128 Version 1.0 Input data Traffic demands for the freeway facilities and ramps are provided in Exhibit 38-1 in 15-minute time periods. Time Period Freeway Facility 1 (I-75 SB) Freeway Facility 2 (SR-826 SB) Mainline demand flow rate (veh/h) Diverge demand flow rate (veh/h) Mainline demand flow rate (veh/h) Merge demand flow rate (veh/h) 1 5400 1400 4000 1400 2 6200 3000 5700 3000 3 6000 3400 5600 3400 4 4500 800 4500 800 Additional input parameters are as follows: • Urban area with level terrain; • Grade: 0%; • Regime 4 is expected; • Base FFS: 65 mi/h (I-75) and 67.1 mi/h (SR-826); • Ramp FFS: 55 mi/h; • Ramp side: right for both facilities; • Lane width: 12 ft; • Right side clearance: 10 ft; • Traffic composition: 12% trucks on both freeway and ramps; • Ramp length: 3588 ft; Exhibit 38-80 Individual Freeway Facilities: (a) I-75 SB and (b) SR-826 SB Exhibit 38-81 Traffic Demands for the Subject Freeway Facilities

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Example Problems Version 1.0 Page 129 • Acceleration lane length: 1500 ft; • No shoulder available; • Deceleration lane length: 700 ft; • Number of ramp lanes: 2; and • Familiar facility users. Performance measures - individual facilities The performance measures for both freeway facilities, if analyzed independently, are presented in Exhibit 38-82 andExhibit 38-83 Exhibit 38-83. Facility 1 (I-75) is undersaturated, while Facility 2 (SR-826) experiences congestion in time periods 2 and 3. Ignoring the interactions between these two facilities would lead to inaccurate estimations of performance for the upstream facility. The merge segment (segment 2) in the SR-826 facility operates at LOS F, and the on-ramp capacity may be affected leading to queue formation and potential spillback. Time period Segment 1 Segment 2 Segment 3 Segment 4 Basic Basic Diverge Basic 1 C C B B 2 C C C A 3 C C C A 4 B B A B Time period Segment 1 Segment 2 Segment 3 Segment 4 Segment 5 Basic Merge Basic Diverge Basic 1 B C C B C 2 C F E F E 3 C F F F E 4 C C C C C Spillback check The analysis of SR-826 using the Freeway Facilities Oversaturated Segment Evaluation provides the expected on-ramp queue for every time period. The first check compares the off-ramp demand to the ramp roadway capacity, as shown in Exhibit 38-84. The ramp queue starts to develop during time period 2. At the end of this time period, a ramp queue length of 1188 ft is expected, yielding a queue storage ratio of 0.33. Therefore, spillback is not expected during time period 2. During time period 3 a ramp queue length of 5160 ft is expected with a queue storage ratio of 1.41. Therefore, spillback will occur during time period 3. Exhibit 38-82 Performance Measures for I- 75 (Freeway Facility 1) Exhibit 38-83 Performance Measures for SR- 826 (Freeway Facility 2)

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Example Problems Chapter 38 System Analyses (Draft) Page 130 Version 1.0 Time period Total number of queued vehicles Number of queued vehicles in each lane Average vehicle spacing (ft) Queue length (ft) Ramp length (ft) Queue storage ratio Spillback occurs? [A] [B] = [A]/2 [C] [D] = [B]*[C] [E] [F] = [D]/[E] 1 0 0 - 0 3588 0.00 No 2 38.3 19.15 62 1188 0.33 No 3 159.1 79.55 65 5160 1.44 Yes 4 0 0 - 0 0.00 Yes Spillback analysis Since spillback is expected to occur, the methodology described in Appendix A (Exhibit 38-A8 through Exhibit 38-A11) is applied to evaluate its impacts on I- 75 SB. The application of the methodology for each time period is presented below. Time period 1 No oversaturated conditions occur, therefore no additional calculations are needed for this time period. Time period 2 During time period 2, the downstream merge segment operates at LOS F and the on-ramp capacity is expected to be reduced. Step 1 - Calculate background density for unblocked lanes on each segment in the case of queue spillback The diverge segment at I-75 has 5 lanes and Regime 4 (two blocked lanes) is expected. Therefore, when queue spillback occurs this segment operates with two blocked lanes (lanes 1 and 2) and three unblocked lanes (lanes 3 through 5). The capacity per lane at the diverge segment SC(3) is 2,350 pc/h/ln or 11750 pc/h. For the time step level analysis, the capacity is converted to 48.95 passenger cars per time step (ts), Therefore, the capacity for the unblocked portion of the segment is given by Equation 38-A11: 𝑆𝐶𝐸𝑄 𝑖,𝑁,𝑁𝑄 = 𝑆𝐶 𝑖,𝑁 − 𝑁𝑄 × 𝐶𝐴𝐹 The capacity adjustment factor CAFBL is obtained from Exhibit 38-3. For a segment with 5 directional lanes and 2 blocked lanes, an adjustment factor CAFBL = 0.67 is applied. Therefore, the equivalent capacity of the unblocked portion is given by: 𝑆𝐶𝐸𝑄 3, 5, 3 = 48.95 × 0.67 = 38.8𝑝𝑐/𝑡𝑠 𝑜𝑟 7872 𝑝𝑐/ℎ Exhibit 38-84 Estimation of Queue Length and Storage Ratio at the SR- 826 On-Ramp

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Example Problems Version 1.0 Page 131 The unblocked background density KBUB is calculated next. For time period 2, an expected demand of 4165.8 pc/h for the mainline is used in the calculations. The KBUB parameter of the unblocked lanes is computed as the density of a 3- lane basic segment with a capacity SCEQ = 7872 pc/h: 𝐾𝐵𝑈𝐵 3, 5, 3 = 30.4 𝑝𝑐/ℎ/𝑚𝑖 Step 2 - Initialize the freeway facility When spillback occurs, the subject freeway facility is analyzed as a link-node structure similar to the oversaturated procedure for freeway facilities. The facility structure is also expanded to consider the ramp segments. Exhibit 38-85 illustrates the structure for the current analysis. Node 4.1 represents the interface between the diverge segment and the ramp roadway, while node 4.2 represents the interface between the ramp roadway and the merge at the downstream facility. Step 2C - Determine queue influence area (QIA) The queue influence area is obtained as function of the segment FFS, as shown in Exhibit 38-5. Therefore, for a FFS = 65mi/h, the QIA length is equal to 1060 ft. Step 2F - Determine initial number of vehicles at the off-ramp The ramp speed at the expected demand is obtained as: 𝑆 = 1 − 0.109 × 𝑣1000 × 𝑆 𝑆 = 1 − 0.109 × 16791000 × 55 = 44.9𝑚𝑖ℎ Next, the ramp background density is obtained: 𝑅𝐾𝐵 = 𝑣𝑆 = 167944.9 = 37.4 𝑝𝑐/𝑚𝑖/𝑙𝑛 Exhibit 38-85 Link-node Structure for Spillback Analysis – I-75 SB

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Example Problems Chapter 38 System Analyses (Draft) Page 132 Version 1.0 The initial number of vehicles in the ramp is then computed as: 𝑅𝑁𝑉 3,0,2,1 = 37.4 × 35885280 × 2 = 50.8 𝑝𝑐 Step 2G - Determine the capacity of the downstream terminal The capacity of the merge is obtained by analyzing the downstream freeway facility using the oversaturated segment evaluation procedure and aggregating the parameter ONRO for an hourly flow rate. During this time period, the merge capacity is constant at 13.4 pc/ts or 3217 pc/h, while the ramp demand is 14 pc/ts or 3369 pc/h. Given the demand and capacity at the merge, the queue in the ramp roadway increases by 0.6 pc for every time step. Exhibit 38-86 illustrates the ramp queue and the total number of vehicles in the ramp, considering an initial number of 50.8 pc in the ramp at the start of the time period as previously computed. Step 9A - Perform spillback analysis The flow RF that can travel across the ramp node 4.1 and enter the ramp roadway is obtained as the minimum of demand (RI), the ramp roadway capacity (RC) and the constrained capacity due to a downstream queue in the ramp (RSTG), as shown in Equation 38-A20: 𝑅𝐹 𝑖, 𝑡,𝑝 = 𝑚𝑖𝑛 𝑅𝐼 𝑖, 𝑡,𝑝, 𝑘 ,𝑅𝐶 𝑖, 𝑘 ,𝑅𝑆𝑇𝐺 𝑖, 𝑡,𝑝, 𝑘 The capacity of the ramp roadway for a 2-lane ramp with FFS = 55mph, is equal to 4,400 pc/h or 18.3 pc/ts. Therefore, the capacity of the ramp roadway is not a constraint to ramp flow. The other potential capacity constraint RSTG is calculated through Equation 38-A22: 𝑅𝑆𝑇𝐺 𝑖, 𝑡,𝑝, 𝑘 = 𝑅𝐹 𝑖, 𝑡 − 1,𝑝, 𝑘 + 𝑅𝐾𝑄 𝑖, 𝑡,𝑝, 𝑘 𝑥 𝑅𝐿 𝑘 𝑥 𝑅𝑁 𝑘 – 𝑅𝑁𝑉 𝑖, 𝑡 − 1,𝑝, 𝑘 The constraint RSTG is dependent on the number of vehicles in the ramp RNV, which increases progressively as the queue grows along the ramp. Exhibit 38-94 compares the decreasing value of RSTG with the ramp input RI during time period 2. At the end of the time period, the capacity is still greater than demand, therefore no spillback occurs at the end of this time period as predicted by the queue spillback check previously described. Exhibit 38-86 Queued Vehicles and Total Number of Vehicles in the Ramp – Time Period 2

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Example Problems Version 1.0 Page 133 Since spillback does not occur, no additional calculations for the mainline are required. Step 30 - Calculate segment performance measures Since spillback does not occur during this time period, the performance measures for the mainline do not need to be recalculated. The ramp, however, experiences queueing. Therefore, the ramp speed in this time period is calculated using Equation 38-A61 through Equation 38-A63: 𝑅𝐹 𝑖,𝑝, 𝑘 = 4 × 𝑅𝐹 𝑖, 𝑡,𝑝, 𝑘 = 1679.5 pc/h/ln 𝑅𝐾 𝑖,𝑝, 𝑘 = 160 × 𝑅𝑁𝑉 𝑖, 𝑡,𝑝, 𝑘 = 71.6 pc/mi/ln 𝑆𝑅 𝑖,𝑝, 𝑘 = 𝑅𝐹 𝑖,𝑝, 𝑘𝑅𝐾 𝑖, 𝑝, 𝑘 = 1679.571.6 = 31.9mi/h Time period 3 The same steps are repeated for time period 3. The ramp analysis is summarized in Exhibit 38-88. For this time period, the ramp demand is 15.4 pc/ts, while the merge capacity is 13.9 pc/ts. Since demand is greater than capacity, the number of vehicles increases gradually, causing the capacity constraint RSTG to decrease each time step. At time step 14, the value of RSTG becomes equal to the merge capacity (13.9 pc/ts), which implies that the ramp has reached jam density and the maximum flow that can enter the ramp is equal to the flow that departs the ramp. Therefore, queue spillback into the mainline starts at time step 15. Exhibit 38-87 Ramp Capacity and Ramp Inputs – Time Period 2

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Example Problems Chapter 38 System Analyses (Draft) Page 134 Version 1.0 After the onset of queue spillback, the number of unserved vehicles at the exit is computed every time step through the parameter OFRUV(i,t,p). Then, the expected length of the mainline queue OFRLQ(i,t,p) is computed based on the number of unserved vehicles and the ramp queue density RKQ, as shown in Equation 38-A33: 𝑂𝐹𝑅𝐿𝑄 𝑖, 𝑡,𝑝 = 𝑂𝐹𝑅𝑈𝑉 𝑖, 𝑡,𝑝𝑅𝐾𝑄 𝑖, 𝑡,𝑝 The ramp queue density RKQ is obtained using Equation 38-A21: 𝑅𝐾𝑄 𝑖, 𝑡,𝑝, 𝑘 = 𝐾𝐽– 𝐾𝐽 – 𝑅𝐾𝐶 𝑥 𝑅𝐹 𝑖, 𝑡 − 1,𝑝𝑅𝐶 𝑖, 𝑡,𝑝 𝑅𝐾𝑄 𝑖, 𝑡,𝑝, 𝑘 = 190– 190 – 46.5 × 13.87 / 18.33 = 81.4 pc/mi/ln Exhibit 38-89 illustrates the expected spillback queue length during time period 3. The parameter OFRLQ represents the length of the queue if all unserved vehicles were queued in a single line. Given the segment geometry (Exhibit 38- 90), the operating regimes and flow modes can be obtained as a function of OFRLQ: Exhibit 38-88 Ramp Capacities and Ramp Inputs – Time Period 3 Exhibit 38-89 Spillback Queue Length – Segment 3 (Diverge) – I-75 SB

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Example Problems Version 1.0 Page 135 • 0 < OFRLQ ≤ 1,400 ft: Regime 1 • 1400 ft < OFRLQ ≤ 3000 ft: Regime 4, with increased turbulence • 3000 ft < OFRLQ: Regime 4, with lane blockage (queue extends upstream beyond the diverge) As previously shown in Exhibit 38-89, the maximum queue length OFRLQ at time period 3 is equal to 4696 ft. Since queues develop along lanes 1 and 2, at the end of time period 3 the back of queue will be located 848ft upstream of the boundary of segments 2 and 3. The length of the queue influence area (QIA) is 1060 ft, and when it is added to the back of the queue it does not reach the upstream node of segment 2. Therefore, segment 2 capacity is not affected by the turbulence area upstream of the queue (Exhibit 38-91). Step 30 - Calculate segment performance measures The ramp speed is computed similarly to time period 2: 𝑅𝐹 𝑖,𝑝, 𝑘 = 4 × 𝑅𝐹 𝑖, 𝑡,𝑝, 𝑘 = 1707 𝑝𝑐/ℎ/𝑙𝑛 𝑅𝐾 𝑖,𝑝, 𝑘 = 160 × 𝑅𝑁𝑉 𝑖, 𝑡,𝑝, 𝑘 = 108.4 𝑝𝑐/𝑚𝑖/𝑙𝑛 𝑆𝑅 𝑖,𝑝, 𝑘 = 𝑅𝐹 𝑖,𝑝, 𝑘𝑅𝐾 𝑖,𝑝, 𝑘 = 1707108.4 = 21.5 𝑚𝑖/ℎ Exhibit 38-90 Available Queue Storage – Segment 3 (Diverge) – I-75 SB Exhibit 38-91 Back of Queue Length, Including QIA, at the End of Time Period 3

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Example Problems Chapter 38 System Analyses (Draft) Page 136 Version 1.0 For the freeway facility, performance measures are computed for the blocked and unblocked portions of each segment. Segment 3 (diverge) – blocked portion Similar to the ramp, the flow through the blocked portion is aggregated for this time period: 𝑆𝐹𝐵𝐿 𝑖,𝑝 = 4 × 𝑡𝑖𝑚𝑒𝑠 𝑆𝐹𝐵𝐿 𝑖, 𝑡,𝑝 = 3030 𝑝𝑐/ℎ The average density is obtained as the sum of two separate components. The average number of vehicles in the blocked portion of the segment is computed as: 𝐾𝐵𝐿 𝑖,𝑝 = 160 × 𝑁𝑉(𝑖, 𝑡,𝑝) = 51 𝑝𝑐/𝑚𝑖/𝑙𝑛 The increase in density due to the lane blockage ΔK is obtained as: ∆𝐾(𝑖,𝑝) = 1𝑆 × 𝑁 ∆𝑁𝑉(𝑖, 𝑡,𝑝) = 20.1 𝑝𝑐/𝑚𝑖/𝑙𝑛 The total density is then computed as: 𝐾(𝑖,𝑝) = 𝐾𝐵𝐿(𝑖,𝑝)+ ∆𝐾(𝑖,𝑝) = 70.1 𝑝𝑐/𝑚𝑖/𝑙𝑛 Finally, the speed in the blocked lanes is obtained through the fundamental equation: 𝑆𝐵𝐿(𝑖,𝑝) = 𝑆𝐹𝐵𝐿(𝑖,𝑝)𝑁(𝑖,𝑝) × 𝐾(𝑖,𝑝) = 30302 × 70.1 = 21.2𝑚𝑖/ℎ Segment 3 (diverge) – unblocked portion The same process is repeated for the unblocked portion of the segment, except the ΔK component is omitted as no queues occur in these lanes: 𝑆𝑈𝐵(𝑖,𝑝) = 56.1𝑚𝑖/ℎ Time period 4 During time period 4, the congestion at the downstream facility (SR-826) dissipates, which allows the ramp to discharge at the ramp roadway capacity (4,400 pc/h, or 18.33 pc/ts). Given the low ramp demand during this time period, the queue can be cleared quickly (9 time steps, or 135s). After the 10th time step, the freeway facility returns to undersaturated conditions.

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Example Problems Version 1.0 Page 137 EXAMPLE PROBLEM 4: ON-RAMP QUEUE SPILLBACK ANALYSIS INTO A SINGLE-LANE ROUNDABOUT IN LOS ANGELES, CALIFORNIA This example problem illustrates the analysis methodology when there is spillback from an on-ramp into a single-lane roundabout. The example is based on an existing ramp terminal at Bellflower Blvd @ Century Freeway (I-105) in Los Angeles, California. Example Problem Data The traffic and geometric characteristics of this location are as follows (the layout of the site is shown in Exhibit 38-92): • The roundabout has one-lane approaches, • The adjusted flow rates for all movements and O-Ds are shown in Exhibit 38-92(b), • There are no heavy vehicles present at this location, • U-turn movements are negligible, • There is no pedestrian activity in the vicinity of the roundabout, • The total length of the ramp is 1657 ft, and • The on-ramp connecting the roundabout to the freeway is metered at a rate cRM = 800 pc/h. Step 3: Determine Circulating Flow Rates This step calculates all circulating flow rates at the roundabout. For example, for the NB approach, the circulating flow is calculated using Equation 22-11: 𝑣 , , = 𝑣 , + 𝑣 , + 𝑣 , = 100 + 500 + 100 = 700 𝑝𝑐/ℎ Similarly, for the other approaches the resulting conflicting flows are: Exhibit 38-92 Schematic of the Study Interchange for Example Problem 4

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Example Problems Chapter 38 System Analyses (Draft) Page 138 Version 1.0 𝑣 , , = 0 𝑝𝑐/ℎ 𝑣 , , = 300 𝑝𝑐/ℎ Step 4: Determine Entry Flow Rates per Approach The entry flow rate at each approach is calculated by adding the movement flow rates that enter the roundabout. The entry flow rates are calculated as follows: 𝑣 , , = 𝑣 , + 𝑣 , = 100 + 200 = 300 𝑝𝑐/ℎ 𝑣 , , = 700 𝑝𝑐/ℎ 𝑣 , , = 1600 𝑝𝑐/ℎ Step 5: Determine the Capacity of Each Entry Lane in Passenger Car Equivalents By using the single-lane capacity equation (Equation 22-1), the capacity for each entry lane is calculated as follows: 𝑐 , = 1,380𝑒( . × ) , , = 1,380𝑒( . × )( ) = 1,380 𝑝𝑐/ℎ 𝑐 , = 1,380𝑒( . × ) , , = 1,380𝑒( . × )( ) = 1,016 𝑝𝑐/ℎ 𝑐 , = 1,380𝑒( . × ) , , = 1,380𝑒( . × )( ) = 676 𝑝𝑐/ℎ Step 8: Compute the Volume-to-Capacity Ratio for Each Lane The volume-to-capacity ratios for each entry lane are calculated using Equation 22-16 as follows: 𝑥 = 3001,380 = 0.22 𝑥 = 7001,016 = 0.69 𝑥 = 1,600676 = 2.37 Step 12: Compute 95th Percentile Queues for Each Lane The 95th percentile queue is first computed for each lane without considering spillback effects. For example, the queue for the southbound approach is given as follows (Equation 22-20): 𝑄 , = 900𝑇 𝑥 − 1 + (1 − 𝑥) + 3,600𝑐 𝑥150𝑇 𝑐3,600 𝑄 , = 900(0.25) ⎣⎢⎢ ⎢⎡0.22 − 1 + (1 − 0.22) + 3,6001,380 0.22150(0.25) ⎦⎥⎥ ⎥⎤ 1,3803,600 = 1 𝑣𝑒ℎ Similarly, 𝑄 , = 6 𝑣𝑒ℎ

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Example Problems Version 1.0 Page 139 𝑄 , = 121 𝑣𝑒ℎ These values are rounded to the nearest vehicle. Exhibit 38-93 provides the flows and resulting queues at the roundabout. Approach Circulating Flow Rates (pc/h) Entry Flow Rates (pc/h) Capacity (pc/h) Volume-to- Capacity Ratio 95th Percentile Queues (veh) SB 0 300 1380 0.22 1 EB 300 700 1016 0.69 6 NB 700 1600 676 2.37 121 Step 13: Maximum Throughput for each O-D Movement To calculate the maximum throughput per movement, first the priority order has to be defined, as shown in Exhibit 38-94. The SB is the Rank 1 leg because it is the upstream approach to the on-ramp. The EB is the Rank 2 and the NB is the Rank 3 approach. The capacity for each approach (calculated in Step 3) is used to determine the maximum throughput for each approach and O-D. In this example, it is assumed that the exit lane towards the on-ramp can reach an exit flow rate of 1,300veh/h. Starting from the approach with Rank 1 (southbound approach), first the maximum throughput for the movement that exits through the eastbound leg (the on-ramp) is calculated as follows: 𝜆 , = 𝑚𝑖𝑛 𝑣 , , 𝑐 , × 𝑝 , 3,600ℎ = 𝑚𝑖𝑛 100,1380 × 100300 , 3,6002.77= 100𝑝𝑐/ℎ where 𝜆 , = maximum throughput for the southbound-left movement (pc/h); 𝑣 , = flow rate for the southbound-left movement (pc/h); 𝑐 , = entry lane capacity for the southbound roundabout approach (pc/h); 𝑝 = percent of demand from SB approach into the on-ramp Exhibit 38-93 Flows and Queues at the Roundabout of Example Problem 4 Exhibit 38-94 Priority Order for the Roundabout of Example Problem 4 Equation 38-18

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Example Problems Chapter 38 System Analyses (Draft) Page 140 Version 1.0 ℎ = departure saturation headway into the on-ramp (s/veh) Since the Rank 3 (NB) approach is the only one with a volume-to-capacity ratio over 1, the conflicting flows and the capacity values calculated above are valid. Then, the calculation of the maximum throughput for the remaining movements of the approach which contribute to the conflicting flows for the downstream approaches is as follows (Equation 38-B26): 𝜆 , = 𝑚𝑖𝑛 𝑣 , , 𝑐 , × 𝑝 = 𝑚𝑖𝑛 200, 1,380 × 200300 = 200𝑝𝑐/ℎ where 𝜆 , = maximum throughput for the southbound-through movement (pc/h); 𝑣 , = flow rate for the southbound-through movement (pc/h); 𝑐 , = entry lane capacity for the southbound roundabout approach (pc/h); 𝑝 = percent of demand from SB approach for through movement The maximum throughput for each approach and O-D is calculated considering the maximum throughput on the on-ramp accounting for higher- rank approaches: 𝜆 , = 𝑚𝑖𝑛 𝑣 , , 𝑐 , × 𝑝 , 3,600ℎ − 𝜆= 𝑚𝑖𝑛 500,1016 × 500700 , 3,6002.77 − 100 = 500 𝑝𝑐/ℎ 𝜆 , = 𝑚𝑖𝑛 𝑣 , , 𝑐 , × 𝑝 = 𝑚𝑖𝑛 100, 1,016 × 100700 = 100 𝑝𝑐/ℎ 𝜆 , = 𝑚𝑖𝑛 𝑣 , , 𝑐 , × 𝑝 , 3,600ℎ − 𝜆 − 𝜆= 𝑚𝑖𝑛 1,500, 678 × 1,5001,600 , 3,6002.77 − 100 − 500 = 634 𝑝𝑐/ℎ The maximum throughput to the on-ramp is lower than the exit capacity (1,300 veh/h), thus the northbound approach flow rate is limited by its own approach capacity. Step 14: Maximum Exit Flow Rate into the On-Ramp The maximum throughput from the roundabout to the on-ramp, 𝜆 , is calculated adding up the maximum throughput on the on-ramp from the higher- rank approaches as follows: 𝜆 , = 𝜆 , + 𝜆 , + 𝜆 , = 100 + 500 + 634 = 1,234 𝑝𝑐/ℎ This total on-ramp demand flow rate is lower than the exit demand (Equation 22-12), which has a rate of: 𝑣 , , = 𝑣 , + 𝑣 , + 𝑣 , = 100 + 500 + 1500 = 2,100 𝑝𝑐/ℎ Equation 38-19

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Example Problems Version 1.0 Page 141 Step 15: On-Ramp Metering Capacity Once the saturation flow rate at the exit leg towards the on-ramp is calculated, given the metering rate, the maximum exit flow rate into the on-ramp is: 𝑐 , = 𝑚𝑖𝑛 𝑐 , 3600ℎ = 𝑚𝑖𝑛 800, 3,6002.77 = 800 𝑝𝑐/ℎ Step 16: On-Ramp Storage Ratio and Queue Spillback Length The on-ramp storage LONR is calculated in passenger cars, considering an average spacing of 25 ft, and given that the total length of the ramp is 1657 ft: 𝐿 = 1,65725 = 66 𝑝𝑐 With the maximum exit flow rate into the on-ramp, the number of vehicles that exit the roundabout through the on-ramp during a 15-minute period analysis is obtained by the difference between the on-ramp throughput λ , and the ramp metering rate cRM: 𝑄 = 𝜆 , − 𝑐4 = 1234 − 8004 = 108 𝑝𝑐 The queue storage ratio RQ is then calculated as the ratio between the expected queue and the on-ramp storage: R = 𝑄𝐿 = 10866 = 1.63 Since RQ > 1.0, there will be queues on each approach due to spillback. Step 17: Queue Spillback Distribution per Approach The number of vehicles queued during the 15-minute time period analysis is: 𝑄 = 𝑄 − 𝐿 = 42 𝑝𝑐 The queues due to the on-ramp spillback are assumed to be distributed proportional to the demand flow rates to the on-ramp per approach and added to the 95th percentile queues estimated for the undersaturated conditions (Equation 22-20): 𝑄 , = 𝑄 × 𝜆 ,𝑣 + 𝑄 , = 42 × 1001234 + 1 = 4 𝑝𝑐 𝑄 , = 𝑄 × 𝜆 ,𝑣 + 𝑄 , = 17 + 6 = 23 𝑝𝑐 𝑄 , = 𝑄 × 𝜆 ,𝑣 + 𝑄 , = 22 + 121 = 142 𝑝𝑐 Step 18: Average Delay per Approach To estimate the average delay per approach, both the control delay and the delay due to the on-ramp capacity limitation must be estimated. The average control delay per approach (Equation 22-17) is:

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Example Problems Chapter 38 System Analyses (Draft) Page 142 Version 1.0 𝑑 = 36001380 + 900(0.25) 0.22 − 1 + (0.22 − 1) + 36001380 × 0.22450(0.25) + 5× 𝑚𝑖𝑛 0.22,1 = 4.44 𝑠/𝑣𝑒ℎ 𝑑 = 14.47 𝑠/𝑣𝑒ℎ 𝑑 = 635.86 𝑝𝑐/ℎ The additional delay due to the on-ramp spillback (Equation 38-B37) is: 𝑑 = 3600800 + 900(0.25) 2100800 − 1 + 2100800 − 1 + 3600800 × 2100800450(0.25) + 5× 𝑚𝑖𝑛 2100800 , 1 𝑑 = 747.94 𝑠/𝑣𝑒ℎ Therefore, the total average delay per approach is: 𝑑 , = 𝑑 + 𝑑 × 1001234 = 65.05 𝑠/𝑣𝑒ℎ 𝑑 . = 𝑑 + 𝑑 × 5001234 = 317.54 𝑠/𝑣𝑒ℎ 𝑑 , = 𝑑 + 𝑑 × 6341234 = 1020.14 𝑠/𝑣𝑒ℎ

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Example Problems Version 1.0 Page 143 5. REFERENCES [1] University of Florida Transportation Institute, "NCHRP 15-57 - Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets," National Cooperative Highway Research Program, Washington DC, 2020. [2] L. Elefteriadou, M. Armstrong, Y. Zheng and G. Riente, "Highway Capacity Manual (HCM) Systems Analysis Methodology," Federal Highway Administration, Washington, DC., 2016. [3] E. Aakre and A. Aakre, "Modeling cooperation in usignalized intersections," in The 6th International Workshop on Agent-based Mobility, Traffic and Transportation Models, Methodologies and Applications (ABMTRANS), 2017. [4] B. Robinson, L. Rodegerdts, W. Scarbrough, W. Kittelson, R. Troutbeck, W. Brilon, L. Bondzio, K. Courage, M. Kyte, J. Mason, A. Flannery, E. Myers and J. Bunker, "Roundabouts: An Informational Guide," Federal Highway Administration, Washington, DC, 2000. [5] L. Rodegerdts and G. Blackwelder, "Analytical Analysis of Pedestrian Effects on Roundabout Exit Capacity," in National Roundabout Conference , 2005. [6] R. Kimber and E. Hollis, "Traffic queues and delays at road junctions," Transport and Road Research Laboratory Report. [7] F. Sasahara, L. Elefteriadou and S. Dong, "Lane-by-Lane Analysis Framework for Conducting Highway Capacity Analyses at Freeway Segments," Transportation Research Record, pp. 523-535, 2018. [8] F. Sasahara, L. Carvalho, T. Chowdhury, Z. Jerome, L. Elefteriadou and A. Skabardonis, "Predicting Lane-by-Lane Flows and Speeds for Freeway Segments," Transportation Research Record, 2020.

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Appendix A: Off-ramp Queue Spillback Analysis Chapter 38 System Analyses (Draft) Page 144 Version 1.0 APPENDIX A: OFF-RAMP QUEUE SPILLBACK ANALYSIS Chapter 10, Freeway Facilities evaluates the performance of each segment individually using standard 15-minute time periods. If any segment within the facility yields a LOS F (v/c > 1), the analysis continues with the oversaturated procedure, using smaller time steps. Similarly, in order to determine whether there is queue spillback from a freeway off-ramp, systems analysis is first conducted using 15-minute time periods. If the analysis shows that any of the ramps are expected to experience queue spillback, the oversaturated procedure must be used to estimate the spillback impacts on the freeway mainline lanes, even if the segment-wide performance is not at an LOS F. The methodology framework for conducting a spillback check at diverge critical points is presented in Exhibit 38-A1 and described in more detail in the remainder of this appendix. CAPACITY CHECKS The procedure first determines whether capacity is exceeded at any of the critical points along the diverge section. Exhibit 38-A1 Off-Ramp Queue Spillback Check Flowchart

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Appendix A: Off-ramp Queue Spillback Analysis Version 1.0 Page 145 Case A: Ramp Roadway Demand at the study diverge ramp (𝑣 , as defined in Chapter 14) is compared against the capacity of the ramp roadway using Exhibit 14-12, replicated in Exhibit 38-A2. Source: HCM 6th Ed. Exhibit 14-12 Case B: Ramp Terminal Demand at the downstream urban street intersection approach is compared against the estimated capacity of the approach. If the ramp terminal comprises two interdependent intersections, the analyst must proceed to Chapter 23, Ramp Terminals and Alternative Intersections. Otherwise, depending on the type of intersection located at the end of the ramp roadway, the respective capacities are obtained from one of the following chapters: Chapter 19, Signalized Intersections; Chapter 20, Two-Way Stop-Control Intersections; Chapter 21, All- Way Stop Control Intersections; Chapter 22, Roundabouts. The ramp terminal control will generate queues even during undersaturated operations. The recommended approach for evaluating queues is as follows: • Signalized Intersections: Although an oversaturated approach is expected to create longer queues that are growing in time and are more likely to spill back into the freeway diverge, it cannot be guaranteed that the queues at an undersaturated approach will not affect the freeway mainline. Therefore, the methodology estimates the queue length and compares it to the available storage length for each analysis period. The arriving demand at the intersection may be constrained by the ramp roadway capacity, and for this reason the ramp roadway capacity check must be conducted first. • Unsignalized Intersections: A LOS better than F at the intersection is not sufficient to guarantee that spillback will not occur. For unsignalized intersections (TWSC, AWSC and roundabouts) the user is advised to proceed to the second step of the check methodology (comparison of queue length). Case C: Downstream Merge Junction Queue spillback may also occur on freeway-to-freeway connectors, and this is a common issue in high-demand urban interchanges. In this case, the bottleneck is located at the downstream merge segment and occurs when the discharge rate into the downstream merge is lower than the off-ramp demand. Consequently, the queue may spill back into the upstream freeway lanes. In this case, the merge capacity of the downstream freeway facility must be modeled using the Chapter 10, Freeway Facilities analysis method. For oversaturated conditions, the methodology estimates the queue length at the on-ramp (as Exhibit 38-A2 Capacity of Ramp Roadways (veh/h)

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Appendix A: Off-ramp Queue Spillback Analysis Chapter 38 System Analyses (Draft) Page 146 Version 1.0 described in Chapter 25, Freeway Facilities Supplemental). This queue length value should be used as input for queue spillback analysis as described below. Similar to urban street intersections, the arriving demand at downstream merge may also be constrained by the ramp roadway capacity. Therefore, the entering ramp demand at the merge is the minimum value of the exiting flow rate at the diverge and the ramp roadway capacity. QUEUE LENGTH ESTIMATION In this stage the procedure estimates the expected queue length for any conditions where demand exceeds capacity. Three cases may occur: Case A: Ramp Roadway Queue forms as a result of demand exceeding capacity at the entrance to the ramp roadway and is expected to affect operations. To determine the extent of the impact, the queue growth during each analysis period is estimated as: 𝑄 = (𝑣 − 𝑐 ) × 𝑓 × 𝑃𝐻𝐹 × 𝑡i where 𝑄 = queue growth during analysis period i (pc); 𝑣 = off‐ramp demand for the period (pc/h); 𝑐 = capacity of the off-ramp roadway (pc/h); 𝑓 = adjustment factor for heavy vehicle presence; 𝑃𝐻𝐹 = peak hour factor; and 𝑡 = analysis period i (h). The ramp queue during the first time period of the analysis must be zero, otherwise the time-space domain boundaries for the analysis need to be re- evaluated. The accumulated queue length at the end of analysis period t is the cumulative value of 𝑄 until 𝑡: 𝑄 = 𝑄 where 𝑄 = accumulated queue length at the end of analysis period 𝑡 (pc); 𝑄 = queue growth during analysis period 𝑖 (pc); and 𝑡 = the current analysis period. The Study Period is defined as “The time interval within a day for which facility performance is evaluated, consisting of one or more consecutive analysis periods” (Chapter 9, Glossary and Symbols). Therefore, the study period t refers to the time boundaries defined in Step A-1 on the Freeway System Methodology, and is composed of N analysis periods, which typically have a 15-min duration. The maximum queue length 𝑄 during the entire analysis period is the maximum value of 𝑄 obtained using Equation 38-A2 and is used as input for the next stage of the spillback check procedure. Equation 38-A1 Equation 38-A2

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Appendix A: Off-ramp Queue Spillback Analysis Version 1.0 Page 147 Case B: Ramp Terminal Spillback occurs when the resulting queues from the downstream ramp terminal intersection exceeds the available ramp storage. For all cases, the procedure estimates the maximum throughput v at the downstream intersection approach. That maximum throughput is limited by the capacity of the ramp roadway, 𝑐 under Case A: 𝑣 = 𝑚𝑖𝑛(𝑣 , 𝑐 ) × 𝑓 × 𝑃𝐻𝐹 where 𝑣 = maximum entering flow rate for the intersection approach (veh/h); 𝑣 = off‐ramp demand for the period (pc/h); 𝑐 = capacity of the off-ramp roadway (pc/h); 𝑓 = adjustment factor for heavy vehicle presence; and 𝑃𝐻𝐹 = peak hour factor; If the off-ramp demand exceeds its capacity, the ramp roadway acts as an upstream bottleneck and limits the demand to the intersection approach. This step ensures that the incoming demand at intersection does not exceed the capacity of the ramp roadway. The calculations of throughput for each intersection type are described below. Signalized Intersections: The methodology of Chapters 19 and 31 evaluates the performance of individual lane groups for a subject approach. It also estimates the back of queue length 𝑄 (Equation 31-149) or a percentile back-of- queue length 𝑄% (Equation 31-150). In some cases, only one high-demand movement at the intersection approach is the bottleneck that results in spillback, yielding an unbalanced lane usage pattern at the ramp. Field observations have shown that urban street intersection failures may occur at one lane group. As drivers position themselves in a specific lane at the ramp to anticipate the downstream signal, the lane usage in the ramp becomes unbalanced, as shown in Exhibit 38-A3. At off-ramps with two or more lanes, the estimated queue lengths for each intersection lane group must be associated with specific ramp lanes. Exhibit 38- A4 illustrates an example of a typical ramp terminal for a two-lane off-ramp. Drivers that desire to take a left turn at the intersection will position themselves in the leftmost lane (Ramp Lane 1), while drivers who intend to turn right will Equation 38-A3 Exhibit 38-A3 Examples of Unbalanced Ramp Lane Usage: (a) Norfolk/VA and (b) Tampa/FL

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Appendix A: Off-ramp Queue Spillback Analysis Chapter 38 System Analyses (Draft) Page 148 Version 1.0 likely choose the rightmost lane (Ramp Lane 2). Analyst judgement is required to define the grouping of intersection lane groups into ramp lanes. By using the results of the queue estimation procedure, the number of queued vehicles in a given ramp lane 𝑛 is estimated as follows: 𝑄 , = 𝑄 , = 𝑄%, × 𝑁 where 𝑄 , = number of queued vehicles in Ramp Lane k, during a 15-min interval; 𝑄 , = number of queued vehicles from Lane Group m associated with ramp lane k, during a 15-min interval; 𝑄 %, = estimated back of queue length (nth percentile), as defined in Equation 31-150 (measured in veh/ln); and 𝑁 , = number of approaching lanes for Lane Group 𝑚. For reference, Equation 31-150 can be seen below: 𝑄% = (𝑄 + 𝑄 )𝑓 % + 𝑄 where 𝑄 = average back-of-queue estimate for lane group 𝑖 (veh/ln); 𝑄% = percentile back-of-queue size (veh/ln); and 𝑓 % = percentile back-of-queue factor. Unsignalized Intersections Each unsignalized intersection type has its own methodology to estimate queue length. The TWSC methodology estimates the 95th percentile queue length for minor movements with Equation 20-68, while the 95th percentile queue length for AWSC approaches is estimated with Equation 21-33. For roundabouts, the 95th percentile queue length for a given lane is provided by Equation 22-20. Regarding intersection lane groups and ramp lanes, the same procedure discussed above for signalized intersections is applied. Case C: Downstream Merge For freeway-to-freeway connectors, the estimated queue length at the downstream merge is estimated using the Chapter 10, Freeway Facilities oversaturated methodology, Equation 25-21. For this specific type of connector, Exhibit 38-A4 Spillback Occurrence by Lane at an Off-Ramp / Weaving Segment Equation 38-A4

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Appendix A: Off-ramp Queue Spillback Analysis Version 1.0 Page 149 the demand difference among ramp lanes can be considered negligible for the purposes of this analysis. QUEUE STORAGE RATIOS AND SPILLBACK CHECKS Next, the procedure estimates the queue storage ratio (𝑅 ) for the ramp roadway queues. If 𝑅 exceeds 1.00, then spillback is expected to occur. The calculations for each of the three possible cases are provided below. Case A: Ramp Roadway If the demand exceeds the capacity of the ramp roadway, this step estimates the queue storage ratio (RQ) for the ramp roadway queues as follows: 𝑅 = 𝐿 𝑄𝐿 𝑁 where 𝑄 = maximum number of vehicles queued on the ramp (veh); 𝐿 = available queue storage (ft/ln); 𝐿 = average vehicle spacing in stationary queue (ft/veh); and 𝑁 = number of lanes in diverge ramp. In Case A, the bottleneck is the entry to the off-ramp, and the ramp itself would not necessarily have a queue present. This case estimates the impacts of the queue as it extends along the deceleration lane. The queue length upstream of the ramp roadway (𝑄 ) is estimated based on the “leftover” demand that is not served by the off-ramp’s available capacity: 𝑄 = (𝑣 − 𝑐 ) × 𝑓 × 𝑃𝐻𝐹 × 𝐿 × 𝑡i where 𝑄 = length of queue beyond ramp storage distance (ft); 𝑣 = demand for the off‐ramp (pc/h); 𝑐 = capacity of the off-ramp (pc/h); 𝑓 = adjustment factor for heavy vehicle presence; 𝑃𝐻𝐹 = peak hour factor; 𝐿 = average vehicle spacing in stationary queue (ft/veh); and 𝑡 = analysis period i (h). Case B: Downstream Intersection When demand exceeds capacity at the intersection, the methodology considers the queues for all lanes from the ramp gore to the stop bar, as well as the channelization at the stop bar. The total storage length 𝐿 for the ramp can be estimated as the sum of lane lengths for a 𝑖 number of different sections (a section is defined as a uniform segment with a homogenous number of lanes) as follows: 𝐿 = 𝑁 × 𝐿 Equation 38-A5 Equation 38-A5 assumes all lanes have the same storage. If that is not the case, the analyst should calculate the total queue storage as a sum of the storage of each lane. Equation 38-A6 Equation 38-A7

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Appendix A: Off-ramp Queue Spillback Analysis Chapter 38 System Analyses (Draft) Page 150 Version 1.0 where 𝑁 = number of lanes in section 𝑖; and 𝐿 = length in section 𝑖 (ft). The individual ramp storage for each of the 𝑘 lanes in the off-ramp, 𝐿 , , can be estimated by assigning the intersection lane groups to ramp lanes, as previously described: 𝐿 , = 𝑁 , × 𝐿 where 𝑁 , = number of lanes in section 𝑖 that are associated to ramp lane 𝑘; and 𝐿 = length in section 𝑖 (ft). Finally, the ramp queue ratio for every ramp lane 𝑘 is obtained as: 𝑅 , = 𝑄 , 𝐿 , where 𝑄 , = queue length associated to ramp lane 𝑘; and 𝐿 , = available ramp storage for ramp lane 𝑘. Next, the total storage length is calculated. The example from Exhibit 38-A4 illustrates a common off-ramp geometry with three different sections from the stop bar to the gore point: • Section 1: 4 lanes with length L1 - two lanes (LG1) are associated with ramp lane 1, and two lanes (LG2) are associated with ramp lane 2 • Section 2: 3 lanes with length L2 - one lane (LG1) is associated with ramp lane 1, and two lanes (LG2) are associated with ramp lane 2 • Section 3: 2 lanes with length L3 - one lane (LG1) is associated with ramp lane 1, and one lane (LG2) is associated with ramp lane 2 Therefore, the available ramp storage LR is calculated as: 𝐿 = (4 × 𝐿 )+ (3 × 𝐿 ) + (2 × 𝐿 ) The ramp storage for each ramp lane is as follows: 𝐿 , = (2 × 𝐿 )+ (1 × 𝐿 )+ (1 × 𝐿 ) 𝐿 , = (2 × 𝐿 )+ (2 × 𝐿 )+ (1 × 𝐿 ) Equation 38-A8 Equation 38-A9

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Appendix A: Off-ramp Queue Spillback Analysis Version 1.0 Page 151 Case C: Downstream Merge The queue storage ratio for freeway-to-freeway connections is estimated as follows: 𝑅 = 𝑄 × 𝐿𝐿 𝑁 where 𝑄 = downstream on-ramp queue length (veh); 𝐿 = available queue storage distance (ft/ln); 𝐿 = average vehicle spacing in stationary queue (ft/veh); and 𝑁 = number of lanes in the diverge ramp. The queue length at the downstream on-ramp 𝑄 is obtained from the Freeway Facility Oversaturated Segment Evaluation procedure (Chapter 25) through the parameter ONRQ (Equation 25-21). The parameter ONRQ(i, t, p) is defined as the “unmet demand that is stored as a queue on the on-ramp roadway at node i during time step t in time interval p (veh)” and is computed at every 15- s time step. The on-ramp queue length at the end of a time period p is obtained by the ONRQ value at the last time step of the time period p. Equation 38-A10

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Appendix A: Off-ramp Queue Spillback Analysis Chapter 38 System Analyses (Draft) Page 152 Version 1.0 EVALUATION OF OFF-RAMP QUEUE SPILLBACK IMPACTS Chapter 14 provides three LOS checks for diverge segments, and failure (LOS F) may occur in any of the following two cases: • the total demand flow rate on the approaching upstream freeway segment exceeds the capacity of the upstream freeway segment; • the off-ramp demand exceeds the capacity of the off-ramp. Chapter 14 also provides a LOS evaluation based on the density of the ramp influence area (Exhibit 14-3), but it only yields a LOS range of A through E; failure due to excessive density is not considered in the methodology. The first case of LOS F is addressed by the Oversaturated Segment Evaluation procedure (HCM Chapter 10) and is not the focus of this methodology. The Queue Spillback Analysis, described in this document targets the second case of LOS F, when the off-ramp demand exceeds the capacity of the off-ramp. The methodology of this appendix also addresses cases of spillback due to insufficient capacity at the ramp terminal downstream of an off-ramp. The methodology described in the first section of this Appendix presents the necessary steps to determine whether spillback from an off-ramp is expected to occur, based on a standard 15-min period analysis. If spillback is expected to occur, this section provides the methodology for evaluating the impact on the freeway performance. The approach is based on the Freeway Facilities Oversaturated Segment Evaluation (HCM Chapter 25), where performance measures are computed at the 15-s time step level. Evaluation of operations along off-ramp segments To evaluate the interaction between the freeway mainline and the downstream off-ramp terminal, the link-node approach used by the HCM Chapter 25 to evaluate oversaturated freeway facilities is expanded, with additional links and nodes to represent the off-ramp segment. As shown in Exhibit 38-A5, the mainline node for the off-ramp (Node 3) is connected to the off-ramp segment, which has a three-node structure: • Ramp node 3.1: interface between the diverge segment (exit lanes) and the upstream end of the ramp proper. The volume that flows through this node is equivalent to the amount of vehicles that are able to leave the freeway; • Ramp node 3.2: interface between the ramp proper and the arterial intersection approach. The volume that flows through this node is equivalent to the amount of vehicles that are able to leave the ramp proper and enter the intersection; • Ramp node 3.3: the last node in the off-ramp represents the discharge capacity of the arterial intersection approach. The volume that flows through this node is equivalent to the amount of vehicles that are able to enter the intersection.

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Appendix A: Off-ramp Queue Spillback Analysis Version 1.0 Page 153 The geometry of an off-ramp is seldom a homogenous road segment, and additional lanes are frequently added closer to the arterial intersection approach. Exhibit 38-A6 illustrates a sample off-ramp, considering its entire length from the deceleration lane to the stop bar at the downstream signalized intersection. The ramp roadway is the uniform ramp segment with a downstream boundary defined by the point where additional lanes are provided. When modeling the off-ramp geometry, the method considers the channelization at the approach as imbalances in the turning movements may cause queues on a subset of lanes. Exhibit 38-A6 shows a typical queue formation resulting from a left-turn movement that operates with insufficient capacity. In this scenario, the approaching left-turn vehicles are positioned in the leftmost lane and spillback may occur even if not all lanes of the approach are oversaturated. The type of ramp terminal is an important input into the analysis. Signalized intersections operate in cyclical patterns, and therefore those have fluctuating queue lengths. For certain demand scenarios, this can result in queues backing up into the freeway and then discharging multiples times within a 15-min time period. Stop-controlled intersections and downstream merge segments (in the case of a freeway-to-freeway connection), on the other hand, have a more uniform discharging rate. For cases other than signalized intersections, off-ramp queues Exhibit 38-A5 Expanded Link-Node Structure to Evaluate the Off-Ramp Segment Exhibit 38-A6 Sample Geometry of an off- Ramp Considering the Arterial Intersection with Heavy Demanded Left-Turn

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Appendix A: Off-ramp Queue Spillback Analysis Chapter 38 System Analyses (Draft) Page 154 Version 1.0 are assumed to develop or discharge linearly based on the relationship between demand and capacity. Evaluation of operations on the freeway mainline: spillback regimes The impact of queue spillback on the freeway mainline varies as a function of the queue length and the lanes blocked. Four spillback regimes are defined [2]: Regime 1 The queue ends within the deceleration lane and does not spill back into the mainline freeway (Exhibit 38-A7 (a)). During undersaturated conditions, the deceleration lane serves as a transition zone between speeds on the mainline (typically 55 – 75 mi/h) and advisory speeds posted along the off-ramp (typically 20 – 50 mi/h). When queues begin to form on the deceleration lane, the available deceleration distance is reduced and speeds along the rightmost lane are affected. Regime 2 The queue of vehicles extends upstream beyond the deceleration lane, but sufficient lateral clearance on the right-hand shoulder allows for additional queue storage. In this case there is no transition zone within the deceleration lane and drivers decelerate and join the back of the queue more abruptly, resulting in turbulence and reduced speeds in the rightmost lane (Exhibit 38-A7 (b)). If no lateral clearance exists immediately upstream of the deceleration lane, Regime 2 conditions are not possible. In some cases, this regime does not occur even if storage is available; this depends on local driver behavior and is site-specific. Regime 3 The queue extends to the rightmost lane of the freeway mainline (Exhibit 38- A7 (c)). This may occur either when there is no shoulder available for additional queue storage, or when drivers choose to queue in the rightmost lane once the deceleration lane is entirely occupied. Non-exiting vehicles on the rightmost lane are delayed or change lanes, which causes increased turbulence and reduced speeds in both rightmost lanes. Regime 4 The queue blocks the rightmost lane, and drivers occasionally or often use the adjacent freeway mainline lane next to the rightmost freeway mainline lane to force their way into the queue, blocking thus an additional lane (Exhibit 38- A7(d)). During this regime, speed and capacity are significantly reduced. The effects of spillback vary from site to site and from time period to time period due to driver behavior and site geometry. Data collection at locations around the US has shown that at some sites drivers block the adjacent lane, while at other sites they do not, regardless of the queue spillback length at the site.

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Appendix A: Off-ramp Queue Spillback Analysis Version 1.0 Page 155 Glossary of variable definitions This glossary defines internal variables used in the methodology for off- ramp queue spillback evaluation. The structure of the variables is similar to the one used in HCM Chapter 25 – Freeway Facilities Supplemental. Facility variables • QIA(i, p): Length of the queue influence area (ft) for segment i during time period p, measured from the back of the queue. Segment variables • KBBL(i,j): background density (pc/mi/ln) at the blocked lanes in segment i, when queue spillback occurs at a downstream segment j • KBUB(i,j): background density (pc/mi/ln) at the unblocked lanes in segment i, when queue spillback occurs at a downstream segment j • LCR(i,t,p): rate of lane change maneuvers in the queue influence area upstream of a queue from an off-ramp, for segment i during time period p and time step t. • LD(i,p): available deceleration lane length (ft) for segment i during time period p. This variable is used to calculate performance measures for ramp segments (Chapter 14 - LD.) • MQ1(i,t,p): mainline queue length of off-ramp unserved vehicles in the rightmost mainline lane, for segment i during time period p in time period t. • MQ2(i,t,p): mainline queue length of off-ramp unserved vehicles in the rightmost mainline lane, for segment i during time period p in time period t. If Regime 4 is not expected to occur, this parameter value is set to zero. • NQ(i): number of blocked lanes if the off-ramp queue backs up into the freeway mainline. This parameter is a function of the prevailing spillback regime at segment i as provided by the analyst. The value for this parameter is an input and can be either 1 (Regime 3 - one blocked lane) or 2 (Regime 4 – two blocked lanes); • OFRFUP(i,t,p): flow that can exit at the closest off-ramp downstream of i during time step t in time period p. Exhibit 38-A7 Off-Ramp Queue Spillback Regimes

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Appendix A: Off-ramp Queue Spillback Analysis Chapter 38 System Analyses (Draft) Page 156 Version 1.0 • OFRLQ(i,t,p): queue length of off-ramp unserved vehicles for diverge segment i during time period p in time period t. • OFRUV(i,t,p): number of off-ramp unserved vehicles for segment i during time period p in time period t. • SBKQ (i,t,p): spillback queue density for segment i during time period p in time period t. • SBLC(i,t,p): number of lane change maneuvers within the Queue Influence Area at node i, during time step t in time period p. • SBLQ(i,t,p): queue length within segment i during time period p in time period t, caused by a downstream off-ramp bottleneck. • SBQS(i,p): total available off-ramp queue storage (ft) for a diverge segment i during time period p, if the subject segment has an off-ramp bottleneck. It is calculated as a function of the available storage lengths in the deceleration lane, shoulder and prevailing spillback regime. • SCEQ(i,N,NQ): equivalent capacity of the unblocked portion of a segment i with N total lanes and NQ blocked lanes. • SL(i,p): available shoulder length (ft) for segment i during time period p. If the value of SL is greater than zero, any off-ramp queues that exceed the deceleration lane will occupy the shoulder before blocking mainline lanes. • TIA(i,p): total influence area (ft) of a queue from an off-ramp bottleneck on segment i, during time period p in time period t. It is calculated as the sum of parameters QIA(i,t,p) and MQ(i,t,p). Node variables • CAFBL(i,t,p): capacity adjustment when one or more lanes of segment i are entirely blocked during time period p in time period t. This is used to calculate friction effects that cause through vehicles to slow down due to the presence of a queue in the rightmost lanes. • CAFUP(i,t,p): capacity adjustment factor of node i during time step t in time period. This capacity adjustment factor affects approaching vehicles within the queue influence area (QIA) upstream of an off-ramp queue. This factor accounts for the turbulence caused by intense lane changing within the queue influence area as vehicles adjust their position when there is a downstream off-ramp queue. • MFBL(i,t,p): mainline flow rate that can cross the blocked portion of node i during time step t in time period p. • MFUB(i,t,p): mainline flow rate that can cross the unblocked portion of node i during time step t in time period p. • MIBL(i,t,p): maximum flow desiring to enter the blocked portion of node i during time step t in time period p. • MIUB(i,t,p): maximum flow desiring to enter the unblocked portion of node i during time step t in time period p.

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Appendix A: Off-ramp Queue Spillback Analysis Version 1.0 Page 157 • MO2BL(i,t,p): maximum number of passenger cars that can enter the blocked portion of segment i, during time step t and time period p, due to the presence of a queue in the downstream ramp segment. • MO2UB(i,t,p): maximum number of passenger cars that can enter the unblocked portion of segment i, during time step t and time period p, due to the presence of a queue in the downstream ramp segment. • NEXTOFR(i): index of the nearest downstream diverge segment relative to subject node i. • OFRDIST(i): distance (ft) from node i to the start of the deceleration lane at the nearest downstream off-ramp. • OFRPCT(i,j): percent of the off-ramp demand at segment j over the mainline entering volume at segment i. Ramp variables • RC(i,p): capacity of the ramp proper (pc/h) during time period p in time period t. Capacity values for the ramp proper are provided in HCM Exhibit 14-12. • RF(i,t,p,k): flow (pc/ts) that can enter the ramp proper at segment i during time period p in time period t and level k. • RI(i,t,p,k): maximum flow (pc/ts) desiring to enter the off-ramp on segment i during time period p in time period t and level k, including queues accumulated from previous time periods. • RKB(i,t,p,k): ramp proper queue density (pc/mi/ln) for segment i during time period p in time period t and level k. • RL(i): length of ramp proper (ft) for segment i. • RN(i): number of ramp lanes for segment i. • RNV(i,t,p,k): maximum number of passenger cars within the ramp of segment i at the end of time step t during time period p and level k. The number of vehicles is initially based on the calculations of Chapters 12, 13, and 14, but, as queues grow and dissipate, input–output analysis updates these values during each time step. • RSTG(i,t,p,k): maximum number of passenger cars that can enter the ramp level k of segment i, during time step t and time period p, due to the presence of a queue in the downstream ramp segment. • RUV(i,t,p,k): number of unserved vehicles at the entrance of the ramp proper of segment i at the end of time step t during time period p and level k. Any values of RUV greater than zero indicate the occurrence of queue spillback from an off-ramp.

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Appendix A: Off-ramp Queue Spillback Analysis Chapter 38 System Analyses (Draft) Page 158 Version 1.0 Intersection (ramp terminal) variables • ID (i,t,p,k): discharge capacity (pc/ts) for intersection movement k in segment i during time period p in time period t. • IF(i,t,p): flow (pc/ts) that can enter the intersection on segment i, level k, during time period p in time period t. • II(i,t,p,k): maximum flow (veh/ts) desiring to enter the intersection on segment i, level k, during time period p in time period t, including queues accumulated from previous time periods. • IL(i,k): storage length of movements at intersection of segment i, for level k (ft) • INV(i,t,p,k): number of vehicles at the intersection of segment i, for level k at the end of time step t during time period p • IO(i,t,p): flow (pc/ts) that can be discharged from the intersection on segment i, level k, during time period p in time period t. • ISTG(i,k): total available storage length at intersection of segment i, for level k (ft) • IUV (i,t,p,k): number of unserved vehicles at the entrance of the intersection of segment i, for level k, at the end of time step t during time period p

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Appendix A: Off-ramp Queue Spillback Analysis Version 1.0 Page 159 Evaluation of operations on the freeway mainline: step-by-step methodology description The methodology for evaluating off-ramp queue spillback is integrated to the core methodology for Freeway Facilities Oversaturated Segment Evaluation (HCM Chapter 25). Exhibit 38-A8 through Exhibit 38-A11 show the core methodology, highlighting additions and changes to address off-ramp queue spillback. Exhibit 38-A8 Freeway Facilities Oversaturated Segment Evaluation Procedure, Adapted for Off-Ramp Queue Spillback Evaluation

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Appendix A: Off-ramp Queue Spillback Analysis Chapter 38 System Analyses (Draft) Page 160 Version 1.0 Exhibit 38-A9 Freeway Facilities Oversaturated Segment Evaluation Procedure, Adapted for Off-Ramp Queue Spillback Evaluation - Continued

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Appendix A: Off-ramp Queue Spillback Analysis Version 1.0 Page 161 Exhibit 38-A10 Freeway Facilities Oversaturated Segment Evaluation Procedure, Adapted for Off-Ramp Queue Spillback Evaluation - Continued

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Appendix A: Off-ramp Queue Spillback Analysis Chapter 38 System Analyses (Draft) Page 162 Version 1.0 Exhibit 38-A11 Freeway Facilities Oversaturated Segment Evaluation Procedure, Adapted for Off-Ramp Queue Spillback Evaluation - Continued

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Appendix A: Off-ramp Queue Spillback Analysis Version 1.0 Page 163 Step 1 - Calculate background density for unblocked lanes on each segment in the case of queue spillback The first step in the Oversaturated Segment Evaluation procedure computes a background density (KB), for each segment at the start of each time period, defined as the expected density when there is no queueing on the segment. It is used as a reference to estimate how many vehicles occupy a given segment at undersaturated conditions, creating an initial reference point for oversaturated analyses. When Regime 3 or Regime 4 occur, there is blockage of one or more freeway lanes in the affected segments, and the through vehicles aim to move to the unblocked lanes. The capacity of the unblocked lanes must be calculated at the initialization step, to be used as a reference value. For a segment i with N lanes, a subset NQ of lanes will be blocked when spillback occurs (NQ = 1 for Regime 3 and NQ = 2 for Regime 4). Therefore, the capacity of the unblocked lanes will be equivalent to a similar segment with (N - NQ) lanes, adjusted for the impact of the blockage using a capacity adjustment factor CAFBL. The values of CAFBL are equal to the Incident Capacity Adjustment Factors of Chapter 11, Freeway Reliability Analysis (Exhibit 11-23), as there are currently no data available to accurately assess the impacts of blockage due to spillback. These values may be conservative, as during incidents capacities may be further reduced due to the presence of police vehicles. Exhibit 38-A12 presents the recommended values for 𝐶𝐴𝐹 . Directional Lanes 1 Blocked Lane 2 Blocked Lanes 2 0.70 N/A 3 0.74 0.51 4 0.77 0.50 5 0.81 0.67 6 0.85 0.75 7 0.88 0.8 8 0.89 0.84 The equivalent capacity SCEQ of segment 𝑖, with 𝑁 lanes and 𝑁𝑄 blocked lanes, is estimated as: 𝑆𝐶𝐸𝑄(𝑖,𝑁,𝑁𝑄) = 𝑆𝐶(𝑖,𝑁 − 𝑁𝑄) × 𝐶𝐴𝐹 Exhibit 38-A13 presents an example of a basic 4-lane directional segment operating in Regime 4 (2 blocked lanes). The capacity of the unblocked lanes will be equivalent to the capacity of a 2-lane basic segment with a capacity adjustment factor CAFBL = 0.50 (4 directional lanes with 2 blocked lanes). For the segment of Exhibit 38-A13, capacity at ideal conditions is: • 𝑐 = 2,400 𝑝𝑐/ℎ (Capacity per lane) or • 𝑆𝐶 = 9,600 𝑝𝑐/ℎ (Segment capacity) Exhibit 38-A12 Capacity Adjustment Factors for Lane Blockage (CAFBL) as a Function of the Number of Directional Lanes and the Number of Blocked Lanes Equation 38-A11 Exhibit 38-A13 Equivalent Segment Capacity for Unblocked Lanes When Lane Blockage Occurs

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Appendix A: Off-ramp Queue Spillback Analysis Chapter 38 System Analyses (Draft) Page 164 Version 1.0 When Regime 4 occurs (2 blocked lanes), the equivalent capacity 𝑆𝐶𝐸𝑄 is obtained as the equivalent capacity of a 2-lane segment multiplied by a corresponding 𝐶𝐴𝐹 of 0.5 (Exhibit 38-A12): 𝑆𝐶𝐸𝑄 = 2 × 2,400 × 0.5 = 2,400 𝑝𝑐/ℎ Next, the unblocked queue density KBUB is calculated. This parameter estimates the queue density of the uncongested portion of a given segment operating under a two-pipe regime due to a queue spillback from a downstream off-ramp. To estimate this value, the method first determines the ratio of the Expected Demand (ED) that will move to the uncongested side of the segment. When queue spillback occurs in a diverge segment j, the parameter OFRPCT(j) is defined as the percent of the off-ramp demand over the mainline entering volume 𝑣 : 𝑂𝐹𝑅𝑃𝐶𝑇(𝑗) = 𝑣 (𝑗)𝑣 (𝑗) For any segment i, upstream of segment j and affected by the off-ramp spillback from segment j, the ratio of vehicles traveling towards the off-ramp at segment i is given by OFRPCT(j), while the ratio of vehicles traveling through in the unblocked lanes is given by (1- OFRPCT(j)). Therefore, the unblocked queue density KBUB at any segment i upstream of an off-ramp spillback in a segment j is given by: 𝐾𝐵𝑈𝐵(𝑖, 𝑗) = 𝐾𝐵 𝐸𝐷(𝑖) × 1 − 𝑂𝐹𝑅𝑃𝐶𝑇(𝑖) , 𝑆𝐶𝐸𝑄(𝑗) where KBUB(I, j)= background density at the unblocked lanes in segment i, when queue spillback occurs at the downstream segment ED(i) = expected demand at segment i , as defined in HCM Chapter 25 𝑂𝐹𝑅𝑃𝐶𝑇(𝑖)= rate of off-ramp flow and mainline flow at segment i KB(v, c) = density at a segment with demand flow rate v and capacity c, as provided by HCM Chapters 12 (basic), 13 (weaving) and 14 (merge and diverge) Step 2 - Initialize the freeway facility These calculations are performed at the start of the analysis, to prepare the flow calculations for the first time step and specify return points, such as background density (KB), for later time steps. This subsection presents the additional parameters required for queue spillback analysis. (a) Number of mainline blocked lanes The number of mainline blocked lanes is stored in the parameter NQ(i) and is determined by the prevalent queue spillback regime as provided by the analyst. If the back of an off-ramp queue is calculated to reach the freeway mainline, two possible spillback regimes may occur: • Regime 3: blockage of one lane in the freeway mainline → Set NQ(i) = 1 • Regime 4: blockage of two lanes in the freeway mainline → Set NQ(i) = 2 Equation 38-A12 Equation 38-A13

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Appendix A: Off-ramp Queue Spillback Analysis Version 1.0 Page 165 The analyst should select one of these two regimes based on prevailing driver behavior at the site and in the vicinity of the site. (b) Shoulder length The available shoulder length must be input by the analyst for queue spillback analysis and is stored under the parameter SL(i) for oversaturated calculations. (c) Deceleration lane length The deceleration lane length is provided by the analyst for the analyses of diverge segments and is stored under the parameter LD(i) for oversaturated calculations. (d) Spillback queue storage length The maximum storage length for off-ramp queues on segment i is computed as a function of the segment length L(i), the deceleration lane length LD(i) and the number of queued lanes NQ(i). Exhibit 38-A14 provides guidance on measuring each of the components required for Regimes 3 and 4. Exhibit 38-A15 illustrates queue length measurements for special cases of queue spillback, when a shoulder is present, but its storage length is not sufficient to accommodate the unserved vehicles. Regime 3A (Exhibit 38-A15(a)) occurs when there is blockage of one mainline lane in addition to the shoulder. Regime 4A (Exhibit 38-A15(b)) occurs when there is blockage of two mainline lanes in addition to the shoulder. Step 2A - Model off-ramp geometry The three-level node structure for the off-ramp shown in Exhibit 38-A5 must be modeled to reflect the geometric characteristics of the site, as illustrated in Exhibit 38-A14 Maximum Off-Ramp Queue Storage Length at Diverge Segments with Occurrence of (a) Regime 3 Queue Spillback And (b) Regime 4 Queue Spillback, when no Shoulder is Available Exhibit 38-A15 Maximum Off-Ramp Queue Storage Length at Diverge Segments with Occurrence of (A) Regime 3a Queue Spillback and (B) Regime 4a Queue Spillback, when Shoulder is Available

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Appendix A: Off-ramp Queue Spillback Analysis Chapter 38 System Analyses (Draft) Page 166 Version 1.0 Exhibit 38-A6. This is accomplished by setting a “branch” structure, where a node can connect to multiple links downstream. If a node is connected to more than one downstream link, the flow through the node will be constrained by the downstream link with the highest queue storage ratio. The ramp structure must be modeled from the downstream end towards the upstream end: • For the most downstream location provide one node for each lane group or movement at the approach; • For the next upstream change in alignment provide one node for each ramp proper lane connecting to a distinct lane group downstream. The data structure used in the methodology computations should be adjusted according to this “branch” structure. Most parameters in the Oversaturated Segment Evaluation methodology are computed as a 3- dimensional array (i, t, p), where i is the segment index in the freeway facility and t refers to a specific time step within a given time period p. In the case of two-lane ramps that need to be evaluated independently, a new dimension k will be added to the ramp parameter arrays to account for the specific lane under analysis. Lanes are numbered right from left; therefore, k=1 stands for the rightmost lane and k=2 for the leftmost lane of the ramp. Example 1 – In this example, there is only one lane connecting the freeway exit to the entry leg of the downstream roundabout. Therefore, only one node is required at each location (single branch structure, with k=1 in all nodes), as shown in Exhibit 38-A16. Example 2 – A single-lane ramp connects with a stop-controlled T- intersection ramp terminal (Exhibit 38-A17). The intersection node is comprised of two branches (k=2), while the ramp proper has only one lane (k=1). Each movement of the intersection (LT and RT) is represented by a node, and when there is a queue on either one of the movements, the one with the longest length will constrain the flow of vehicles from the ramp proper. Exhibit 38-A16 Node Structure for Example 1

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Appendix A: Off-ramp Queue Spillback Analysis Version 1.0 Page 167 Example 3 – A two-lane ramp connects with a signalized intersection ramp terminal (Exhibit 38-A18). Both the intersection and the ramp proper nodes comprise of two branches each (k=2). At the downstream end, one node is defined for each lane group at the intersection (LT and RT). According to the ramp geometry, left-turning drivers will be positioned along ramp lane 2, while right-turning drivers will be located along ramp lane 1. Therefore, two nodes are also defined at the upstream location. If the queue storage ratio for any of the ramp lanes reaches 1, vehicle flow in the respective upstream node will be constrained, resulting in queue spillback on the freeway mainline. Step 2B - Determine spillback regime for each diverge segment Field observations [1] have shown that locations that experience recurring queue spillback always have the same type of spillback regime when the queue extends beyond the deceleration lane (Regime 3 or 4). Regime 4 occurs often at ramp junctions with a lane drop. At these locations, the exiting traffic can access the off-ramp with a single lane change. Therefore, drivers are more likely to wait until they are closer to the exit to change lanes, blocking the adjacent through lane. However, not all lane drop exits experience a Regime 4 queue spillback. Regime 4 occurs more frequently in locations with more aggressive driver Exhibit 38-A17 Node Structure for Example 2 Exhibit 38-A18 Node Structure for Example 3

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Appendix A: Off-ramp Queue Spillback Analysis Chapter 38 System Analyses (Draft) Page 168 Version 1.0 behavior. Local information and driver behavior should be taken into consideration in determining the prevailing regime at a given site. For operational analyses of existing locations, it is recommended that the analyst provides the expected spillback regime based on observed field conditions. For planning level purposes where no field data is available, Exhibit 38-A19 provides the expected queue spillback regime as a function of the number of exiting lanes and driver aggressiveness. Ramp Geometry Driver Aggressiveness Low Medium High Diverge Regime 3 Regime 3 Regime 3 Lane Drop Regime 3 Regime 4 Regime 4 Step 2C - Determine queue influence area (QIA) Chapter 14 provides the following definition for the ramp influence area for off-ramps operating under steady conditions: “For right-hand off-ramps, the ramp influence area includes the deceleration lane(s) and Lanes 1 and 2 of the freeway for a distance of 1,500 ft upstream of the diverge point.” When there is queue spillback in one or more freeway lanes, drivers would react to the presence of the queue further upstream resulting in increasing lane changes and additional turbulence upstream of the ramp influence area (Exhibit 38-A20). In this step the methodology estimates the length of the Queue Influence Area (QIA), measured upstream from the back of queue. The length of Queue Influence Area is based on time needed for arriving drivers to react to partial lane blockage and adjust their speeds and positions. Research [1] has shown that traffic speeds upstream of the back of queue are negatively affected at a headway distance of 10.95s. Therefore, the influence area represents the distance traversed by a vehicle during 10.95s with a speed consistent with the traffic stream. The length of the QIA is estimated as a function of the segment free-flow speed (FFS), as shown in Exhibit 38-A21. The exact location of the QIA varies as a function of the queue length. The QIA values are shorter than the ramp influence distance of 1,500 ft. However, the two concepts are very different and are used differently in analyzing ramp operations: the ramp influence area is used to analyze undersaturated conditions, while the QIA is used to analyze oversaturated conditions. Since drivers can only detect a downstream queue visually, they have shorter times to react when compared to the presence of Exhibit 38-A19 Default Spillback Regimes as a Function of Ramp Geometry and Driver Aggressiveness Exhibit 38-A20 Queue Influence Area with Increased Turbulence

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Appendix A: Off-ramp Queue Spillback Analysis Version 1.0 Page 169 undersaturated off-ramps, where signing and navigation information is provided in advance and allows drivers to adjust their position earlier. Segment FFS (mi/h) Queue Influence Area (ft) 50 810 55 900 60 980 65 1060 70 1140 75 1220 When Regimes 3 or 4 occur and lane blockage is present in the mainline, the estimated QIA is added to the queue length to determine the extent of spillback effects. If an upstream node is located within the combined length of the queue and QIA, capacity adjustment factors must be applied to account for the spillback effects. Step 2D - Determine ramp proper capacity and speed The first off-ramp parameter to be determined is its capacity (RC), defined as function of the ramp free-flow speed and is obtained from HCM Exhibit 14-12, replicated below in Exhibit 38-A22. The RC is compared to the off-ramp demand, and if the demand-to-capacity ratio is greater than 1.0 then spillback is expected to occur. Determining the speed-flow relationship at the ramp proper is also critical for the analysis. Ramp speeds can be obtained through the following equation: 𝑆 = 1 − 0.109 × 𝑣1000 × 𝑆 where 𝑆 = ramp speed (mi/h); 𝑣 = ramp demand flow rate (pc/h) 𝑆 = ramp free-flow speed (mi/h) The speed-flow relationship for ramps is linear and speed decreases with higher ramp flows, as presented in Exhibit 38-A23. The maximum allowed values of vR are bounded by ramp capacity, consistent with guidance provided by Chapter 14 – Merge and Diverge segments (Exhibit 14-12). Exhibit 38-A21 Queue Influence Area as Function of the Segment FFS Exhibit 38-A22 Capacity of Ramp Proper for Off-Ramps Equation 38-A14

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Appendix A: Off-ramp Queue Spillback Analysis Chapter 38 System Analyses (Draft) Page 170 Version 1.0 The ramp density at capacity (RKC) is not necessarily equal to 45 pc/mi/ln as assumed for freeway mainline lanes. This parameter is required to evaluate the queue density at the ramp proper when operating in oversaturated conditions. The ramp density at capacity can be found by dividing the capacity by speed. Exhibit 38-A24 summarizes the values of RKC as a function of the Ramp FFS. Ramp FFS (mi/h) Capacity (pc/h/ln) RKC (pc/mi/ln) 55 2200 40.0 50 2100 42.0 45 2100 46.7 40 2000 50.0 35 2000 57.1 30 1900 63.3 25 1900 76.0 20 1900 90.0 15 1800 120 Step 2E - Determine intersection storage capacity The storage capacity at the intersection, ISTG, is obtained as the sum of the available storage of every lane group, multiplied by the number of lanes. If the off-ramp has multiple branches at the intersection (k > 1), then the available storage capacity must be computed for each branch k individually. This distinction is necessary to evaluate cases with unbalanced demands at the intersection, when the queues developed in one oversaturated movement may extend upstream and block the throughput of all movements at the off-ramp. ISTG is estimated as: 𝐼𝑆𝑇𝐺(𝑖, 𝑝, 𝑘) = 𝑁𝑚 𝑥 𝐿𝑚 𝑀𝑚 𝑥 𝐿 where Nm = number of lanes serving movement m at the intersection Lm = storage length for movement m at the intersection (ft) N = number of movements at the approach Lh = average vehicle spacing in stationary queue (ft/veh) (HCM Equation 31-155) Exhibit 38-A23 Speed-flow Curves for Freeway Ramps Exhibit 38-A24 Ramp Density at Capacity as a Function of Ramp FFS Equation 38-A15

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Appendix A: Off-ramp Queue Spillback Analysis Version 1.0 Page 171 Step 2F - Determine initial number of vehicles at the off-ramp The computation of the number of vehicles in the facility at every time step is critical for deriving performance measures of oversaturated freeway facilities. Similar to the Freeway Facilities Oversaturated Segment Evaluation methodology, the estimation of the number of vehicles in the ramp during oversaturated conditions requires a reference value for undersaturated conditions to be computed during the initialization steps. First, the initial number of vehicles on the ramp during undersaturated conditions is determined as an initial reference point. The density at an off-ramp segment can be obtained by dividing the off-ramp flow rate (vR) by its speed (SR, obtained through Equation 38-A15). Then, the total number of vehicles is obtained by multiplying the ramp density by the ramp length (RL) and number of lanes (RN), as follows 𝑅𝑁𝑉(𝑖, 0,0, 𝑘) = 𝑣 ,𝑆 𝑥 𝑅𝐿(𝑖, 𝑘)𝑥 𝑅𝑁(𝑖, 𝑘) where 𝑅𝑁𝑉(𝑖, 0,0, 𝑘)) = number of vehicles in the ramp proper at the initialization step IN(i,k) = off-ramp demand at the first time period in the analysis (pc/h) 𝑄 = off-ramp free-flow speed (mi/h) The initial number of vehicles in the intersection approach are also determined as an initial reference point, as follows: 𝐼𝑁𝑉(𝑖, 0,𝑝, 𝑘) = 𝐼𝑁(𝑖, 𝑘) 𝑥 𝑄 where 𝐼𝑁𝑉(𝑖, 𝑡, 𝑝,𝑘)=number of vehicles at the intersection of segment 𝑖, for level 𝑘 at the end of time step 𝑡 during time period 𝑝 𝐼𝑁(𝑖, 𝑘) = number of lanes serving the subject approach 𝑘; and 𝑄 = back-of-queue length for the subject approach 𝑘 (veh). The back-of-queue length 𝑄 is estimated using equations corresponding to the intersection type at the ramp terminal (Exhibit 38-A25). Intersection type Reference Equation Signalized 31-149 TWSC 20-68 AWSC 21-33 Roundabout 22-20 At signalized intersections, due to their cyclic nature, queues form and discharge at different times for different movements. Therefore, a reference point within the cycle must be selected as a starting point in the methodology. The methodology assumes pretimed signalization or converts actuated control to the equivalent pretimed pattern. Typical signalized intersections at ramp terminals have the off-ramp approach as the minor movement, with a start of green on the Equation 38-A16 Exhibit 38-A25 Reference HCM Equations for Back-of-Queue Length Estimation

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Appendix A: Off-ramp Queue Spillback Analysis Chapter 38 System Analyses (Draft) Page 172 Version 1.0 right side of the barrier (Exhibit 38-A26). It is recommended setting a reference point at the onset of green for phases 3 and 7, as the back-of-queue lengths at this time can be easily estimated using the methodology of Section 4, HCM Chapter 31. Step 2G - Determine the capacity of the downstream terminal The methodology to evaluate the capacity of the terminal is specific to each intersection type and relies mostly on the respective HCM chapters (19 through 23). Signalized Intersections For a signalized intersection approach, the capacity for each movement at each time step is a function of the signal phase sequence and the capacities of the individual movements at the intersection. Exhibit 38-A27 illustrates a sample signalized intersection approach from an off-ramp, with two lane groups: left- turn (Phase 3) and right turn (Phase 8). Exhibit 38-A26 Selection of a Cycle Reference Point to Determine the Initial Number of Vehicles Within the Approach

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Appendix A: Off-ramp Queue Spillback Analysis Version 1.0 Page 173 Input Parameters The required parameters to evaluate the capacity of a ramp terminal capacity are generally the same required for standard signalized intersection analyses, as listed in Exhibit 19-11. Arrival type: Chapter 19 of the HCM (Exhibit 19-14) provides guidelines for selecting the appropriate Arrival Types based on the characteristics of arterial operations, such as quality of progression and coordination. For an off-ramp approach to the intersection, vehicles arrivals can be considered random. Therefore, Arrival Type 3 (random arrivals) is recommended to analyze the off- ramp approach at a signalized ramp terminal. Phase duration and effective green time: The duration of each phase at the signal can be fixed (pre-timed control), or variable (semi-actuated or actuated control). For the former case, phase duration is known. For the latter, an average phase duration is estimated as described in Section 2 of HCM Chapter 31 – Signalized Intersections Supplemental. The effective green time g for each phase can then be computed according to HCM Equation 19-3: 𝑔 = 𝐷 − 𝑙 − 𝑙 where 𝑔 = effective green time (s) 𝐷 = phase duration (s) 𝑙 = start-up lost time = 2.0 (s) 𝑙 = clearance lost time = 𝑌 + 𝑅 – 𝑒 (s) Converting approach capacity from time periods to time steps The standard signalized intersection analysis is performed in 15-min periods, while the queue spillback evaluation requires a 15-second approach compatible with the Freeway Facilities oversaturated methodology. Therefore, an adjustment is necessary to calculate the capacities of each movement in 15- second intervals. The cycle length C can be divided into n time steps, with a duration of 15 s each seen in Exhibit 38-A28. If an integer number of time steps is not obtained, Exhibit 38-A27 Sample Signalized Intersection Approach from an Off-Ramp Equation 38-A17

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Appendix A: Off-ramp Queue Spillback Analysis Chapter 38 System Analyses (Draft) Page 174 Version 1.0 the difference is included in the first time-step of the next cycle. Then, green times for each time step from 1 to n are computed. This procedure must be repeated for every time step within the 15 minutes time period, resulting in a total of 900/15 = 60 time-steps. The capacity ID for each approach and for each time step, is then obtained by multiplying its respective green time by its capacity, as shown: 𝐼𝐷(𝑖, 𝑡,𝑝, 𝑘) = 𝑁 𝑠 𝐺𝑇(𝑖, 𝑡,𝑝,𝑚) × 𝑓 Where 𝑁 = number of lanes serving movement k 𝑠 = saturation flow rate for movement k (veh/h/ln) 𝐺𝑇(𝑖, 𝑡,𝑝,𝑚) = green time for each movement m (s) The green time parameter GT(i,t,p,m) measures the available green time for a given intersection movement m, downstream of a freeway segment i, in time step t and time period p. It can range from 0 (when the movement has red through the entire time step length) to 15 (movement has green through the entire time step length). The heavy vehicle factor fHV needs to be applied to the equation for intersection discharge to make the units used in intersection capacity (veh/h) consistent with the flow rates used in uninterrupted flow methods (pc/h). Step 2H - Determine reference index for next downstream off-ramp This step is essential for building the computational engine for this procedure, but it is not important for understanding the overall methodology. The Freeway Systems methodology uses the parameter OFRF(i,t,p) to store the off-ramp flow rate at diverge segment i. When a segment upstream of an off- ramp is evaluated for queue spillback, the off-ramp flow rate must be referenced in order to estimate the incoming flows for the blocked and non-blocked lanes. Therefore, a new variable NEXTOFR(i), is introduced to reference the index of the closest diverge segment downstream of segment i. This is illustrated in Exhibit 38-A28 Conversion of Green Times to Time Steps Equation 38-A18

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Appendix A: Off-ramp Queue Spillback Analysis Version 1.0 Page 175 Exhibit 38-A29, where the node (i+2) represents a diverge segment with an off- ramp flow 𝑣 . When the queue extends upstream to node i, the approaching flow 𝑣 is segregated into two groups: the exiting vehicles that will join the back of the queue, and the through vehicles that will use the non-blocked lanes. For nodes 𝑖 and 𝑖 + 1, the closest downstream off-ramp is located at node (i+2), therefore the following parameter is computed: 𝑁𝐸𝑋𝑇𝑂𝐹𝑅(𝑖) = 𝑖 + 2 The use of the parameter NEXTOFR facilitates referencing diverge segments downstream of a given segment 𝑖 and will be used for the spillback analysis procedure described over the next section. Step 9A - Perform spillback analysis This is a new step in the Freeway Facilities Analysis method (Exhibit 38-A8). In this step, spillback effects in a diverge segment are determined after the off- ramp flow OFRF is determined (steps 7/8). (a) Determine ramp input, RI The ramp input, RI, represents demand, and it is the number of vehicles that wish to travel through the ramp proper node during a given time step. It takes into account the off-ramp demand, OFRF (as defined in the Freeway Facilities Oversaturated methodology) and the number of off-ramp unserved vehicles from the previous time step, RUV. The OFRF parameter already takes into consideration any bottleneck segments upstream of the diverge that may meter the off-ramp demand (HCM Equations 25-23 through 25-25). The RI is calculated as: 𝑅𝐼(𝑖, 𝑡,𝑝) = 𝑂𝐹𝑅𝐹(𝑖, 𝑡,𝑝) + 𝑅𝑈𝑉(𝑖, 𝑡 − 1,𝑝) where OFRF(I, t, p) = flow that can exit the off-ramp 𝑖 during time step 𝑡 in time period 𝑝 RUV(I, t, p, k)= number of unserved vehicles at the off-ramp exit at segment 𝑖, during time step 𝑡 in time period 𝑝 Calculate flow to the off-ramp and number of unserved vehicles The ramp maximum flow RF represents capacity, i.e., the number of vehicles that are able to enter the ramp proper by crossing the boundary node between the diverge segment and the ramp proper. It is calculated as the minimum of three variables: RI, RC and RSTG. Exhibit 38-A29 Illustration of Mainline Flow Rate Split into Blocked and Unblocked Lanes Equation 38-A19

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Appendix A: Off-ramp Queue Spillback Analysis Chapter 38 System Analyses (Draft) Page 176 Version 1.0 𝑅𝐹(𝑖, 𝑡,𝑝) = 𝑚𝑖𝑛 𝑅𝐼(𝑖, 𝑡,𝑝, 𝑘),𝑅𝐶(𝑖, 𝑘),𝑅𝑆𝑇𝐺(𝑖, 𝑡,𝑝, 𝑘) The parameters RI and RC have been previously defined. The parameter RSTG represents the maximum number of vehicles that can enter the ramp due to a queue inside the ramp proper. The calculations follow the same approach taken by the Mainline Output 2 (MO2) parameter (Equation 25-11). It starts by calculating the maximum number of vehicles allowed on the ramp at a given ramp queue density RKQ: 𝑅𝐾𝑄(𝑖, 𝑡,𝑝, 𝑘) = 𝐾𝐽– (𝐾𝐽 – 𝑅𝐾𝐶)𝑥 𝑅𝐹(𝑖, 𝑡 − 1,𝑝)𝑅𝐶(𝑖, 𝑡,𝑝) The calculation of RKQ takes an approach similar to the calculation of the mainline queue density KQ (Equation 25-10), with the following remarks on the inputs: • The jam density parameter KJ uses the same value adopted for the mainline calculations • The ramp density at capacity RKC is determined based on the ramp FFS (Exhibit 38-A24) • The parameters SF (segment flow) and SC (segment capacity) from Equation 25-10 are replaced with RF (ramp flow, previously defined) and RC (ramp capacity, previously defined) The maximum ramp storage constraint RSTG is then calculated using an approach similar to the Mainline Output 2 (MO2) parameter from the Oversaturated segment evaluation procedure. This constraint limits the number of vehicles able to enter the off-ramp due to the presence of a queue within the ramp proper. RTTG is calculated as: 𝑅𝑆𝑇𝐺(𝑖, 𝑡,𝑝, 𝑘) = 𝑅𝐹(𝑖, 𝑡 − 1,𝑝, 𝑘) + 𝑅𝐾𝑄(𝑖, 𝑡,𝑝, 𝑘)𝑥 𝑅𝐿(𝑘)𝑥 𝑅𝑁(𝑘)− 𝑅𝑁𝑉(𝑖, 𝑡 − 1,𝑝, 𝑘) Next, the number of unserved vehicles at the ramp entrance RUV is calculated. For each time step, the number of unserved vehicles is computed as the value from the previous time step, plus the difference between demand (RI) and throughput (RF) at the ramp node. RUV is calculated as: 𝑅𝑈𝑉(𝑖, 𝑡,𝑝, 𝑘) = 𝑅𝑈𝑉(𝑖, 𝑡 − 1,𝑝 , 𝑘)+ 𝑅𝐼(𝑖, 𝑡,𝑝, 𝑘)− 𝑅𝐹(𝑖, 𝑡,𝑝, 𝑘) where K = number of different branches at the intersection If there are multiple branches k at the ramp proper (two lane ramps), RI and RF are compared for each branch k to obtain RUV for each branch k. The total number of unserved vehicles at the ramp RUV(i,t,p) is then obtained as the sum of RUV for each lane: 𝑅𝑈𝑉(𝑖, 𝑡,𝑝) = 𝑅𝑈𝑉(𝑖, 𝑡,𝑝, 𝑘) (b) Calculate approach input, II The intersection approach input II is the number of vehicles that wish to travel through the intersection node during a given time step, i.e., its demand. It Equation 38-A20 Equation 38-A21 Equation 38-A22 Equation 38-A23 Equation 38-A24

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Appendix A: Off-ramp Queue Spillback Analysis Version 1.0 Page 177 takes into account the off-ramp flow RF and the number of unserved vehicles on the approach from the previous time step IUV. II is calculated as: 𝐼𝐼(𝑖, 𝑡,𝑝, 𝑘) = 𝑅𝐹(𝑖, 𝑡,𝑝, 𝑘)+ 𝐼𝑈𝑉(𝑖, 𝑡,𝑝, 𝑘) (c) Calculate maximum ramp output The maximum allowable ramp output (RO) is calculated as a function of the available storage space within the intersection approach, minus the number of vehicles present at the previous time step and the number of vehicles discharged (IDC) in the present time period. RO is estimated as: 𝑅𝑂(𝑖, 𝑡,𝑝, 𝑘) = 𝐼𝑆𝑇𝐺(𝑖, 𝑘)− 𝐼𝑉(𝑖, 𝑡 − 1,𝑝, 𝑘) + 𝐼𝐷𝐶(𝑖, 𝑡,𝑝, 𝑘) (d) Calculate intersection approach flow and number of unserved vehicles The intersection flow IF represents the number of vehicles that are able to cross the boundary node between the ramp proper and the intersection (i.e., its capacity). It is computed as the minimum value between the number of vehicles that wish to enter the intersection and the maximum number of vehicles allowed to enter the intersection due to the available queue storage in the intersection: 𝐼𝐹(𝑖, 𝑡,𝑝, 𝑘) = 𝑚𝑖𝑛 𝐼𝐼(𝑖, 𝑡,𝑝, 𝑘),𝑅𝑂(𝑖, 𝑡,𝑝, 𝑘) If the number of vehicles trying to enter the intersection exceeds the amount of vehicles allowed to enter the intersection, then the number of total unserved vehicles must be computed and considered in the intersection input II during the next time period: 𝐼𝑈𝑉(𝑖, 𝑡,𝑝, 𝑘) = 𝐼𝑈𝑉(𝑖, 𝑡 − 1,𝑝, 𝑘)+ 𝐼𝐼(𝑖, 𝑡,𝑝, 𝑘)− 𝑅𝑂(𝑖, 𝑡,𝑝, 𝑘) (e) Update number of vehicles at the ramp terminal intersection The number of vehicles at the intersection, NV, is updated every time step based on the NV from the previous time step, plus the number of vehicles that enter the intersection approach minus the number of vehicles that are discharged. The maximum allowable total number of vehicles is function of the available storage at the intersection, ISTG. NV is calculated as: 𝐼𝑁𝑉(𝑖, 𝑡,𝑝) = 𝐼𝑁𝑉(𝑖, 𝑡 − 1,𝑝) + 𝐼𝐹(𝑖, 𝑡,𝑝, 𝑘) − 𝐼𝐷𝐶(𝑖, 𝑡,𝑝, 𝑘) (f) Calculate number of unserved vehicles at the off-ramp The number of unserved vehicles, OFRUV, at the entrance of the ramp proper is updated every time step as the difference between the number of vehicles that wish to enter the ramp proper (RI) and the flow through the ramp node (RF): 𝑂𝐹𝑅𝑈𝑉(𝑖, 𝑡,𝑝) = 𝑅𝐼(𝑖, 𝑡,𝑝) − 𝑅𝐹(𝑖, 𝑡,𝑝) (g) Calculate intersection approach output The intersection flow, IO, represents the actual number of vehicles discharging from the intersection approach. It is computed as the minimum value between the intersection discharge capacity and the sum of number of vehicles present in the intersection and the intersection input demand: Equation 38-A25 Equation 38-A26 Equation 38-A27 Equation 38-A28 Equation 38-A29 Equation 38-A30 Equation 38-A31

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Appendix A: Off-ramp Queue Spillback Analysis Chapter 38 System Analyses (Draft) Page 178 Version 1.0 𝐼𝑂(𝑖, 𝑡,𝑝, 𝑘) = 𝑚𝑖𝑛 𝐼𝐷𝐶(𝑖, 𝑡,𝑝, 𝑘), 𝐼𝑉(𝑖, 𝑡 − 1,𝑝, 𝑘) + 𝐼𝐼(𝑖, 𝑡,𝑝, 𝑘) (h) Update number of vehicles at the ramp proper The number of vehicles at the ramp proper, RNV, at the end of each time step is calculated based on the number of vehicles from the previous time step plus the number of vehicles that entered the ramp minus the number of vehicles that left the ramp: 𝑅𝑁𝑉(𝑖, 𝑡,𝑝, 𝑘) = 𝑅𝑁𝑉(𝑖, 𝑡 − 1,𝑝, 𝑘)+ 𝑅𝐹(𝑖, 𝑡,𝑝, 𝑘)− 𝐼𝐹(𝑖, 𝑡,𝑝, 𝑘) (i) Determine the back-of-queue length and spillback regime Field observations have shown that off-ramp queues blocking mainline lanes are typically not stationary. These queues usually consist of a platoon of closely spaced vehicles moving at very low speeds (< 15mph). The spacing between vehicles is also longer than the average vehicle spacing in stationary queues, represented in the HCM by Lh (Equation 31-155). Therefore, the density of the spillback queue follows the queue density at the ramp (RKQ, as previously defined), which allows the estimation of the queue length OFRLQ. This parameter estimates the total queue length upstream of the off-ramp if all unserved vehicles formed a single queue: 𝑂𝐹𝑅𝐿𝑄(𝑖, 𝑡,𝑝) = 𝑂𝐹𝑅𝑈𝑉(𝑖, 𝑡,𝑝)𝑅𝐾𝑄 (𝑖, 𝑡,𝑝) Next, the mainline queue length, SBLQ, is compared to the available spillback queue storage for the prevalent spillback regime for the given time step, as follows: If OFRLQ = 0 → Regime 0 If 0 < OFRLQ ≤ LD → Regime 1 If SBLQ > LD : If SL(i,p) > 0: If OFRLQ < (LD + SL) → Regime 2 Else: Regime 3 / 4 Finally, the queue length in the mainline lanes MQ1 (lane 1) and MQ2 (lane 2) are obtained as a function of the expected spillback regime. The total queue length OFRLQ minus the available storage lengths at the deceleration lane and shoulder computes the queue length that the associated blockage. If the site experiences Regime 3: 𝑀𝑄1(𝑖, 𝑡,𝑝, 𝑘) = 𝑂𝐹𝑅𝐿𝑄(𝑖, 𝑡,𝑝, 𝑘)− 𝐿𝐷(𝑖)– 𝑆𝐿(𝑖) 𝑀𝑄2(𝑖, 𝑡,𝑝, 𝑘) = 0 If the site experiences Regime 4: 𝑀𝑄1(𝑖, 𝑡,𝑝) = 𝑀𝑄2(𝑖, 𝑡,𝑝) = [𝑂𝐹𝑅𝐿𝑄(𝑖, 𝑡,𝑝) − 𝐿𝐷(𝑖)– 𝑆𝐿(𝑖) ] / 2 (a) Check for impacts on upstream nodes The freeway nodes upstream of a congested off-ramp may be affected by spillback as queues grow. When this occurs, the methodology calculates the Equation 38-A32 Equation 38-A33 Equation 38-A34 Equation 38-A35

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Appendix A: Off-ramp Queue Spillback Analysis Version 1.0 Page 179 length of the queue in the upstream segment. The length of the queue within the subject segment will then be used to evaluate whether the capacity of any upstream node is affected by the queue. For upstream segments that may be affected by spillback, the queue length within the segment (measured from its downstream end) must be computed and stored in the parameter SBLQ. This check is performed for every node upstream of a congested off-ramp (Exhibit 38-A30). When queue spillback occurs in a downstream off-ramp, the length of the mainline queue measured from the start of the deceleration lane is known from the previous step. If a given segment has any queues blocking one or more lanes, three possible scenarios may occur at the node (Exhibit 38-A31): 1. Lane blockage: Queues extend through the entire segment and reach the upstream node, causing the subject node to operate in a two-pipe regime. The blocked lanes operate in a congested regime, with their capacity constrained by the off-ramp capacity. The unblocked lanes, on the other hand, operate at uncongested conditions with a small reduction in capacity due to the friction of through vehicles passing along congested lanes. For the through lanes, an adjustment factor CAFBL is applied. This condition occurs when the Spillback Queue length SBLQ(i) is equal or greater than the Segment Length L(i). Exhibit 38-A30 Procedure for Evaluating the Impact of Queue Spillback on Upstream Nodes and Determination of the Queue Length within Upstream Segments

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Appendix A: Off-ramp Queue Spillback Analysis Chapter 38 System Analyses (Draft) Page 180 Version 1.0 2. Increased turbulence: Queues extend partially through the segment and the upstream node is located within the Queue Influence Area (QIA). This region is characterized by intense turbulence as vehicles quickly perform lane changes to adjust their position reacting to the queue ahead, and all lanes in node i have their capacity reduced by an adjustment factor CAFUP. This condition occurs when the sum of the Spillback Queue length SBLQ(i) and the Queue Influence Area QIA(i) is equal or greater than the segment length L(i). 3. No effect: Queues extend partially through the segment, but the upstream node is located within the Queue Influence Area (QIA). For this condition, no capacity adjustment factors are applied to the node i. This condition occurs when the sum of the Spillback Queue length SBLQ(i) and the Queue Influence Area QIA(i) is smaller than the segment length L(i). (b) Calculate capacity adjustment factors Based on how upstream nodes are affected as described under Step 6B (Lane Blockage, Increased Turbulence or No Effect), the corresponding impacts on capacity are computed in this step. This section describes the calculations of capacity adjustments depending on how upstream nodes are affected. Lane blockage adjustment factor When one or more lanes are blocked, the subject node is analyzed as a two- pipe operation, with a congested flow in one or more lanes of the ramp side and uncongested flow in the remaining lanes. The capacity of these lanes is equal to the number of queued vehicles discharged at the downstream segment. The flow rate attempting to cross the node through the congested lanes is equal to the off-ramp flow rate (OFRF) at the closest downstream off-ramp. Increased turbulence adjustment factor When a node falls under the Increased Turbulence case (Exhibit 38-A31b), all lanes are affected by the turbulence caused by the intense lane changing. In this case, an adjustment factor CAFUP is applied uniformly to the node capacity: 𝐶𝐴𝐹𝑈𝑃(𝑖, 𝑡,𝑝) = 1 − 0.52 × 𝐿𝐶𝑅(𝑖, 𝑡,𝑝) . Exhibit 38-A31 Illustration of Different Impacts of an off-Ramp Queue at Node i: (a) Lane Blockage, (b) Increased Turbulence and (c) No Effect Equation 38-A36

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Appendix A: Off-ramp Queue Spillback Analysis Version 1.0 Page 181 The parameter LCR estimates the rate of lane change maneuvers performed by vehicles within the Queue Influence Area trying to adjust their position when spillback occurs. Vehicles traveling towards the exit ramp will move to the shoulder lane attempting to join the back of the queue, while vehicles traveling through will move to the median lanes in order to avoid the queue. Therefore, the lane change rate LCR is computed as: 𝐿𝐶𝑅(𝑖, 𝑡,𝑝) = 𝑆𝐵𝐿𝐶(𝑖, 𝑡,𝑝)𝑆𝐹(𝑖, 𝑡,𝑝) The parameter SBLC estimates the number of lane change maneuvers performed by vehicles within the Queue Influence Area trying to adjust their position when spillback occurs. Vehicles traveling towards the exit ramp will move to the shoulder lane attempting to join the back of the queue, while vehicles traveling through will move to the median lanes in order to avoid the queue. In order to compute SBLC for a given node, the number of vehicles driving toward the off-ramp must be estimated for each freeway lane. For each lane 𝑖, the parameter pi represents the percent of the off-ramp demand 𝑣 traveling on the subject lane. In order to estimate the values of pi as a function of the distance from the off-ramp to the subject node, the following steps and assumptions are used: (a) Within the influence area (1,500 ft from the exit point), the off-ramp demand flow rate 𝑣 is entirely positioned in the two rightmost lanes, according to the guidance provided in HCM Chapter 14. Therefore, the sum of the off-ramp flow rate percentages in the ramp influence area p1,R and p2,R is equal to 1. The methodology to estimate lane-by-lane flow distribution in freeway segments allows the estimation of the Lane Flow Ratio (LFR) for lanes 1 and 2. The proportion between p1,R and p2,R can then be estimated as follows: 𝑝 , = 𝐿𝐹𝑅𝐿𝐹𝑅 + 𝐿𝐹𝑅 𝑝 , = 𝐿𝐹𝑅𝐿𝐹𝑅 + 𝐿𝐹𝑅 (b) According to the guidance provided in HCM Chapter 14, the influence of ramps rarely extends beyond 8,000 ft. Therefore, for any nodes located beyond 8,000 from the off-ramp, the distribution of pi is taken as equal among all N freeway lanes: 𝑝 = 1𝑁 (c) At intermediate distances from the off-ramp  ranging between 1,500 ft and 8,000 ft, the distribution values of pi can be obtained through linear interpolation between the cases previously described. Equation 38-A37 Equation 38-A38 Equation 38-A39

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Appendix A: Off-ramp Queue Spillback Analysis Chapter 38 System Analyses (Draft) Page 182 Version 1.0 The value of pi as function of the distance from off-ramp exit can then be obtained through the following equation: 𝑝 = 𝑝 , + 1𝑁 − 𝑝 ,𝑅 × (𝑑 − 1,500)6500 As the lane-by-lane distribution of the off-ramp flow is known, the number of lane change maneuvers, SBLC, can then be estimated. For Regime 3 cases (one blocked lane), the number of lane changes is obtained as follows: 𝑆𝐵𝐿𝐶(𝑖, 𝑡, 𝑝) = 𝑣 (1 − 𝑝 ) + (𝑖 − 1) × 𝑣 𝑝 The equation adds the number of through vehicles in lane 1 that move to lane 2 to avoid the queue and the number of exiting vehicles in the remaining lanes that adjust their position to join the back of the queue, multiplied by the necessary number of lane changes. Exhibit 38-A33 illustrates an example of the proposed equation applied to a 4-lane segment. For Regime 4 cases, the following equation is applied to obtain SBLC: 𝑆𝐵𝐿𝐶(𝑖, 𝑡,𝑝) = 2 × 𝑣 (1 − 𝑝 ) + 𝑣 (1 − 𝑝 ) + (𝑖 − 2) × 𝑣 𝑝 Exhibit 38-A34 illustrates an example of the proposed equation applied to a 4-lane segment. Exhibit 38-A32 Distribution of pi as Function of Distance from the Off- Ramp Exit, for a 3-Lane Segment Equation 38-A40 Equation 38-A41 Exhibit 38-A33 Illustration of Lane Change Maneuvers Within the Queue Influence Area in a 4-Lane Segment With Regime 3 Equation 38-A42 Exhibit 38-A34 Illustration of Lane Change Maneuvers Within the Queue Influence Area in a 4-Lane Segment With Regime 4

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Appendix A: Off-ramp Queue Spillback Analysis Version 1.0 Page 183 Step 9 - Calculate mainline input The Oversaturated Segment Evaluation procedure computes the Mainline Input (MI) for each node, in every time step. It is defined as the maximum flow desiring to enter the subject node during the current time step. An adjustment is necessary when the subject node is operating in a two-pipe regime, as the blocked and unblocked portions will be subject to different input demands. Since exiting and through drivers segregate when approaching a queue, the mainline input demand in the blocked side consists of the off-ramp demand, while the remaining demand will move to the unblocked portion. When node i operates in a two-pipe regime, the Mainline Input (MI) parameter is split into two components: MIUB, representing the mainline input in the unblocked lanes, and MIBL, representing the mainline input joining the back of the queue. These parameters are computed as follows: 𝑀𝐼𝐵𝐿(𝑖, 𝑡,𝑝) = 𝑂𝐹𝑅𝐹(𝑁𝐸𝑋𝑇𝑂𝐹𝑅(𝑖), 𝑡,𝑝) 𝑀𝐼𝑈𝐵(𝑖, 𝑡,𝑝) = 𝑀𝐼(𝑖, 𝑡, 𝑝)− 𝑀𝐼𝐵𝐿(𝑖, 𝑡,𝑝) Step 12 - Calculate on-ramp maximum output If there is a merge segment upstream of an off-ramp bottleneck, the capacity of on-ramp output may be affected due to the blockage caused by the spillback queue. The Oversaturated Segment evaluation procedure calculates the on-ramp maximum output through HCM Equation 25-18, based on a series of potential constraints that include ramp metering, the on-ramp capacity, the capacity of the merge, or the presence of downstream queues. At high demands on both the freeway and the on-ramp, zipper merge (one-to-one) is expected to occur. Therefore, a new capacity constraint is added to Equation 25-18, included in the equation below in bold font and illustrated in Exhibit 38-A35: 𝑂𝑁𝑅𝑂(𝑖, 𝑡,𝑝) = 𝑚𝑖𝑛 ( ⎩⎪⎪ ⎪⎪⎨ ⎪⎪⎪ ⎪⎧ 𝑅𝑀(𝑖, 𝑡,𝑝)𝑂𝑁𝑅𝐶(𝑖, 𝑡,𝑝) 𝑚𝑎𝑥 ( ⎩⎪⎪⎪ ⎨⎪ ⎪⎪⎧𝑚𝑖𝑛 𝑀𝐹(𝑖 + 1, 𝑡 − 1,𝑝)+ 𝑂𝑁𝑅𝐹(𝑖, 𝑡 − 1,𝑝)𝑀𝑂3(𝑖, 𝑡 − 1,𝑝)+ 𝑂𝑁𝑅𝐹(𝑖, 𝑡 − 1,𝑝) −𝑀𝐼(𝑖, 𝑡,𝑝)𝑚𝑖𝑛 𝑆𝐶(𝑖, 𝑡,𝑝)𝑀𝐹(𝑖 + 1, 𝑡 − 1,𝑝)+ 𝑂𝑁𝑅𝐹(𝑖, 𝑡 − 1,𝑝)𝑀𝑂3(𝑖, 𝑡 − 1,𝑝)+ 𝑂𝑁𝑅𝐹(𝑖, 𝑡 − 1,𝑝)2𝑁(𝑖,𝑝)𝑹𝑭(𝑶𝑭𝑹𝑵𝑬𝑿𝑻(𝒊), 𝒕,𝒑))𝟐 × 𝑵𝑸 𝑶𝑭𝑹𝑵𝑬𝑿𝑻(𝒊) Equation 38-A43 Equation 38-A44 Equation 38-A45

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Appendix A: Off-ramp Queue Spillback Analysis Chapter 38 System Analyses (Draft) Page 184 Version 1.0 If one or more lanes are blocked due to a downstream off-ramp bottleneck, the throughput in Lane 1 will be equal to the maximum exit throughput in the congested off-ramp if the site operates in Regime 3, or 50% of the maximum exit throughput in the off-ramp, if it operates in Regime 4. It is assumed that the on- ramp and the flow arriving from the upstream on Lane 1 contribute equally to the downstream Lane 1 flow, and thus the on-ramp maximum output, in this case, is assumed to be half of the downstream throughput in Lane 1. Step 21 - Calculate mainline output (2) The Oversaturated Segment Evaluation methodology calculates the maximum number of vehicles, MO, that can exit a node, constrained by a downstream bottleneck or by merging on-ramp traffic. Among the potential constraints to calculate MO, the Mainline Output 2 accounts for the growth of queues on a downstream segments, eventually limiting the maximum number of vehicles that can enter it. When there is a queue in a downstream segment caused by a downstream off-ramp bottleneck, the segment is expected to operate under two distinct densities (Exhibit 38-A36). Therefore, the total number of vehicles in the downstream segment takes into account two different density values: the ramp queue density (RKB), prevailing at the queued area in red, and the background density (KB), prevailing in the remaining area of the segment (blue). If there are no spillback effects, the segment operates with a uniform density. In this case, the constraints for the unblocked and blocked portions (MO2UB and MO2BL, respectively) are calculated proportionately to the number of unblocked and blocked lanes: Exhibit 38-A35 Impact of a queue spillback on the discharge capacity of an upstream on-ramp Exhibit 38-A36 Illustration of Different Density Values Within One Diverge Segment

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Appendix A: Off-ramp Queue Spillback Analysis Version 1.0 Page 185 𝑀𝑂2𝑈𝐵(𝑖, 𝑡,𝑝) = 𝑀𝑂2(𝑖, 𝑡,𝑝) × 1 − 𝑁𝑄(𝑖)𝑁(𝑖) 𝑀𝑂2𝐵𝐿(𝑖, 𝑡, 𝑝) = 𝑀𝑂2(𝑖, 𝑡,𝑝) × 𝑁𝑄(𝑖)𝑁(𝑖) If node i operates under Increased Turbulence (node is in the Queue Influence Area), the unblocked portion of segment i will operate similar to a regular segment. Therefore, the component MO2UB is equal to MO2 but proportional to the number of lanes in the unblocked portion: 𝑀𝑂2𝑈𝐵(𝑖, 𝑡,𝑝) = 𝑀𝑂2(𝑖, 𝑡,𝑝) × 1 − 𝑁𝑄(𝑖)𝑁(𝑖) For the blocked portion of segment i, the parameter is calculated as equal to MO2 proportional to the number of lanes in the blocked portion plus an additional number of vehicles due to the presence of a partial queue. This additional number of vehicles is obtained by the bold terms in the following equation, which takes into account the difference between the queue spillback density (RKQ) and the segment queue density (KQ), multiplied by the queue length: 𝑀𝑂2𝐵𝐿(𝑖, 𝑡,𝑝) = 𝑀𝑂2(𝑖, 𝑡,𝑝) × 𝑁𝑄(𝑖)𝑁(𝑖) + 𝑆𝐵𝐿𝑄(𝑖, 𝑡 − 1,𝑝) × 𝑁𝑄(𝑖, 𝑡 − 1,𝑝)× [𝑅𝐾𝑄(𝑂𝐹𝑅𝑁𝐸𝑋𝑇(𝑖), 𝑡 − 1,𝑝)− 𝐾𝑄(𝑖 − 1, 𝑡 − 1,𝑝)] If node i experiences lane blockage, the values of queue density must be computed for both the unblocked (KQUB) and blocked (KQBL) portions of segment i. For the unblocked portion, the queue density KQUB is calculated similarly to Equation 25-10, but the inputs for segment flow (SF) and segment capacity (SC) are replaced by their equivalent parameters SFUB and SCEQ: 𝐾𝑄𝑈𝐵(𝑖, 𝑡,𝑝) = 𝐾𝐽 − [(𝐾𝐽 − 𝐾𝐶)] × 𝑆𝐹𝑈𝐵(𝑖, 𝑡 − 1,𝑝)]/𝑆𝐶𝐸𝑄(𝑖,𝑝) The queue density for the blocked portion is computed as equal to the ramp queue density: 𝐾𝑄𝐵𝐿(𝑖, 𝑡,𝑝) = 𝑅𝐾𝑄(𝑂𝐹𝑅𝑁𝐸𝑋𝑇(𝑖), 𝑡 − 1,𝑝) With the queue density values for both the blocked and unblocked portions known, the MO2 components MO2BL and MO2UB can be computed: 𝑀𝑂2𝑈𝐵(𝑖, 𝑡,𝑝) = 𝑆𝐹𝑈𝐵(𝑖, 𝑡 − 1,𝑝)− 𝑂𝑁𝑅𝐹(𝑖, 𝑡,𝑝)+ 𝐾𝑄𝑈𝐵(𝑖, 𝑡,𝑝) × 𝐿(𝑖) × 𝑁(𝑖,𝑝) −𝑁𝑄(𝑖,𝑝) − 𝑁𝑉(𝑖, 𝑡 − 1,𝑝) 𝑀𝑂2𝐵𝐿(𝑖, 𝑡,𝑝) = 𝑆𝐹𝐵𝐿(𝑖, 𝑡 − 1,𝑝) − 𝑂𝑁𝑅𝐹(𝑖, 𝑡,𝑝)+ [𝐾𝑄𝐵𝐿(𝑖, 𝑡,𝑝) × 𝐿(𝑖) × 𝑁𝑄(𝑖,𝑝)] − 𝑁𝑉(𝑖, 𝑡 − 1,𝑝) Step 22 - Calculate mainline flow The Oversaturated Segment Evaluation procedure computes the Mainline Flow through a subject node as the minimum of several variables, as presented in HCM Equation 25-16. If the node experiences spillback, the calculation of Mainline Flow must consider the flow through both the blocked and the unblocked portions of the node. Therefore, the Mainline Flow (MF) parameter is split into two components in an approach similar to the Mainline Input: the Equation 38-A46 Equation 38-A47 Equation 38-A48 Equation 38-A49 Equation 38-A50 Equation 38-A51 Equation 38-A52 Equation 38-A53

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Appendix A: Off-ramp Queue Spillback Analysis Chapter 38 System Analyses (Draft) Page 186 Version 1.0 component MFUB represents flow across the node in the unblocked lanes, while the component MFBL represents the flow across the node in the blocked lanes. For both components, the resulting flow is computed as the minimum value between input and the maximum allowed flow. For MFUB, the maximum allowed flow is equal to the capacity of unblocked lanes in the downstream segment, represented by the parameter SCEQ as computed in the initialization step: 𝑀𝐹𝑈𝐵(𝑖) = 𝑚𝑖𝑛 𝑀𝐼𝑈𝐵(𝑖, 𝑡,𝑝), 𝑆𝐶𝐸𝑄(𝑖, 𝑡,𝑝),𝑀𝑂2𝑈𝐵(𝑖, 𝑡,𝑝) For MFBL, the maximum allowed flow is equal to the flow allowed to enter the nearest downstream off-ramp RF, as presented in the following equation: 𝑀𝐹𝐵𝐿(𝑖) = 𝑚𝑖𝑛 (𝑀𝐼𝐵𝐿(𝑖, 𝑡,𝑝),𝑅𝐹(𝑁𝐸𝑋𝑇𝑂𝐹𝑅(𝑖), 𝑡,𝑝,𝑀𝑂2𝐵𝐿(𝑖, 𝑡,𝑝)) Next, the Mainline Flow MF through node i is computed as the sum of the blocked and unblocked portions, as follows: 𝑀𝐹(𝑖, 𝑡,𝑝) = 𝑀𝐹𝑈𝐵(𝑖, 𝑡,𝑝)+ 𝑀𝐹𝐵𝐿(𝑖, 𝑡,𝑝) Step 25 - Update number of vehicles in the blocked portion of the segment The number of vehicles in the blocked portion NVBL during increased turbulence is updated based on the number of vehicles in the previous time step and considers the number of vehicles that are able to leave the current and upstream segment : 𝑁𝑉𝐵𝐿(𝑖, 𝑡,𝑝) = 𝑁𝑉𝐵𝐿(𝑖, 𝑡 − 1,𝑝) + 𝑀𝐹𝐵𝐿(𝑖 − 1, 𝑡,𝑝)+ 𝑂𝑁𝑅𝐹(𝑖 − 1, 𝑡,𝑝)−𝑀𝐹𝐵𝐿(𝑖, 𝑡,𝑝)− 𝑂𝐹𝑅𝐹(𝑖, 𝑡,𝑝) Step 30 - Calculate segment performance measures The aggregated segment flow for a 15-min time period is obtained as the sum of flows for every time step (HCM Equation 25-30): 𝑆𝐹(𝑖,𝑝) = 𝑇𝑆 𝑆𝐹(𝑖, 𝑡,𝑝) Similarly, the aggregated off-ramp ramp is aggregated at a 15-min time period: 𝑂𝐹𝑅𝐹(𝑖,𝑝) = 𝑇𝑆 𝑂𝐹𝑅𝐹(𝑖, 𝑡,𝑝) The additional density in the queued lanes is obtained by aggregating the additional number of vehicles ΔNV(i,t,p) in the off-ramp queue: ∆𝐾(𝑖,𝑝) = 1𝑆 × 𝑁 ∆𝑁𝑉(𝑖, 𝑡,𝑝) Similar to the mainline, the flow in the ramp roadway is also aggregated: Equation 38-A54 Equation 38-A55 Equation 38-A56 Equation 38-A57 Equation 38-A58 Equation 38-A59 Equation 38-A60

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Appendix A: Off-ramp Queue Spillback Analysis Version 1.0 Page 187 𝑅𝐹(𝑖,𝑝, 𝑘) = 𝑇𝑆 𝑅𝐹(𝑖, 𝑡,𝑝, 𝑘) The aggregated density at the ramp is calculated as the average of the number of vehicles inside the ramp along the time period: 𝑅𝐾(𝑖,𝑝, 𝑘) = 1𝑆 𝑅𝑁𝑉(𝑖, 𝑡,𝑝, 𝑘) Finally, the speed at the ramp for a time period p is obtained by dividing the total ramp flow in the time period by its average density: 𝑆𝑅(𝑖,𝑝, 𝑘) = 𝑅𝐹(𝑖,𝑝, 𝑘)𝑅𝐾(𝑖,𝑝, 𝑘) Equation 38-A61 Equation 38-A62 Equation 38-A63

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Appendix B: On-Ramp Queue Spillback Analysis Chapter 38 System Analyses (Draft) Page 188 Version 1.0 APPENDIX B: ON-RAMP QUEUE SPILLBACK ANALYSIS Queue spillback into an urban street intersection may occur when the freeway merge segment has insufficient capacity to process the ramp’s demand. Spillback may also occur in cases of ramp metering. This appendix presents the methodology for determining whether spillback will occur from an on-ramp into the upstream intersection. The methodology considers signalized intersections, two-way stop- controlled intersections, all-way stop controlled intersections, and roundabouts. The procedure first estimates the demand approaching the on-ramp (determined based on the upstream intersection’s configuration), and then estimates the capacity of the off-ramp. The Chapter 10, Freeway Facilities methodology for oversaturated conditions can estimate the resulting queue length, however, the user must input the on-ramp demand flow rate. The methodology framework for conducting this spillback check is presented Exhibit 38-B1 . Exhibit 38-B1 Procedure for Detecting Spillback Occurrence at an On-Ramp

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Appendix B: On-Ramp Queue Spillback Analysis Version 1.0 Page 189 DEMAND ESTIMATION The first step in the methodology calculates the entering demand flow rate at the on-ramp (𝑣 ), as a function of the upstream intersection configuration and operations. Under low demand conditions, the on-ramp demand flow rate is calculated as the sum of the demands on each of the intersection approaches that discharge into the ramp. However, if any of these movements is operating over capacity, the total throughput to the ramp will be constrained by the capacity of these oversaturated movements. Hence, this check ensures that the on-ramp demand is not overestimated. The analysis approach for each of four intersection types is presented next. Case A: Signalized intersections The throughputs of a signalized intersection are highly dependent on several parameters such as phasing sequences, actuation, cycle lengths, and permitted- protected phasing, among others. The methodology of this chapter identifies the movements that discharge to the on-ramp and their operational characteristics (permitted or protected). For example, typical diamond interchanges will include a left-turn movement, a right-turn movement and a through movement (which will typically have negligible flow). The on-ramp demand 𝑣 is computed as the sum of the throughputs of each movement that discharges into the on-ramp. The throughput of a given movement i is obtained as the minimum value of its demand and capacity: 𝑣 = min (𝑣 , 𝑐 ) where 𝑣 = on-ramp demand (veh/h); 𝑣 = demand for movement 𝑖 at the intersection (veh/h); 𝑐 = demand for movement 𝑖 at the intersection (veh/h); 𝑁 = number of intersection movements that discharge into the on-ramp If all movements operate below capacity, the on-ramp demand is obtained as the sum of the movement demands. If any of the ramp terminal movements that discharge into the on-ramp operates over capacity, the total throughput to the on-ramp will be lower than the sum of the corresponding intersection movements. Unsignalized Movements In the case of unsignalized movements discharging into the on-ramp, the demand for these movements must also be compared to their capacity. The potential capacity cp,i of an unsignalized movement can be computed by aggregating its saturation flow rates at different phases throughout a cycle. If the unsignalized movement is free-flowing and there are no other conflicting movements discharging to the on-ramp, its saturation flow rate sFF is obtained by HCM Equation 19-8, with the applicable adjustment factors applied: Equation 38-B1

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Appendix B: On-Ramp Queue Spillback Analysis Chapter 38 System Analyses (Draft) Page 190 Version 1.0 𝑠 = 𝑠 𝑓 𝑓 𝑓 𝑓 𝑓 𝑓 𝑓 𝑓 𝑓 𝑓 𝑓 𝑓 𝑓 Where 𝑠 = saturation flow rate for unsignalized movement during free-flow (veh/h/ln); 𝑠 = base saturation flow rate (pc/h/ln) All other adjustment factors are as described in Equation 19-8. If the unsignalized movement must yield to a conflicting movement discharging to the on-ramp, the permitted saturation flow rate sp is calculated based on HCM equation 31-100: 𝑠 = 𝜆 𝑒 ,1 − 𝑒 , Where: 𝑠 = permitted saturation flow rate for unsignalized movement (veh/h/ln); 𝜆 = throughput of the conflicting movement (veh/h/ln) 𝑡 = critical headway = 4.5 (s); 𝑡 = follow-up headway = 2.5 (s) The throughput of the conflicting movement 𝜆 is determined as a function of the flow profile of the respective conflicting movement. The effective green (𝑔) of the conflicting movement is divided into a queue service time (𝑔 ) and a green extension time (𝑔 ), each with a specific flow profile: • If the conflicting movement occurs during the queue service time (𝑔 ), 𝜆 is equal to the saturation flow rate s of the conflicting movement; • If the conflicting movement occurs during the green extension time (𝑔 ), 𝜆 is equal to the arrival flow rate during the green 𝑞 (Equation 19-32) of the conflicting movement. Case B – Two-Way Stop Controlled (TWSC) intersections The TWSC intersection analysis is based on the calculation of the potential capacities of each movement, based on factors such as priority order, conflicting flow, and critical gap. With very few adjustments, estimating the on-ramp throughput from this intersection type is a relatively straightforward task. The procedure first identifies the movements that discharge to the on-ramp and their respective ranks (priority orders). The evaluation of freeway-arterial interactions assumes that for TWSC interchanges the urban street will always be the major street. Exhibit 38-B2 illustrates a typical TWSC intersection at a freeway interchange, where movements discharging into the on-ramp are numbered Equation 38-B2

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Appendix B: On-Ramp Queue Spillback Analysis Version 1.0 Page 191 according to their ranks, using the default numbering of Chapter 20 (Exhibit 20- 1). Similarly to signalized intersections, there are three movements turning into the ramp, and their respective flows are discussed below: 1. Rank 1 Movement (Right Turn from the Major Street): This movement is considered unimpeded, experiencing zero delay. The only physical constraint able to limit the throughput of this movement is its saturation flow rate if demand is very high. Therefore, the maximum throughput λRT (veh/h) for this right-turn movement is given by: 𝜆 = 𝑚𝑖𝑛 (𝑣 , 𝑠 ) where 𝜆 = departure rate from major street right turn into the on-ramp (veh/h); 𝑣 = demand flow rate for the major street right turn; and 𝑠 = saturation flow rate for a right-turn movement (veh/h). 2. Rank 2 Movement (Left Turn from the Major Street): The maximum throughput for this movement is limited by its potential capacity (𝑐 , ), as defined in Equation 20-36. Therefore, the maximum throughput (veh/h) for this left-turn movement is given by: 𝜆 = 𝑚𝑖𝑛 (𝑣 , 𝑐 , ) where 𝜆 = departure rate from the major-street left-turn into the on-ramp (veh/h); 𝑣 = demand flow rate for the major street left turn; and 𝑐 , = potential capacity for the major street left turn (veh/h). Exhibit 38-B2 Schematic of Movements Turning to an On-Ramp from a TWSC Intersection Equation 38-B3 Equation 38-B4

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Appendix B: On-Ramp Queue Spillback Analysis Chapter 38 System Analyses (Draft) Page 192 Version 1.0 3. Rank 3 Movement (Through Movement from the Minor Street): Similar to rank 2 movements, the maximum throughput for this movement is limited by its potential capacity (𝑐 , ), as defined in Equation 20-47. Therefore, the maximum throughput λTh (veh/h) for this through movement is given by: 𝜆 = 𝑚𝑖𝑛 (𝑣 , 𝑐 , ) where 𝜆 = departure rate from the minor street through into the on-ramp (veh/h); 𝑣 = demand flow rate for the minor street through; and 𝑐 , = potential capacity for the minor street through (veh/h). Finally, the total on-ramp demand flow rate 𝑣 can be estimated as follows: 𝑣 = 𝜆 + 𝜆 + 𝜆 where 𝜆 = departure rate from major street right turn into the on-ramp (veh/h) (Equation 38-B3); 𝜆 = departure rate from the major-street left-turn into the on-ramp (veh/h) (Equation 38-B4); and 𝜆 = departure rate from the minor street through into the on-ramp (veh/h) (Equation 38-B5). Case C – All-Way Stop Controlled (AWSC) intersections The AWSC methodology uses departure headways (ℎ ) for each approach, making the calculation of the on-ramp flow straightforward. Exhibit 38-B3 illustrates the movements discharging into an on-ramp from an AWSC intersection. Equation 38-B5 Equation 38-B6 Exhibit 38-B3 Schematic of Movements Turning to an On-Ramp from an AWSC Intersection

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Appendix B: On-Ramp Queue Spillback Analysis Version 1.0 Page 193 The on-ramp demand flow rate can be obtained directly from the departure headways of the three movements combined: 𝑣 = 3600ℎ , + 3600ℎ , + 3600ℎ , where 𝑣 = on-ramp flow rate (veh/h); ℎ , = departure headway for the major street right turn(s); ℎ , = departure headway for the major street left turn(s); and ℎ , = departure headway for the minor street through(s). Case D: Roundabouts The Roundabouts methodology is based on the calculation of the potential capacities of each approach, based on three main variables: the critical and the follow-up headways, and the circulating flow (Equation 22-21 through Equation 22-23). Both critical and follow-up headway values can be obtained from Chapter 33. The methodology considers each approach independently. To analyze roundabouts within a system it is first necessary to estimate the on-ramp throughput from a roundabout. The procedure first identifies the movements that discharge to the on-ramp and their respective ranks (priority orders). Exhibit 38-B4 illustrates a typical roundabout, where movements discharging into the on-ramp are numbered according to their ranks. In contrast to other types of intersections, the approach furthest from the on-ramp has priority as it enters the circulating stream without any significant conflicting traffic (other than occasional U-turns). The operation of each of these movements is as follows: Equation 38-B7 Exhibit 38-B4 Schematic of Movements Turning to an On-Ramp from a Roundabout

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Appendix B: On-Ramp Queue Spillback Analysis Chapter 38 System Analyses (Draft) Page 194 Version 1.0 Rank 1 Movement (Left-Turn from the Third Upstream Approach from the On- Ramp): This movement has priority over the other movements because it enters the circulating stream first. Also, because the on-ramp does not have an approach into the roundabout, this movement is most often unopposed by the circulating stream (except for occasional U-turns in the intersection). Therefore, the maximum throughput 𝜆 (veh/h) for this left-turn movement is given by: 𝜆 = 𝑚𝑖𝑛 (𝑣 , 𝑐 ) where 𝜆 = departure rate from the third upstream approach into the on-ramp (veh/h); 𝑣 = demand flow rate for the third upstream approach into the on-ramp; and 𝑐 = potential capacity for the approach (veh/h). Rank 2 Movement (Through from the Second Upstream Approach, Most Likely an Off-Ramp): The maximum throughput for this movement is limited by the upstream approach departure rate and its own potential lane capacity (𝑐 ), as defined in Equations 22-21 through 22-23. Therefore, the maximum throughput 𝜆 veh/h) for this through movement is given by: 𝜆 = 𝑚𝑖𝑛(𝑣 , 𝑐 ) where 𝜆 = departure rate from the second upstream approach into the on-ramp (veh/h); 𝑣 = demand flow rate for the second upstream approach into the on-ramp (veh/h); and 𝑐 = potential capacity for the approach (veh/h). Rank 3 Movement (Right-Turn for the First Upstream Approach): Similar to rank 2 movements, the maximum throughput for this movement is limited by the immediately upstream approach and its own potential capacity (c3 ), as defined in Equation 22-21 through Equation 22-23. Therefore, the maximum throughput 𝜆 (veh/h) for this right-turn movement is given by: 𝜆 = 𝑚𝑖𝑛(𝑣 , 𝑐 ) where 𝜆 = departure rate from the first upstream approach into the on-ramp (veh/h); 𝑣 = demand flow rate for the first upstream approach into the on-ramp; and 𝑐 = potential capacity for the approach (veh/h). Finally, the total on-ramp demand flow rate 𝑣 can be estimated as follows: Equation 38-B8 Equation 38-B9 Equation 38-B10

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Appendix B: On-Ramp Queue Spillback Analysis Version 1.0 Page 195 𝑣 = 𝜆 + 𝜆 + 𝜆 The total on-ramp demand flow rate can be calculated by the same method for roundabouts with a higher number of approaches. CAPACITY ESTIMATION Capacity at the on-ramp must be estimated in order to predict the occurrence of queue spillback. Three cases may occur: Case 1: Ramp Metering is Active In this case, the metering rate is a required user input (veh/h) and is stored in the existing variable 𝑅𝑀(𝑖, 𝑡,𝑝), as defined in Chapter 25. The maximum output flow rate 𝑂𝑁𝑅𝑂(𝑖, 𝑡,𝑝) that can enter the merge point takes into consideration the ramp metering rate as one of its possible constraints (Equation 25-18) and is properly adjusted if the ramp metering becomes the restricting factor to the on- ramp discharge. 𝑂𝑁𝑅𝑂(𝑖, 𝑡,𝑝) is defined as follows: “𝑂𝑁𝑅𝑂(𝑖, 𝑡,𝑝) - maximum output flow rate that can enter the merge point from on- ramp 𝑖 during time step t in time interval 𝑝; it is constrained by Lane 1 (shoulder lane) flow on segment 𝑖 and the segment 𝑖 capacity or by a queue spillback filling the mainline segment from a bottleneck further downstream, whichever governs” Case 2: No Ramp Metering, Oversaturated Merge Segment In this case, the ramp merge capacity can be computed by aggregating the ONRO parameter into a 15-minute period and then converted into an hourly flow rate. Case 3: No Ramp Metering, Undersaturated Merge Segment This case does not require any adjustments to the Chapter 10 - Freeway Systems methodology. Equation 38-B11 RM(i,t,p) is defined in Chapter 25 as the maximum allowable rate of an on-ramp meter at the on-ramp node i during time interval p, measured in veh/h. RM(i,t,p) is also one of the inputs used in calculating the maximum on-ramp output (Equation 25-18)

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Appendix B: On-Ramp Queue Spillback Analysis Chapter 38 System Analyses (Draft) Page 196 Version 1.0 EVALUATION OF ON-RAMP QUEUE SPILLBACK IMPACTS This section describes the methodological modifications required to address the occurrence of queue spillback from an on-ramp. The occurrence of queue spillback affects each type of intersection differently. The methods outlined here address signalized intersections, two-way stop-controlled (TWSC) intersections, all-way stop-controlled (AWSC) intersections, and roundabouts. Signalized Intersections Exhibit 38-B5 presents the core methodology for evaluating the performance of signalized intersections, with proposed modifications to address impacts from an on-ramp queue spillback. New steps and modified steps to the methodology are described in the following paragraphs.

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Appendix B: On-Ramp Queue Spillback Analysis Version 1.0 Page 197 Step 7A - Determine intersection throughput to on-ramp The volume of vehicles that enters a freeway on-ramp is a function of the demands and capacities of each individual intersection movements that discharge into the ramp. A typical signalized intersection within a diamond interchange is shown in Exhibit 38-B6, with three movements discharging into the on-ramp (SBL, EBT and NBR). Exhibit 38-B5 Signalized Intersections Methodology With Adjustments to Address On- Ramp Queue Spillback

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Appendix B: On-Ramp Queue Spillback Analysis Chapter 38 System Analyses (Draft) Page 198 Version 1.0 The total throughput from the intersection into the on-ramp λONR is the sum of the throughput from each of the contributing movements: 𝜆 = 𝜆 + 𝜆 + 𝜆 The throughput for each movement i is the minimum value of its demand and capacity: 𝜆 = 𝑚𝑖𝑛(𝑣 , 𝑐 ) where vi = demand flow rate for intersection movement i (veh/h) ci = capacity for intersection movement i (veh/h), as provided by Equation 19-16 Unsignalized movements, which are common for right-turn movements to the on-ramp, are unrestricted. The capacity of these movements can be estimated as the saturation flow rate (Equation 19-8), with an adjustment factor for right turns fRT (Equation 19-13). If all movements at the intersection are undersaturated, (vi ≤ ci for every i), then Equation 38-B12 is simplified and the total on-ramp demand throughput λONR is as follows: 𝜆 = 𝑣𝑖𝑖 Step 7B. Obtain merging capacity using freeway facilities methodology This step computes the merging capacity into the freeway cmerge. Three potential bottlenecks can limit the on-ramp discharge into the freeway: • Capacity of the on-ramp (Exhibit 14-12) • Capacity at the merge segment, when oversaturated conditions occur at the freeway facility; • An active ramp metering RM The procedure to obtain cmerge is presented in Exhibit 38-B7. The freeway facility must be analyzed using the Freeway Facilities methodology (Chapter 10) Exhibit 38-B6 Typical Signalized Intersection Ramp Terminal in a Diamond Interchange Equation 38-B12 Equation 38-B13 Equation 38-B14

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Appendix B: On-Ramp Queue Spillback Analysis Version 1.0 Page 199 to evaluate whether the merging capacity is constrained by oversaturated conditions in the mainline. If the freeway facility is undersaturated (LOS A-E), the merging capacity cmerge takes the minimum value between the on-ramp capacity and the ramp metering rate, if present. If the freeway facility is oversaturated (LOS F), the Oversaturated Segment Evaluation procedure described in Chapter 25 can provide the maximum on- ramp output ONRO, computed at a time-step level (15 seconds). The merging capacity cmerge can then be computed by aggregating the parameter ONRO to an hourly flow rate: 𝑐 = 𝑇𝑆 𝑂𝑁𝑅𝑂(𝑖, 𝑡,𝑝) where ONRO(I, t, p) = maximum output flow rate that can enter the merge point from on- ramp 𝑖 during time step t in time interval p T = number of time steps in 1 h (integer). T is set as a constant of 240 in the computational engine, or equal to four times the value of S; S = number of computational time steps in an analysis period (integer). 𝑆 is set as a constant of 60 in the computational engine, corresponding to a 15-s interval and allowing a minimum segment length of 300 ft; and t = time step index. Equation 38-B15

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Appendix B: On-Ramp Queue Spillback Analysis Chapter 38 System Analyses (Draft) Page 200 Version 1.0 Step 7C. Plot Queue Accumulation Polygon for the On-Ramp In this step, a Queue Accumulation Polygon (QAP) must be built for the on- ramp, considering the throughput from all contributing movements within the cycle. Exhibit 38-B8 illustrates a sample intersection which will be used to describe this step. The application of this methodology requires that the first analyzed time period is undersaturated. Based on this requirement, the QAP starts with zero vehicles inside the on-ramp. The on-ramp QAP for this example is provided in Exhibit 38-B9. The cycle starts with the SBL green discharging into the on-ramp at a throughput rate λSBL, while the on-ramp discharges to the freeway merge at a rate cmerge. Therefore, the number of vehicles within the on-ramp grows at a rate equal to (λSBL - cmerge). When the number of vehicles along the on-ramp reaches the maximum ramp storage length LONR, vehicles from the intersection can only be discharged to the on-ramp at the same the rate they are discharged from the on-ramp into the freeway. The number of vehicles within the on-ramp is then Exhibit 38-B7 Step 7B - Estimation of Merging Capacity in a Freeway Ramp

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Appendix B: On-Ramp Queue Spillback Analysis Version 1.0 Page 201 maintained and it is equal to LONR until the end of the green for the SBL movement. At the end of the SBL green, the vertical difference between the projected number of vehicles (dashed line) and the actual number of vehicles inside the on-ramp represent the number of unserved vehicles for the SBL approach. This additional queue can be considered in a multiperiod analysis for the signalized intersection or interchange, using the methods provided in Chapter 23 – Ramp Terminals and Alternative Intersections. The slope of the red line connecting the number of vehicles in the end and start of the green represent the reduced capacity of the SBL movement due to queue spillback. For the remainder of the cycle, the NBR movement discharges at a constant rate into the on-ramp, as this is an unsignalized movement. Given that the discharge capacity cmerge is greater than the on-ramp demand λNBR, the vehicles along the on-ramp are discharged to the freeway until the on-ramp is cleared. Therefore, the NBR movement does not have its capacity affected by queue spillback. This procedure can be applied for both pretimed and actuated control types, since the core methodology can address both controller types. If the signal is actuated, the average phase duration lengths are applied, as obtained in Step 6. Step 7D. Calculate adjusted capacities for the affected movements Based on the on-ramp QAP developed in the previous step, the adjusted capacity cSP must be calculated for every movement affected by the queue spillback. For the example of Exhibit 38-B9, the adjusted capacity for the SBL Exhibit 38-B8 Sample Intersection for Calculation of a QAP for the On-Ramp

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Appendix B: On-Ramp Queue Spillback Analysis Chapter 38 System Analyses (Draft) Page 202 Version 1.0 movement cSBL,SP can be obtained from the QAP as the slope of the red line (cSBL,SP - cmerge) as follows: 𝑐 , − 𝑐 − 𝑁(𝑔 ) −𝑁(0)𝑔 where N(g ) = number of queued vehicles along the on-ramp at t = g1 (end of green for phase 1); N(0) = number of queued vehicles along the on-ramp at t = 0 (start of the cycle); G = effective green time for phase 1 The adjusted capacity of the SBL movement cSBL,SP is then computed as: 𝑐 , = 𝑐 + 𝑁(𝑔 )− 𝑁(0)𝑔 If the queue develops and fully discharges during every cycle, then subsequent cycles will have the same discharge. However, if there are residual queues at the on-ramp by the end of the cycle, the QAP must then be plotted again for the following cycle with an initial queue equal to the number of queued vehicles in the end of the present cycle. This process must be then repeated for a number of cycles N= 900/C, sufficient to analyze the entire 15-minute period. The adjusted capacity for each movement is estimated as the average of the discharge rates during each cycle. Step 8. Determine delay The calculations for obtaining delay at the intersection approaches do not need to be modified. The only change required is replacing the input value of the demand-to-capacity ratio X (Equation 19-17) for the adjusted value Xsp, estimated using the adjusted capacity due to spillback: Equation 38-B16 Exhibit 38-B9 On-Ramp Queue Accumulation Polygon During Queue Spillback Equation 38-B17

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Appendix B: On-Ramp Queue Spillback Analysis Version 1.0 Page 203 𝑋 = 𝑣𝑐 Two-Way Stop-Controlled (TWSC) Intersections The operation of TWSC intersections is based on determining the priorities of movements arriving at the intersection. Minor street movements have lower priority and must stop before entering the intersection. Left-turning drivers from the major street must yield to oncoming major-street through or right turning traffic, but they are not required to stop in the absence of oncoming traffic. The methodologies for evaluating the operations of TWSC intersections are based on gap acceptance theory. Drivers from lower priority movements must select a suitable gap in order to proceed through the intersection. According to previous research [3], during oversaturated conditions and when queue spillback occurs drivers show cooperative behavior, with higher priority vehicles often yielding to those with lower priority, as illustrated in Exhibit 38-B10. In such cases, the gap acceptance model is no longer valid, and a new approach must be used to evaluate the intersection performance. When queue spillback occurs at a TWSC intersection the maximum throughput to the on-ramp (exit capacity) is constrained by the discharge capacity of the freeway merge. It is assumed that during oversaturated conditions the intersection movements that discharge to the on-ramp share the exit capacity proportionately to their demands. Exhibit 38-B11 presents the core methodology for evaluating the performance of TWSC intersections, with proposed modifications to address impacts from an on-ramp queue spillback. New steps and modified steps to the methodology are described in the following paragraphs. Equation 38-B18 Exhibit 38-B10 Illustration of Cooperative Behavior in Unsignalized Intersections With Queue Spillback

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Appendix B: On-Ramp Queue Spillback Analysis Chapter 38 System Analyses (Draft) Page 204 Version 1.0 Step 9A - Determine intersection throughput to on-ramp The throughput to the on-ramp is calculated using the approach described in Step 7A of the queue spillback analysis for signalized intersections (Exhibit 38- B5). The total throughput from the intersection into the on-ramp λONR is the sum of the throughput from each of the contributing movements. For each movement Exhibit 38-B11 TWSC intersections Core Methodology With Adjustments to Address On- Ramp Queue Spillback

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Appendix B: On-Ramp Queue Spillback Analysis Version 1.0 Page 205 i discharging into the on-ramp, the throughput is the minimum value of its demand and its movement capacity: 𝜆 = 𝑚𝑖𝑛 𝑣 , 𝑐 , where vi = demand flow rate for movement i cm,j = movement capacity for movement i (Equations 20-36, 20-37 and 20-40). Step 9B. Obtain merging capacity using the freeway facilities methodology This step computes the merging capacity into the freeway cmerge. The procedure described in Step 7B of the queue spillback analysis for signalized intersections (Exhibit 38-B5) is applied. Step 9C. Determine proportion of time period with queue spillback While signalized intersections operate in a cyclical pattern, stop-controlled intersections have relatively uniform patterns of demand and capacity within a time period. Therefore, the 15-minute aggregated demand and capacity values are assumed to be constant, and the growth and discharge of queues are assumed to be linear. The queue accumulation polygon is used to illustrate the development of queues along the on-ramp (Exhibit 38-B12). For a given time period of T minutes (typically T=15), the intersection yields a throughput λONR to the ramp (Step 5B), while the merge has capacity cmerge. If λONR > cmerge, then queues will develop along the on-ramp until the number of vehicles reach the maximum ramp storage LONR, when queue spillback begins. When that occurs, the maximum rate of vehicles that can enter the on-ramp is limited by the merging capacity cmerge for the rest of the time period. From this relationship shown in Exhibit 38-B12 the spillback time TSB is defined as the amount of time within a time period when spillback is active: Equation 38-B19 Exhibit 38-B12 On-ramp Queue Accumulation Polygon – TWSC Intersection

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Appendix B: On-Ramp Queue Spillback Analysis Chapter 38 System Analyses (Draft) Page 206 Version 1.0 𝑇 = 𝑇 − 𝐿 − 𝑁(0)𝜆 − 𝑐 where TSB = time period with active spillback (minutes) T = duration of analysis time period (minutes) LONR = available queue storage at on-ramp (veh) N(0) = number of queued vehicles along the on-ramp at t = 0 (start of the cycle); cmerge = merging capacity of the on-ramp (veh/h) λONR = discharge from the intersection into the on-ramp (veh/hr) Estimating the spillback time TSB is critical to the methodology, as the aggregated calculations of capacity for each movement depend on the amount of time that the intersection operates under queue spillback. Step 10. Final capacity adjustments In this step, the capacities of the movements affected by spillback are obtained and then aggregated to a time period level. When on-ramp queue spillback occurs at an intersection, movements discharging towards the on-ramp switch to a cooperative approach instead of the priority-based regular operation. When there is queue spillback, the maximum throughput to the on-ramp is equal to the merging capacity cmerge. This capacity is then used by all movements traveling into the on-ramp. The capacity of each affected movement i during spillback ci,SB is obtained proportionally to its demand flow rate: 𝑐 , = 𝑐 × 𝑣∑ 𝑣 where c , = capacity during spillback for movement i (veh/h) V = demand flow rate for movement i (veh/h) C = merging capacity of the on-ramp (veh/h) N = number of movements at the intersection discharging into the on-ramp Finally, the adjusted capacity of each affected movement ci,EQ is obtained as a function of the amount of time within the time period when spillback was present. The adjusted capacity considers the proportion of time there is blockage during queue spillback and consists of the aggregation, at a time period level, of movement capacities cm,i (which is observed during undersaturated conditions) and spillback capacities cSB,i,(which is observed during oversaturated conditions): 𝑐 , = 𝑐 , × 𝑇 + 𝑐𝑚,𝑖 × (𝑇 − 𝑇 )𝑇 where c , = adjusted capacity for movement i (veh/h) Equation 38-B20 Equation 38-B21 Equation 38-B22

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Appendix B: On-Ramp Queue Spillback Analysis Version 1.0 Page 207 C , = capacity during spillback for movement i (veh/h) V = demand flow rate for movement i (veh/h) C = merging capacity of the on-ramp (veh/h) When queue spillback lasts for the entire time period T (for example, in a multi-period analysis), the spillback time TSB is equal to T, and the capacity of each movement i is obtained as the capacity during spillback and Equation 38- B22 becomes: 𝑐 , = 𝑐 , Step 11. Compute movement control delay The average control delay is obtained using Equation 20-64 replacing the movement capacity cm,i by the adjusted capacity cEQ,i: 𝑑 = 3600𝑐 , + 900𝑇 ⎣⎢⎢ ⎢⎡ 𝑣𝑐 , − 1 + 𝑣𝑐 , − 1 + 3600𝑐 , × 𝜆𝑐 ,450𝑇 ⎦⎥⎥ ⎥⎤ + 5 Equation 38-B23 Equation 38-B24

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Appendix B: On-Ramp Queue Spillback Analysis Chapter 38 System Analyses (Draft) Page 208 Version 1.0 ALL-WAY STOP-CONTROLLED (AWSC) INTERSECTIONS The methodology to evaluate queue spillback into AWSC intersections follows the approach developed for TWSC intersections. As shown in Exhibit 38- B13, after the capacities of individual movements during undersaturated conditions are computed (Step 12), the process described for TWSC intersections is performed by new steps 13A through D. The only step in the methodology that differs from the TWSC (13D) is described below. Step 13D – Compute spillback departure headway The AWSC methodology calculates the delay for each approach based on its departure headway instead of capacity. The estimated spillback capacity (cSB,i) is converted to a spillback headway hSB through the following equation: ℎ = 3600𝑐 , ROUNDABOUT RAMP TERMINALS The core methodology presented in Chapter 22 – Roundabouts is shown in Exhibit 38-B14. The additional steps proposed to the methodology are marked in blue. Each of the steps added and modified is discussed in the following Exhibit 38-B13 AWSC Intersections Core Methodology With Adjustments to Address On- Ramp Queue Spillback Equation 38-B25

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Appendix B: On-Ramp Queue Spillback Analysis Version 1.0 Page 209 paragraphs. This methodology is applicable only to single-lane roundabouts. Exhibit 22-9 and Exhibit 38-B15 provide the required input data and potential data sources for roundabout motorized vehicle analysis. Exhibit 38-B14 Roundabouts Methodology With Adjustments to Address On-Ramp Queue Spillback

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Appendix B: On-Ramp Queue Spillback Analysis Chapter 38 System Analyses (Draft) Page 210 Version 1.0 Required Data and Units Potential Data Source Suggested Default Onramp Data On-ramp metering rate (veh/h) Design plans, Field data Must be provided On-ramp storage length LONR(ft) Field data Must be provided Roundabout Data Departure saturation headway into the on-ramp hs (s/veh) Field data 3s/veh Step 13 – Compute the maximum throughput into the on-ramp for every movement The maximum throughput into the on-ramp per movement is calculated using the roundabout priority order in a counterclockwise order starting from the most upstream approach from the on-ramp exit leg. The Rank 1 approach (Exhibit 38-B16) is the one whose flow has the highest priority, given it enters the circulating stream upstream of all other approaches). The next priority movement is the Rank 2 approach, and the last is the Rank 3 approach. Next, the methodology calculates the capacity of the roundabout’s exit lane into the on-ramp. Previous research ( [4] [5]) suggests that the capacity of an exit lane, accounting for pedestrian and bicycle traffic in a typical urban area, is in the range of 1,200 to 1,300 vehicles per hour. Starting from the approach with Rank 1, and proceeding counterclockwise with the rest of the approaches, the capacity for each approach is used to determine the maximum throughput for every movement discharging to the on-ramp. Rank 1 – SB approach. The Rank 1 approach has priority over the other movements connecting to the on-ramp because it enters the circulating stream first. Also, because the on-ramp does not have an approach into the roundabout, the Rank 1 movement is most often unopposed by the circulating stream (except for occasional U-turns along the arterial). Therefore, the maximum throughput λSB-ONR (veh/h) for this left-turn movement is limited by its own lane capacity (cSB) and the maximum throughput to the on-ramp, and it is given by: 𝜆 = 𝑚𝑖𝑛 𝑣 , 𝑐 × 𝑝 , 3,600ℎ Exhibit 38-B15 Required Data and Potential Data Sources – Roundabout Spillback Evaluation Exhibit 38-B16 Priority Order for a Roundabout Upstream of an On-Ramp Equation 38-B26

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Appendix B: On-Ramp Queue Spillback Analysis Version 1.0 Page 211 where λSB-ONR = departure rate from the SB approach into the on-ramp (veh/h) vSB-ONR = demand flow rate for the SB approach into the on-ramp (veh/h) cSB = lane capacity for SB approach (veh/h) (HCM Equation 22-21) pSB-ONR= percent of demand from SB approach into the on-ramp hs = departure saturation headway into the on-ramp (s/veh) Rank 2 – EB approach. The maximum throughput for this Rank 2 movement is limited by its own lane capacity (cEB), as defined in HCM Equations 22-21 through 22-23, and the maximum throughput after considering the departure rate of the upstream Leg 1. Therefore, the maximum throughput λEB-ONR (veh/h) for this movement is given by: 𝜆 = 𝑚𝑖𝑛 𝑣 , 𝑐 × 𝑝 , 3,600ℎ − 𝜆 where λEB-ONR = departure rate from the EB approach into the on-ramp (veh/h) vEB-ONR = demand flow rate for the EB approach into the on-ramp (veh/h) cEB = lane capacity for EB approach (veh/h) (HCM Equation 22-21) pEB-ONR = percent of demand from the EB approach into the on-ramp, Rank 3 – NB approach. Similar to rank 2 movements, the maximum throughput for the NBR (i.e., NB-ONR) movement is limited by its own lane capacity (𝑐 ), as defined in HCM Equation 22-21 through Equation 22-23, and the maximum throughput to the on-ramp after considering departure rates from the upstream approaches. Therefore, the maximum throughput (λNB-ONR) for this right-turn movement is given by: 𝜆 = 𝑚𝑖𝑛 𝑣 , 𝑐 × 𝑝 , 3,600ℎ − 𝜆 − 𝜆 where λNB-ONR = departure rate from the NB approach into the on-ramp (veh/h) vNB-ONR = demand flow rate for the NB approach into the on-ramp (veh/h) cNB = lane capacity for NB approach (veh/h) (HCM Equation 22-21) pNB-ONR = percent of demand from the NB approach into the on-ramp The total on-ramp demand flow rate can be similarly calculated if there are additional approaches to the roundabout. Equation 38-B27 Equation 38-B28

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Appendix B: On-Ramp Queue Spillback Analysis Chapter 38 System Analyses (Draft) Page 212 Version 1.0 Step 14 – Calculate the throughput into the on-ramp The maximum throughput from the roundabout to the on-ramp, 𝜆 is calculated as: 𝜆 = 𝜆 + 𝜆 + 𝜆 Step 15 – Compute on-ramp merging capacity and compare to the maximum throughput to the on-ramp The calculation of the on-ramp merging capacity follows the exact same procedure used in Step 7B of the methodology developed for queue spillback into Signalized Intersections (Exhibit 38-B5). The maximum number of vehicles that can merge into the on-ramp cmerge (estimated using Equation 25-18) is compared to the maximum throughput from the roundabout to the on-ramp, 𝜆 . If cmerge ≤ λONR, then spillback is not expected to occur, and no adjustments are necessary in the procedure. If cmerge > λONR, queues will develop along the on- ramp, and spillback may occur if the queue storage is insufficient. The analyst must then proceed to Step 17 to evaluate the on-ramp Queue Storage Ratio to evaluate whether spillback will occur. Step 17 – Determine the on-ramp storage ratio and queue spillback length With the exit flow rate into the on-ramp (λ ), the expected queue length QONR along the on-ramp during a 15-minute period analysis is: 𝑄 = 𝜆 − 𝑐4 If a multi-period analysis is performed, the queue length for the current time period p must be added to the queue length obtained from the previous time period: 𝑄 , = 𝑄 , + 𝜆 , − 𝑐 ,4 The on-ramp storage ratio is calculated by dividing the available on-ramp storage LR (ft) by the average vehicle spacing , 𝐿 (Equation 31-155): 𝑅 = 𝐿 × 𝑄𝐿 If the on-ramp storage ratio (R ) is greater than 1, queues will form along each approach due to spillback. The value of RQ corresponds to the specific analysis period. If congestion is expected, but RQ < 1 for a single analysis period, multi-period analysis may have to be conducted. Step 18 – Compute the queue spillback distribution per approach When spillback occurs, the total number of vehicles queued during a 15- minute time period analysis (𝑄 ) is calculated as: 𝑄 = 𝑄 − 𝐿 × 𝐿 These queues are assumed to be distributed proportional to the demand flow rates to the on-ramp per approach and added to the 95th percentile queues estimated for the undersaturated conditions (Equation 22-20): Equation 38-B29 Equation 38-B30 Equation 38-B31 Equation 38-B32 Equation 38-B33

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Appendix B: On-Ramp Queue Spillback Analysis Version 1.0 Page 213 𝑄 , = 𝑄 × 𝜆 𝜆 + 𝑄 , 𝑄 , = 𝑄 × 𝜆 𝜆 + 𝑄 , 𝑄 , = 𝑄 × 𝜆 𝜆 + 𝑄 , Where 𝑄 , = queue due to the on-ramp spillback on 𝑖 approach (veh) λ , = maximum throughput for 𝑖 approach into the on-ramp (veh) 𝑄 , = 95th percentile queue on 𝑖 approach (veh) Step 19. Calculate the average control delay per approach To estimate the average delay per approach, the delay due to the on-ramp capacity limitation is estimated and added to the approach control delay calculated in Step 9 (Chapter 22). As indicated in Chapter 22, it is recommended to estimate the approach average control delay through Equation 22-17. Equation 22-17 assumes no residual queue at the start of the analysis period. If queue spillback occurs, the average control delay is significantly affected by the analysis period length. However, Chapter 22 – Roundabouts does not provide a multiperiod analysis method. Therefore, the delay results may not be accurate when there is a queue at the start of the analysis period. However, an iterative process that carries over queues from one time period to the next may be considered [6]. The additional delay (in sec/veh) due to the on-ramp spillback is calculated as follows: 𝑑 = 3600𝑐 + 900𝑇 ⎣⎢⎢ ⎢⎡ 𝜆𝑐 − 1 + 𝜆𝑐 − 1 + 3600𝑐 × 𝜆𝑐450𝑇 ⎦⎥⎥ ⎥⎤ + 5 × 𝑚𝑖𝑛 𝜆𝑐 , 1 where c =merging capacity of the on-ramp (veh/h); λ = exit flow rate into the on-ramp (veh/h); and t = time period (h) (T = 0.25 h for a 15-min analysis). Equation 38-B34 Equation 38-B35 Equation 38-B36 Equation 38-B37

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Appendix C: Lane-by-Lane Analysis for freeway facilities Chapter 38 System Analyses (Draft) Page 214 Version 1.0 APPENDIX C: LANE-BY-LANE ANALYSIS FOR FREEWAY FACILITIES LANE-BY-LANE FLOW MODELS BY SEGMENT TYPE The lane flow ratio (LFR) model for each lane is estimated as a function of the logarithm of the segment volume-capacity ratio (v/c). Additional details on the development of the model is available in [1]. The LFR equation is applied to each lane in the segment except for the leftmost lane, which is estimated as the remaining flow, to ensure the sum of the flow shares from each lane always equals 100%. The equations estimating LFR are as follows: 𝐿𝐹𝑅 = 𝑎 × 𝑙𝑛 𝑣𝑐 + 𝑏 𝐿𝐹𝑅 = 1 − 𝐿𝐹𝑅 where 𝑎 = multiplicative calibration parameter (Equation 38-C3, Equation 38-C5, and Equation 38-C7); 𝑏 = additive calibration parameter (Equation 38-C4, Equation 38-C6, and Equation 38-C8); 𝐿𝐹𝑅 = share of the total flow on lane 𝑖, where 𝑖 ranges from 1 to n-1 (n = total number of segment lanes); 𝐿𝐹𝑅 = share of the total flow on the leftmost lane (lane n); and 𝑣/𝑐 = volume/capacity ratio 0 < ≤ 1 . The model in Equation 38-C1 and Equation 38-C2 can be applied for basic, merge, diverge and weaving segments. For merge and diverge segments, the share of flow is estimated at the area upstream of the ramp. For weaving segments, the share of flow is estimated at the mainline upstream the on-ramp. Volume and capacity are given in veh/h. The calibration parameters 𝑎 and 𝑏 applicable in the analysis of basic segments are as follows: 𝑎 = 𝑎 + 𝐺 × 𝑎 + 𝑡 × 𝑎 + 𝑛 × 𝑎 𝑏 = 𝑏 + 𝐺 × 𝑏 + 𝑡 × 𝑏 + 𝑛 × 𝑏 For merge and diverge segments, the 𝑎 and 𝑏 parameters are as follows, with additional coefficients 𝑎 and 𝑏 to address ramp demand: 𝑎 = 𝑎 + 𝐺 × 𝑎 + 𝑡 × 𝑎 + 𝑛 × 𝑎 + 𝑣1,000 × 𝑎 𝑏 = 𝑏 + 𝐺 × 𝑏 + 𝑡 × 𝑏 + 𝑛 × 𝑏 + 𝑣1,000 × 𝑏 where 𝑎 = multiplicative calibration parameter; Equation 38-C1 Equation 38-C2 Equation 38-C3 Equation 38-C4 Equation 38-C5 Equation 38-C6

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Appendix C: Lane-by-Lane Analysis for freeway facilities Version 1.0 Page 215 𝑎 = empirical constant (Exhibit 38-C1); 𝑎 = empirical coefficient due to impact of grade (Exhibit 38-C1); 𝑎 = empirical coefficient due to impact of access point density (Exhibit 38- C1); 𝑎 = empirical coefficient due to impact of trucks (Exhibit 38-C1); 𝑎 = empirical coefficient due to impact of ramp flow (Exhibit 38-C1); 𝑏 = additive calibration parameter; 𝑏 = empirical constant (Exhibit 38-C1); 𝑏 = empirical coefficient due to impact of grade (Exhibit 38-C1); 𝑏 = empirical coefficient due to impact of access point density(Exhibit 38- C1); 𝑏 = empirical coefficient due to impact of trucks (Exhibit 38-C1); 𝑏 = empirical coefficient due to impact of ramp flow (Exhibit 38-C1); 𝐺 = grade (%); 𝑛 = access point density – number of ramps half a mile upstream and half mile downstream; 𝑡 = truck percentage (%); and 𝑣 = ramp flow (vph). The adjustment factors for the weaving segments address the effect of weaving-specific properties: 𝑎 = 𝑎 + 𝐺 × 𝑎 + 𝑡 × 𝑎 + 𝐼𝐷 × 𝑎 + 𝑣 ,1,000 × 𝑎 + 𝑣 ,1,000 × 𝑎 + 𝐿1,000 × 𝑎+ 𝑉𝑅 × 𝑎 𝑏 = 𝑏 + 𝐺 × 𝑏 + 𝑡 × 𝑏 + 𝐼𝐷 × 𝑏 + 𝑣 ,1,000 × 𝑏 + 𝑣 ,1,000 × 𝑏 + 𝐿1,000 × 𝑏+ 𝑉𝑅 × 𝑏 where 𝑎 = empirical coefficient due to impact of interchange density; 𝑎 = empirical coefficient for length of the weaving segment (Exhibit 38- C2); 𝑎 = empirical coefficient for off-ramp flow (Exhibit 38-C2); 𝑎 = empirical coefficient for on-ramp flow (Exhibit 38-C2); 𝑎 = empirical coefficient for volume ratio (Exhibit 38-C2); 𝐼𝐷 = interchange density, as defined in Chapter 13; 𝑏 = empirical coefficient due to impact of interchange density; 𝑏 = empirical coefficient for length of the weaving segment (Exhibit 38- C2); 𝑏 = empirical coefficient for off-ramp flow (Exhibit 38-C2); 𝑏 = empirical coefficient for on-ramp flow (Exhibit 38-C2); Equation 38-C7 Equation 38-C8 Interchange density, according to Chapter 13, is the number of interchanges within 3 mi upstream and downstream of the center of the subject weaving segment divided by 6, in interchanges per mile (int/mi).

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Appendix C: Lane-by-Lane Analysis for freeway facilities Chapter 38 System Analyses (Draft) Page 216 Version 1.0 𝑏 = empirical coefficient for volume ratio (Exhibit 38-C2); 𝐿 = length of the weaving segment (ft); 𝑉𝑅 = volume ratio (weaving volume/total volume); 𝑣 , = off-ramp flow (veh/h); 𝑣 , = on-ramp flow (veh/h); and The remaining factors have been defined previously. The empirical constants (𝑎 , 𝑏 , and the calibration parameters 𝑎 and 𝑏) are specific for each combination of segment type, lane number and total number of lanes. The values for basic, merge and diverge segments are presented in Exhibit 38-C1, and the values for weaving segments are presented in Exhibit 38-C2. Lane # Parameter Basic Segment Lanes Diverge Segment Lanes Merge Segments Lanes 2 3 4 2 3 4 2 3 4 L1 𝑎 0.18 0.027 0.068 0.0097 -0.075 0.31 0.015 0.0029 -0.077 𝑏 0.52 0.27 0.22 0.44 0.27 0.25 0.59 0.28 0.24 𝑎 0.024 0.021 -0.011 0.0097 0.0077 -0.034 0.015 -0.0029 -0.0030 𝑎 -0.048 -0.0036 -0.0021 -0.0093 0.00080 -0.057 -0.0093 -0.0029 0.011 𝑎 -0.095 -0.0083 -0.059 -0.0097 0.014 -0.028 -0.0047 -0.0029 0.014 𝑏 0.0030 0.0097 -0.034 -0.0098 -0.0081 -0.00016 0.020 0.031 0.040 𝑏 0.008 -0.0029 0.0024 0.0078 0.0014 -0.019 -0.014 -0.0018 -0.027 𝑏 0.0013 0.032 -0.035 0.00057 0.031 0.0052 -0.040 -0.042 -0.041 𝑎 -0.21 -0.067 -0.0087 -0.035 -0.10 0.026 𝑏 -0.13 0.013 -0.021 -0.070 -0.030 0.0091 L2 𝑎 -0.063 -0.025 0.0096 0.29 -0.0082 -0.080 𝑏 0.31 0.29 0.34 0.25 0.38 0.24 𝑎 -0.0060 0.0015 -0.0096 -0.035 -0.0082 0.00048 𝑎 0.0011 0.00027 -0.00054 -0.052 -0.00082 0.013 𝑎 0.0037 -0.0085 -0.0096 -0.030 -0.0026 0.018 𝑏 -0.017 -0.024 -0.0019 0.0019 0.0079 -0.019 𝑏 0.0024 -0.00036 0.00089 -0.0041 -0.00048 -0.0067 𝑏 0.01 -0.041 0.0052 0.0044 -0.0060 0.0010 𝑎 -0.048 -0.0065 -0.12 -0.033 𝑏 -0.073 -0.0091 -0.039 -0.013 L3 𝑎 -0.045 0.27 0.029 𝑏 0.28 0.25 0.25 𝑎 -0.0017 -0.036 -0.0017 𝑎 0.0021 -0.044 -0.0058 𝑎 0.0081 -0.034 -0.0068 𝑏 0.011 0.0034 0.00060 𝑏 -0.0011 0.0092 0.014 𝑏 0.015 0.0016 0.018 𝑎 0.021 -0.079 𝑏 -0.0064 -0.041 The calibrated values for weaving segments are presented in Exhibit 38-C2. Exhibit 38-C1 Adjustment Factors for Lane Flow Distribution on Basic, Merge and Diverge Segments

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Appendix C: Lane-by-Lane Analysis for freeway facilities Version 1.0 Page 217 Para- meter 2-Lane Segments 3-Lane Segments 4-Lane Segments L1 L1 L2 L1 L2 L3 𝑎 0.99 0.64 0.48 -0.13 0.0048 0.12 𝑏 0.40 0.40 0.33 0.24 0.26 0.27 𝑎 -0.21 -0.28 0.11 0.13 -0.0048 -0.12 𝑎 -0.12 -0.055 -0.033 -0.012 -0.0048 0.019 𝑎 0.13 0.0037 -0.035 -0.0025 -0.0048 -0.12 𝑎 0.022 0.075 -0.090 0.072 -0.031 -0.011 𝑎 -0.19 -0.036 0.017 -0.13 0.030 0.051 𝑎 -0.20 0.098 -0.031 0.056 0.0020 -0.041 𝑎 0.0080 0.024 0.089 -0.11 -0.0045 0.12 𝑏 0.069 -0.40 0.039 -0.030 0.045 0.041 𝑏 0.0032 -0.051 0.0045 -0.0043 -0.011 -0.0043 𝑏 -0.016 0.40 -0.020 -0.0067 -0.0050 -0.0026 𝑏 -0.048 -0.14 0.0047 0.065 -0.0089 -0.038 𝑏 0.040 0.039 -0.047 0.063 -0.015 -0.037 𝑏 -0.011 0.15 0.0050 -0.030 0.011 0.020 𝑏 0.078 0.40 0.018 -0.14 0.040 0.15 Notes: The number of lanes parameter represents the freeway section upstream of the weave. Lanes connecting the on-ramp and off-ramp are not included. LFR distribution as function of demand-to-capacity ratio As discussed in the previous section, LFR is obtained as a function of a series of operational factors. From these, the most influencing factor is the demand-to- capacity ratio, as research [7] shows that LFR distributions follow typical patterns depending on the number of lanes. Exhibit 38-C3 demonstrates that, for 2-lane segments, flow distribution follows a “scissors” pattern, with the flow highly concentrated in lane 1 during free-flow conditions. As the demand flow rate for the segment increases, flow gradually migrates to lane 2. During oversaturated conditions, flow is more concentrated in lane 2. Exhibit 38-C2 Adjustment Factors for Lane Flow Distribution on Weaving Segments

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Appendix C: Lane-by-Lane Analysis for freeway facilities Chapter 38 System Analyses (Draft) Page 218 Version 1.0 Next, Exhibit 38-C4 illustrates the LFR distribution for a 3-lane freeway segment. At low demand most of the flow of 3-lane segments is concentrated in the center lane (lane 2), followed by lanes 1 and lane 3. As demand increases, lane flow distribution increases in lane 3, while decreasing in lanes 1 and 2. Exhibit 38-C5 shows the LFR distribution for 4-lane segments. At free-flow conditions, lanes 2 and 3 carry the majority of flow. Lane 4 is typically underused during undersaturated conditions, but for higher demands it carries the majority of flow. The flow distribution patterns shown in the previously exhibits for basic segments are also observed in merge, diverge and weaving segments. Additional Exhibit 38-C3 LFR Distribution for a Sample 2-Lane Segment (Minneapolis/MN) Exhibit 38-C4 LFR Distribution for a Sample 3-Lane Segment (Tampa/FL) Exhibit 38-C5 LFR Distribution for a Sample 4-Lane Segment (Tampa/FL)

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Appendix C: Lane-by-Lane Analysis for freeway facilities Version 1.0 Page 219 factors such as ramp volume, grade, truck percentage influence the boundary values and slopes of the curves, but does not change the typical LFR distribution as function of v/c. Checking for Negative Flows and Lane Capacities After lane flow ratios are obtained, a two-step check must be performed to ensure the estimated flow distribution is reasonable. The first check identifies any estimated negative flows. This issue is more likely to occur in the leftmost lane, as the flows on this lane are obtained by the difference between the total segment flow and the sum of estimated flows in the other lanes. Therefore, if flows on the remaining lanes are overestimated the resulting flow in the leftmost lane may become negative. Exhibit 38-C6 illustrates the procedure for this check. The variables in Exhibit 38-C6 are defined as follows: 𝑖 = index for the subject lane; 𝐿𝐹𝑅 = lane flow ratio on lane i; 𝑣 = flow rate on lane i; ∆ = negative flow on lane i, to be relocated to all other lanes k ≠ i 𝑘 = index for a subject lane to where flow is being relocated 𝑣 = flow rate on lane k; 𝑛 = number of lanes in the segment The second check compares the estimated flow by lane with the respective lane capacities to ensure no lane operates with a demand-to-capacity ratio greater than 1. The procedure is illustrated in Exhibit 38-C7. If any lane is estimated to operate above its capacity, the flow in this given lane is constrained by the capacity value and the exceeding demand is moved to the adjacent lane. Exhibit 38-C6 Check for Negative Lane Flows

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Appendix C: Lane-by-Lane Analysis for freeway facilities Chapter 38 System Analyses (Draft) Page 220 Version 1.0 The variables in Exhibit 38-C7 are defined as follows: 𝑖 = index for the subject lane; 𝑐 = capacity for lane i; 𝑣 = flow rate on lane i; ∆ = exceeding flow on lane i, to be relocated to the adjacent lane 𝑛 = number of lanes in the segment SPEED FLOW CURVES BY LANE AND BY SEGMENT TYPE This section presents the models used to obtain speed-flow curves for each lane in a freeway segment, as a function of two key inputs: free-flow speed (FFS) and lane capacity. The first part discusses the estimation of lane FFS, while the second presents models for obtaining lane capacities. The last part provides the speed-flow models obtained as a function of lane FFS and lane capacities. Lane FFS Field observations have shown that speeds differ among lanes, and they are typically lower in shoulder lanes and higher in median lanes. Models were developed to estimate individual lane FFS by applying a multiplying factor xFFS to the segment FFS. Exhibit 38-C8 summarizes the recommended multipliers which are provided as a function of the segment type and the number of lanes in the segment. As shown, when the number of lanes increases, the range of FFS multipliers increase as well (i.e. there are lower speeds in the shoulder lanes and higher speeds on the median lanes). For 2-lane segments, merge and diverge segments have a higher difference in FFS between the two lanes when compared to basic segments. For 3-lane segments, basic segments show the highest FFS range, while merge segments have more uniform lane FFS. As for 4-lane segments, merge segments show the highest FFS range, followed by basic and merge segments yield similar results. Exhibit 38-C7 Check for Lane Capacity

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Appendix C: Lane-by-Lane Analysis for freeway facilities Version 1.0 Page 221 Segment Type Number of Lanes FFS Multiplier (xFFS) L1 L2 L3 L4 Basic 2 lanes 0.965 1.032 - - 3 lanes 0.934 1.010 1.087 - 4 lanes 0.924 0.989 1.028 1.079 Merge 2 lanes 0.964 1.044 - - 3 lanes 0.955 1.015 1.045 - 4 lanes 0.935 0.991 1.036 1.091 Diverge 2 lanes 0.961 1.035 - - 3 lanes 0.943 1.024 1.068 - 4 lanes 0.933 0.975 1.018 1.074 Weaving 2 lanes 0.969 1.018 - - 3 lanes 0.968 1.023 1.062 - 4 lanes 0.910 0.988 1.053 1.110 The free-flow speed for each lane i is then computed as follows: 𝐹𝐹𝑆 = 𝐹𝐹𝑆 × 𝑥 where 𝐹𝐹𝑆 = free-flow speed for lane i (mi/h); 𝐹𝐹𝑆 = adjusted free-flow speed for the segment average (mi/h) (Equation 12- 5). 𝑥 = FFS multiplier (Exhibit 38-C8); Capacity for Speed Flow Curves by Lane Similar to free-flow speeds, capacities differ among lanes, and they are typically lower in shoulder lanes and higher in median lanes. Center lanes typically have values similar to the segment average. For weaving segments, capacity distributions were observed to be significantly more complex and the breakdown method does not provide reliable results. Capacity is assumed uniform for all lanes within a weaving segment, obtained by Equation 13-5 (based on a maximum density of 43 pc/h/ln): 𝑐 = 𝑐 − [438.2 (1 + 𝑉𝑅) . ] + (0.0765 𝐿 ) + (119.8𝑁 ) where 𝑐 = capacity (per lane) of the weaving segment under equivalent ideal conditions (pc/h/ln); 𝑐 = capacity (per lane) of a basic freeway segment with the same FFS as the weaving segment under equivalent ideal conditions (pc/h/ln). 𝑉𝑅 = volume ratio; 𝐿 = length of weaving segment (ft); and 𝑁 = number of lanes from which weaving maneuvers may be made with either one or no lane changes. Exhibit 38-C9 presents the percent distribution of the total segment capacity across lanes, defining a capacity multiplier xc for each combination of segment type and number of lanes. Exhibit 38-C8 Multipliers to Estimate Lane FFS from Segment FFS Equation 38-C9 Equation 38-C10

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Appendix C: Lane-by-Lane Analysis for freeway facilities Chapter 38 System Analyses (Draft) Page 222 Version 1.0 Segment Type Number of Lanes Capacity Multiplier (xc) L1 L2 L3 L4 Basic 2 lanes 0.44 0.56 3 lanes 0.25 0.35 0.40 4 lanes 0.19 0.25 0.28 0.28 Merge 2 lanes 0.42 0.58 3 lanes 0.23 0.36 0.41 4 lanes 0.21 0.24 0.25 0.30 Diverge 2 lanes 0.42 0.58 3 lanes 0.26 0.34 0.40 4 lanes 0.21 0.24 0.27 0.28 * Lane capacity on weaving segments is assumed to be equal across all lanes (Equation 38-C10) The segment capacities measured from field data may not be equal to the estimated capacities using HCM methodologies. According to the HCM Equation 12-6, the base capacity can be estimated as: c = min[2200 + 10 × (FFS − 50), 2400] The adjusted capacity of a segment is obtained through Equation 12-8: c = 𝑐 × 𝐶𝐴𝐹 The capacity for each lane i is computed as: 𝑐 = 𝑐 × 𝑁 × 𝑥 where 𝑐 = capacity of lane i (pc/h/ln); 𝑐 = adjusted capacity for the segment average (pc/h/ln) (Equation 12-8). 𝑁 = number of lanes in the segment 𝑥 = capacity multiplier (Exhibit 38-C9); Field measurements of capacity have been found to be lower than HCM estimates [8]. Such differences can result in overestimating the overall performance of a segment. Therefore, it is recommended that capacity adjustment factors (CAFs) are applied to adjust the estimated capacities to local conditions. With flow, capacity and FFS by lane determined, HCM equations can be used to estimate the speeds on individual lanes. Segment-wise inputs of flow, capacity and FFS are based on the field measurements, and the methods previously described are applied to estimate their distribution among individual lanes. Speed on each lane i is determined as: 𝑆 = 𝐹𝐹𝑆 − 𝐹𝐹𝑆 − 𝑐45 (𝑣 − 𝐵𝑃 )(𝑐 − 𝐵𝑃 ) where 𝐵𝑃 = breakpoint value on lane i (pc/h/ln) (Equation 38-C15); 𝑐 = capacity on lane i (pc/h/ln) (Equation 38-C13); Exhibit 38-C9 Capacity of Individual Lanes as a Percentage of Segment Capacity, by Segment Type and Number of Lanes Equation 38-C11 Equation 38-C12 Equation 38-C13 Equation 38-C14

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Appendix C: Lane-by-Lane Analysis for freeway facilities Version 1.0 Page 223 𝐹𝐹𝑆 = free-flow speed on lane i(mi/h); 𝑆 = speed (mi/h) on lane i; and 𝑣 = demand flow rate on lane i (pc/h/ln), with 𝑣 = 𝑣 × 𝐿𝐹𝑅 . This model is applied to individual lanes, as the three key parameters (𝐹𝐹𝑆, 𝑐 and 𝑣 ) are input by lane. The breakpoint value (𝐵𝑃) is also determined for each lane: 𝐵𝑃 = [1000 + 40 × (75 − 𝐹𝐹𝑆 )] × 𝐶𝐴𝐹 where 𝐵𝑃 = breakpoint value (pc/h/ln); 𝐹𝐹𝑆 = adjusted free-flow speed (mi/h); and 𝐶𝐴𝐹 = capacity adjustment factor. Equation 38-C15

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Appendix C: Lane-by-Lane Analysis for freeway facilities Chapter 38 System Analyses (Draft) Page 224 Version 1.0 APPLICATION EXAMPLES Example 1 - Diverge Segment from Example Problem 1 This section presents an application of the LFR model for a freeway segment extracted from Example Problem 1 (O-D Based Travel Time Estimation for I-75 NB Freeway in Gainesville, FL). A 3-lane diverge segment (segment 16 of the freeway facility) was selected for lane-by-lane analysis, with the following input data: • Grade (𝐺): 1%; • Heavy vehicles (𝑡): 2%; • PHF = 1.0 • Access point density (𝑛): 1 adjacent ramp; • Mainline hourly demand volume (𝑉): 4848 veh/h; • Capacity adjustment factor (CAF): 1.0 • Off-ramp demand (𝑣 ): 960 veh/h; and • Measured segment capacity (𝑐): 2400 pc/h/ln (7200 veh/h). The mainline hourly demand volume (veh/h) is first converted to a demand flow rate under equivalent base conditions, with a fHV = 0.969: 𝑣 = 𝑉𝑃𝐻𝐹 × 𝑓 = 48481.0 × 0.969 = 5003.1 pc/h The flow ratio for lane 1 (right lane) is obtained by the following equation: 𝐿𝐹𝑅 = 𝑎 × 𝑙𝑛 𝑣𝑐 + 𝑏 The calibration parameters 𝑎 and 𝑏 for lane 1 are obtained as follows: 𝑎 = 𝑎 + 𝐺 × 𝑎 + 𝑡 × 𝑎 + 𝑛 × 𝑎 + 𝑣1000 × 𝑎 𝑎 = −0.075 + 1 × 0.0077 + 2 × 0.0008 + 0 × 0.014 + 9601000 × (−0.067) 𝑎 = −0.116 𝑏 = 𝑏 + 𝐺 × 𝑏 + 𝑡 × 𝑏 + 𝑛 × 𝑏 + 𝑣1000 × 𝑏 𝑏 = 0.26667 + 1 × (−0.00810)+ 2 × 0.00140 + 1 × 0.03129 + 9601000× 0.01324 𝑏 = 0.296 The flow rate on lane 1 can then be obtained by: 𝐿𝐹𝑅1 = −0.116 × 𝑙𝑛 50037200 + 0.296 = 𝟎.𝟑𝟓𝟎 The same procedure is applied to obtain the flow rate on lane 2, using the respective coefficients from Exhibit 38-C1: 𝑎 = 𝑎 + 𝐺 × 𝑎 + 𝑡 × 𝑎 + 𝑛 × 𝑎 + 𝑣1000 × 𝑎

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Appendix C: Lane-by-Lane Analysis for freeway facilities Version 1.0 Page 225 𝑎 = 0.0096 + 1 × (−0.00960)+ 2 × (−0.00054)+ 1 × (−0.0096)+ 9601,000× (−0.048) 𝑎 = −0.0568 𝑏 = 𝑏 + 𝐺 × 𝑏 + 𝑡 × 𝑏 + 𝑛 × 𝑏 + 𝑣1000 × 𝑏 𝑏 = 0.34 + 1 × (−0.0019)+ 2 × (0.00089)+ 1 × 0.0052 + 9601,000 × (−0.073) 𝑏 = 0.275 𝐿𝐹𝑅 = −0.0568 × 𝑙𝑛 50037200 + 0.275 = 𝟎.𝟐𝟗𝟔 Finally, the flow rate on the leftmost lane (lane 3) can be obtained as: 𝐿𝐹𝑅 = 1 − 𝐿𝐹𝑅 − 𝐿𝐹𝑅 = 1 − 0.350 − 0.296 𝐿𝐹𝑅 = 𝟎.𝟑𝟓𝟒 Lane flows can be obtained by multiplying the segment demand by respective LFR values for each lane: 𝑣 = v × 𝐿𝐹𝑅 = 5003.1 × 0.350 = 1753.2 pc/h/ln 𝑣 = v × 𝐿𝐹𝑅 = 5003.1 × 0.296 = 1482.6 pc/h/ln 𝑣 = v × 𝐿𝐹𝑅 = 5003.1 × 0.354 = 1767.3 pc/h/ln Speed calculations Individual free-flow speeds for each lane can be obtained by multiplying the segment FFS (75.4 mi/h) by the corresponding multipliers (Exhibit 38-C6) as follows: 𝐹𝐹𝑆 = 𝐹𝐹𝑆 × 0.943 = 75.4 × 0.943 = 71.1 mph 𝐹𝐹𝑆 = 𝐹𝐹𝑆 × 1.024 = 75.4 × 1.024 = 77.2 mph 𝐹𝐹𝑆 = 𝐹𝐹𝑆 × 1.064 = 75.4 × 1.068 = 80.5 mph Applying factors to the segment capacity, individual lane capacities can be obtained as follows: 𝑐 = 𝑐 × 0.26 = 7200 × 0.26 = 1872 pc/h 𝑐 = 𝑐 × 0.34 = 7200 × 0.34 = 2448 pc/h 𝑐 = 𝑐 × 0.40 = 7200 × 0.40 = 2880 pc/h Breakpoint values for each lane can be obtained: BP1 = [1000+ 40 x (75‐FFS1)] x CAF2 = [1000+ 40 x (75‐71.10)] x 1 = 1156 pc/h BP2 = [1000+ 40 x (75‐FFS2)] x CAF2 = [1000+ 40 x (75‐77.21)] x 1 = 911.6 pc/h BP3 = [1000+ 40 x (75‐FFS3)] x CAF2 = [1000+ 40 x (75‐80.23)] x 1 = 778.9 pc/h Average speed of each lane can be obtained by applying Equation 38-C9 to each lane:

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Appendix C: Lane-by-Lane Analysis for freeway facilities Chapter 38 System Analyses (Draft) Page 226 Version 1.0 𝑆 = 𝐹𝐹𝑆 − 𝐹𝐹𝑆 − 𝑐45 (𝑣 − 𝐵𝑃 )(𝑐 − 𝐵𝑃 ) 𝑆 = 71.1 − 71.1 − 187245 (1753.2 − 1156)(1872 − 1156) = 50.6 mi/h 𝑆 = 77.2 − 77.2 − 244845 (1482.6 − 911.6)(2448 − 911.6) = 74.1 mi/h 𝑆 = 80.5 − 80.5 − 288045 (1767.3 − 778.9)(2880 − 778.9) = 76.8 mi/h The obtained speed-flow curves for each lane are presented and compared to the segment-wise curve in Exhibit 38-C10: Example 2 - Weaving Segment This section presents an application of the LFR model for a weaving segment (Exhibit 38-C11) to estimate the upstream lane flow shares. The following input data is provided: • Number of lanes within the weave (𝑁): 5; • Number of upstream lanes (NUP ): 4; • Grade (𝐺): -0.5%; • Heavy vehicles (𝑡): 3.3%; Exhibit 38-C10 Comparison of Speed-Flow Curves for Each Lane and for the Segment Exhibit 38-C11 Example of LFR Calculation for a Weaving Segment

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Appendix C: Lane-by-Lane Analysis for freeway facilities Version 1.0 Page 227 • Interchange density (𝐼𝐷): 0.67; • Weaving length (𝐿 ): 3920 ft; • Upstream mainline demand flow rate (𝑣 ): 4512 veh/h; • On-ramp demand flow rate (𝑣 , ): 428 veh/h; • Freeway-to-freeway demand (𝑣 ): 3312 veh/h; • Freeway-to-ramp demand (𝑣 ): 1200 veh/h; • Ramp-to-freeway demand (𝑣 ): 404 veh/h; • Ramp-to-ramp demand (𝑣 ): 24 veh/h; • Off-ramp flow rate (𝑣 , ): 1224 veh/h; • Number of weaving lanes (𝑁 ): 2 lanes; • Measured segment free-flow speed (FFS): 70 mi/h; and • PHF = 1.0. The heavy-vehicles adjustment factor can be estimated as (for 𝐸 = 2) 𝑓 = 11 + 𝑃 (𝐸 − 1) = 11 + 0.03(2 − 1) = 0.968 The weaving and non-weaving demands can be adjusted to flow rates under ideal conditions. Because the demands are estimated based on 15-minute intervals, it is assumed that PHF is equal to 1. 𝑣 = 𝑉𝑃𝐻𝐹 × 𝑓 𝑣 = 241 × 0.968 = 24.8 𝑝𝑐/ℎ 𝑣 = 4041 × 0.968 = 417.3 𝑝𝑐/ℎ 𝑣 = 12001 × 0.968 = 1,239.6 𝑝𝑐/ℎ 𝑣 = 3312 1 × 0.968 = 3,421.3 𝑝𝑐/ℎ The weaving and non-weaving flows are given by: 𝑣 = 𝑣 + 𝑣 = 1,239.6 + 417.3 = 1,656.9 𝑝𝑐/ℎ 𝑣 = 𝑣 + 𝑣 = 24.8 + 3,421.3 = 3,446.1 𝑝𝑐/ℎ The volume ratio can be computed as: 𝑉𝑅 = 𝑣𝑣 = 1,656.91,656.9 + 3,446.1 = 0.325 The capacity for a weaving segment is given by the minimum between the density-capacity (𝑐 , from HCM Equation 13-5) and weaving-demand-capacity (𝑐 , from HCM Equation 13-7): 𝑐′ = 𝑐 − [438.2(1 + 𝑉𝑅) . ] + (0.0765𝐿 )+ (119.8𝑁 ) 𝑐 = 2,400 𝑝𝑐/ℎ

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Appendix C: Lane-by-Lane Analysis for freeway facilities Chapter 38 System Analyses (Draft) Page 228 Version 1.0 𝑐′ = 2,400 − [438.2(1 + 0.325) . ] + (0.0765 × 3,920)+ (119.8 × 2)= 2,252.3 𝑝𝑐/ℎ/𝑙𝑛 𝑐 = 𝑐′ × 𝑓 = 2,252.3 × 0.968 = 2,180.4 𝑣𝑒ℎ/ℎ/𝑙𝑛 𝑐′ = 2,400𝑉𝑅 = 2,4000.325 = 7,391.5 𝑝𝑐/ℎ 𝑐 = 𝑐′ × 𝑓𝑁 = 7,391.5 × 0.9684 = 1,788.8 𝑣𝑒ℎ/ℎ/𝑙𝑛 𝑐 = 𝑚𝑖𝑛(𝑐 , 𝑐 ) = 𝑚𝑖𝑛(2,180.4, 1,788.8) = 1,788.8 𝑣𝑒ℎ/ℎ/𝑙𝑛 The estimated capacity is 1,788.8 veh/h/ln. The flow ratio for lane 1 (right lane) is obtained by the following equation: 𝐿𝐹𝑅 = 𝑎 × 𝑙𝑛 𝑣𝑐 + 𝑏 The calibration parameters 𝑎 and 𝑏 for lane 1 are obtained as follows: 𝑎 = 𝑎 + 𝐺 × 𝑎 + 𝑡 × 𝑎 + 𝐼𝐷 × 𝑎 + 𝑣 ,1000 × 𝑎 + 𝑣 ,1000 × 𝑎 + 𝐿1000 × 𝑎+ 𝑉𝑅 × 𝑎 𝑎 = −0.13 + (−0.5)× 0.13 + (3.3) × (−0.012)+ 0.67 × (−0.0025)+ , ×0.072 + ,, × (−0.13)+ ,, × (0.056)+ 0.325 × (−0.11) 𝑎 = −0.1843 𝑏 = 𝑏 + 𝐺 × 𝑏 + 𝑡 × 𝑏 + 𝐼𝐷 × 𝑏 + 𝑣 ,1000 × 𝑏 + 𝑣 ,1000 × 𝑏 + 𝐿1000 × 𝑏+ 𝑉𝑅 × 𝑏 𝑏 = 0.24 + (−0.5) × (−0.03)+ (3.3) × (−0.0043)+ 0.67 × (−0.0067)+ , × 0.065 + ,, × 0.063 + ,, × (−0.03)+ 0.32 × (−0.14) 𝑏 = 0.1790 The flow rate on lane 1 is estimated as: 𝐿𝐹𝑅 = −0.1843 × 𝑙𝑛 4,5124 × 1,788.8 + 0.1790 𝐿𝐹𝑅 = 𝟎.𝟐𝟔𝟒 The same procedure is applied to estimate the flow rate on lane 2, using the respective coefficients from Exhibit 38-C2: 𝑎 = 𝑎 + 𝐺 × 𝑎 + 𝑡 × 𝑎 + 𝐼𝐷 × 𝑎 + 𝑣 ,1000 × 𝑎 + 𝑣 ,1000 × 𝑎 + 𝐿1000 × 𝑎+ 𝑉𝑅 × 𝑎 𝑎 = 0.0048 + (−0.5) × (−0.0048)+ (3.3) × (−0.0048)+ 0.67 × (−0.0048)+ 4281000 × (−0.031)+ 12241000 × (0.03)+ 39201000 × (0.002)+ 0.325× (−0.0045)

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Appendix C: Lane-by-Lane Analysis for freeway facilities Version 1.0 Page 229 𝑎 = 0.0176 𝑏 = 𝑏 + 𝐺 × 𝑏 + 𝑡 × 𝑏 + 𝐼𝐷 × 𝑏 + 𝑣 ,1000 × 𝑏 + 𝑣 ,1000 × 𝑏 + 𝐿1000 × 𝑏+ 𝑉𝑅 × 𝑏 𝑏 = 0.26 + (−0.5) × (0.045)+ (3.3) × (−0.011)+ 0.67 × (−0.005)+ ×(−0.0089)+ × (−0.015)+ × (0.011)+ 0.325 × 0.04 𝑏 = 0.2271 The flow rate on lane 2 can then be obtained by: 𝐿𝐹𝑅 = 0.0176 × 𝑙𝑛 45124 × 1788.8 + 0.2271 𝐿𝐹𝑅 = 𝟎.𝟐𝟏𝟗 The same procedure is applied to obtain the flow rate on lane 3, using the respective coefficients from Exhibit 38-C2: 𝑎 = 𝑎 + 𝐺 × 𝑎 + 𝑡 × 𝑎 + 𝐼𝐷 × 𝑎 + 𝑣 ,1000 × 𝑎 + 𝑣 ,1000 × 𝑎 + 𝐿1000 × 𝑎+ 𝑉𝑅 × 𝑎 𝑎 = 0.12 + (−0.5) × (−0.12)+ (3.3) × 0.019 + 0.67 × (−0.12)+ 4281000× (−0.011)+ 12241000 × 0.051 + 39201000 × (−0.041)+ 0.325 × 0.12 𝑎 = 0.0985 𝑏 = 𝑏 + 𝐺 × 𝑏 + 𝑡 × 𝑏 + 𝐼𝐷 × 𝑏 + 𝑣 ,1000 × 𝑏 + 𝑣 ,1000 × 𝑏 + 𝐿1000 × 𝑏+ 𝑉𝑅 × 𝑏 𝑏 = 0.27 + (−0.5) × 0.041 + (3.3) × (−0.0043)+ 0.67 × (−0.0026)+ , ×(−0.038)+ ,, × (−0.037)+ ,, × 0.0198 + 0.325 × 0.15 𝑏 = 0.3010 The flow rate on lane 3 can then be obtained by: 𝐿𝐹𝑅 = 0.0985 × 𝑙𝑛 4,5124 × 1,788.8 + 0.3010 𝐿𝐹𝑅 = 𝟎.𝟐𝟓𝟔 Finally, the flow rate on the leftmost lane (lane 4) can be obtained as: 𝐿𝐹𝑅 = 1 − 𝐿𝐹𝑅 − 𝐿𝐹𝑅 − 𝐿𝐹𝑅 = 1 − 0.256 − 0.219 − 0.264 𝐿𝐹𝑅 = 𝟎.𝟐𝟔𝟏 Example 3 – Basic Segment A 2-lane basic segment was modeled, and the lane-by-lane performance is compared to field data (CA-1 NB – Santa Cruz/CA). Field measured parameters are as follows: • Free-flow speed: 69.1 mph; • Capacity: 3993 veh/h (1996.5 veh/h/ln); • % Heavy vehicles: 1.7; and

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Appendix C: Lane-by-Lane Analysis for freeway facilities Chapter 38 System Analyses (Draft) Page 230 Version 1.0 • Grade: 3% (rolling). By applying the multiplying factors obtained in Exhibit 38-C8 to the segment FFS, individual FFS can be obtained as follows: 𝐹𝐹𝑆1 = 𝐹𝐹𝑆 × 0.965 = 69.1 × 0.965 = 66.68 𝑚𝑝ℎ 𝐹𝐹𝑆2 = 𝐹𝐹𝑆 × 1.032 = 69.1 × 1.032 = 71.31 𝑚𝑝ℎ Next, lane capacities are obtained by applying the multiplying the factors obtained in Exhibit 38-C9 to the capacity as follows: 𝑐1 = 𝑐 × 44% = 3993 × 44% = 1757 𝑣𝑒ℎ/ℎ 𝑐2 = 𝑐 × 56% = 3993 × 56% = 2236 𝑣𝑒ℎ/ℎ For comparison purposes, HCM methods would obtain the following theoretical capacity: 𝑐 = [2200 + 10 × (𝐹𝐹𝑆 – 50)] × 𝑓𝐻𝑉 = [2200 + 10 × (69.1 − 50) )] × 0.967 = 2312 𝑣𝑒ℎ/ℎ/𝑙𝑛 Therefore, the recommended CAF for this location is obtained by dividing the field-measured by the theoretical values of capacity: 𝐶𝐴𝐹 = 𝑐 𝑐 = 1996.52312 = 0.864 Next, the breakpoint values for each lane can be obtained: 𝐵𝑃1 = [1000 + 40 × (75 − 𝐹𝐹𝑆1)] × 𝐶𝐴𝐹 = [1000 + 40 × (75 − 66.68)] × 0.864 𝐵𝑃1 = 995 𝑣𝑒ℎ/ℎ 𝐵𝑃2 = [1000 + 40 × (75 − 𝐹𝐹𝑆2)] × 𝐶𝐴𝐹 = [1000 + 40 × (75 − 71.31)] × 0.864 𝐵𝑃2 = 857 𝑣𝑒ℎ/ℎ Flows on each lane can be obtained by applying the model described in Equation 38-C1 to the flow rate entering the segment. Next, speeds on individual lanes can be obtained using the speed-flow relationship described in Equation 38-C8. For this location, a sample of 14690 observations (15-min each) was randomly selected, and then predicted values were compared to field data as shown in Exhibit 38-C12.

Highway Capacity Manual: A Guide for Multimodal Mobility Analysis Chapter 38 System Analyses (Draft) Appendix C: Lane-by-Lane Analysis for freeway facilities Version 1.0 Page 231 As observed, the individual speed-flow models can replicate field conditions with good accuracy. Naturally, the oversaturated portion of the speed-flow curve cannot be addressed by the model, as this is already a limitation of the existing method. Exhibit 38-C12 Field × Predicted Speed-Flow Curve for (a) Lane 1 and (b) Lane 2 (CA-1 NB – Santa Cruz/CA)