**Suggested Citation:**"Appendix E: On-Ramp Queue Spillback Analysis." National Academies of Sciences, Engineering, and Medicine. 2020.

*Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets*. Washington, DC: The National Academies Press. doi: 10.17226/25963.

**Suggested Citation:**"Appendix E: On-Ramp Queue Spillback Analysis." National Academies of Sciences, Engineering, and Medicine. 2020.

*Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets*. Washington, DC: The National Academies Press. doi: 10.17226/25963.

**Suggested Citation:**"Appendix E: On-Ramp Queue Spillback Analysis." National Academies of Sciences, Engineering, and Medicine. 2020.

*Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets*. Washington, DC: The National Academies Press. doi: 10.17226/25963.

**Suggested Citation:**"Appendix E: On-Ramp Queue Spillback Analysis." National Academies of Sciences, Engineering, and Medicine. 2020.

*Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets*. Washington, DC: The National Academies Press. doi: 10.17226/25963.

**Suggested Citation:**"Appendix E: On-Ramp Queue Spillback Analysis." National Academies of Sciences, Engineering, and Medicine. 2020.

*Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets*. Washington, DC: The National Academies Press. doi: 10.17226/25963.

**Suggested Citation:**"Appendix E: On-Ramp Queue Spillback Analysis." National Academies of Sciences, Engineering, and Medicine. 2020.

*Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets*. Washington, DC: The National Academies Press. doi: 10.17226/25963.

**Suggested Citation:**"Appendix E: On-Ramp Queue Spillback Analysis." National Academies of Sciences, Engineering, and Medicine. 2020.

*Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets*. Washington, DC: The National Academies Press. doi: 10.17226/25963.

**Suggested Citation:**"Appendix E: On-Ramp Queue Spillback Analysis." National Academies of Sciences, Engineering, and Medicine. 2020.

*Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets*. Washington, DC: The National Academies Press. doi: 10.17226/25963.

**Suggested Citation:**"Appendix E: On-Ramp Queue Spillback Analysis." National Academies of Sciences, Engineering, and Medicine. 2020.

*Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets*. Washington, DC: The National Academies Press. doi: 10.17226/25963.

**Suggested Citation:**"Appendix E: On-Ramp Queue Spillback Analysis." National Academies of Sciences, Engineering, and Medicine. 2020.

*Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets*. Washington, DC: The National Academies Press. doi: 10.17226/25963.

**Suggested Citation:**"Appendix E: On-Ramp Queue Spillback Analysis." National Academies of Sciences, Engineering, and Medicine. 2020.

*Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets*. Washington, DC: The National Academies Press. doi: 10.17226/25963.

**Suggested Citation:**"Appendix E: On-Ramp Queue Spillback Analysis." National Academies of Sciences, Engineering, and Medicine. 2020.

*Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets*. Washington, DC: The National Academies Press. doi: 10.17226/25963.

**Suggested Citation:**"Appendix E: On-Ramp Queue Spillback Analysis." National Academies of Sciences, Engineering, and Medicine. 2020.

*Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets*. Washington, DC: The National Academies Press. doi: 10.17226/25963.

**Suggested Citation:**"Appendix E: On-Ramp Queue Spillback Analysis." National Academies of Sciences, Engineering, and Medicine. 2020.

*Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets*. Washington, DC: The National Academies Press. doi: 10.17226/25963.

**Suggested Citation:**"Appendix E: On-Ramp Queue Spillback Analysis." National Academies of Sciences, Engineering, and Medicine. 2020.

*Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets*. Washington, DC: The National Academies Press. doi: 10.17226/25963.

**Suggested Citation:**"Appendix E: On-Ramp Queue Spillback Analysis." National Academies of Sciences, Engineering, and Medicine. 2020.

*Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets*. Washington, DC: The National Academies Press. doi: 10.17226/25963.

**Suggested Citation:**"Appendix E: On-Ramp Queue Spillback Analysis." National Academies of Sciences, Engineering, and Medicine. 2020.

*Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets*. Washington, DC: The National Academies Press. doi: 10.17226/25963.

**Suggested Citation:**"Appendix E: On-Ramp Queue Spillback Analysis." National Academies of Sciences, Engineering, and Medicine. 2020.

*Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets*. Washington, DC: The National Academies Press. doi: 10.17226/25963.

**Suggested Citation:**"Appendix E: On-Ramp Queue Spillback Analysis." National Academies of Sciences, Engineering, and Medicine. 2020.

*Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets*. Washington, DC: The National Academies Press. doi: 10.17226/25963.

**Suggested Citation:**"Appendix E: On-Ramp Queue Spillback Analysis." National Academies of Sciences, Engineering, and Medicine. 2020.

*Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets*. Washington, DC: The National Academies Press. doi: 10.17226/25963.

**Suggested Citation:**"Appendix E: On-Ramp Queue Spillback Analysis." National Academies of Sciences, Engineering, and Medicine. 2020.

*Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets*. Washington, DC: The National Academies Press. doi: 10.17226/25963.

**Suggested Citation:**"Appendix E: On-Ramp Queue Spillback Analysis." National Academies of Sciences, Engineering, and Medicine. 2020.

*Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets*. Washington, DC: The National Academies Press. doi: 10.17226/25963.

**Suggested Citation:**"Appendix E: On-Ramp Queue Spillback Analysis." National Academies of Sciences, Engineering, and Medicine. 2020.

*Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets*. Washington, DC: The National Academies Press. doi: 10.17226/25963.

**Suggested Citation:**"Appendix E: On-Ramp Queue Spillback Analysis." National Academies of Sciences, Engineering, and Medicine. 2020.

*Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets*. Washington, DC: The National Academies Press. doi: 10.17226/25963.

**Suggested Citation:**"Appendix E: On-Ramp Queue Spillback Analysis." National Academies of Sciences, Engineering, and Medicine. 2020.

*Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets*. Washington, DC: The National Academies Press. doi: 10.17226/25963.

**Suggested Citation:**"Appendix E: On-Ramp Queue Spillback Analysis." National Academies of Sciences, Engineering, and Medicine. 2020.

*Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets*. Washington, DC: The National Academies Press. doi: 10.17226/25963.

**Suggested Citation:**"Appendix E: On-Ramp Queue Spillback Analysis." National Academies of Sciences, Engineering, and Medicine. 2020.

*Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets*. Washington, DC: The National Academies Press. doi: 10.17226/25963.

**Suggested Citation:**"Appendix E: On-Ramp Queue Spillback Analysis." National Academies of Sciences, Engineering, and Medicine. 2020.

*Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets*. Washington, DC: The National Academies Press. doi: 10.17226/25963.

**Suggested Citation:**"Appendix E: On-Ramp Queue Spillback Analysis." National Academies of Sciences, Engineering, and Medicine. 2020.

*Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets*. Washington, DC: The National Academies Press. doi: 10.17226/25963.

**Suggested Citation:**"Appendix E: On-Ramp Queue Spillback Analysis." National Academies of Sciences, Engineering, and Medicine. 2020.

*Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets*. Washington, DC: The National Academies Press. doi: 10.17226/25963.

**Suggested Citation:**"Appendix E: On-Ramp Queue Spillback Analysis." National Academies of Sciences, Engineering, and Medicine. 2020.

*Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets*. Washington, DC: The National Academies Press. doi: 10.17226/25963.

**Suggested Citation:**"Appendix E: On-Ramp Queue Spillback Analysis." National Academies of Sciences, Engineering, and Medicine. 2020.

*Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets*. Washington, DC: The National Academies Press. doi: 10.17226/25963.

**Suggested Citation:**"Appendix E: On-Ramp Queue Spillback Analysis." National Academies of Sciences, Engineering, and Medicine. 2020.

*Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets*. Washington, DC: The National Academies Press. doi: 10.17226/25963.

**Suggested Citation:**"Appendix E: On-Ramp Queue Spillback Analysis." National Academies of Sciences, Engineering, and Medicine. 2020.

*Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets*. Washington, DC: The National Academies Press. doi: 10.17226/25963.

**Suggested Citation:**"Appendix E: On-Ramp Queue Spillback Analysis." National Academies of Sciences, Engineering, and Medicine. 2020.

*Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets*. Washington, DC: The National Academies Press. doi: 10.17226/25963.

**Suggested Citation:**"Appendix E: On-Ramp Queue Spillback Analysis." National Academies of Sciences, Engineering, and Medicine. 2020.

*Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets*. Washington, DC: The National Academies Press. doi: 10.17226/25963.

**Suggested Citation:**"Appendix E: On-Ramp Queue Spillback Analysis." National Academies of Sciences, Engineering, and Medicine. 2020.

*Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets*. Washington, DC: The National Academies Press. doi: 10.17226/25963.

**Suggested Citation:**"Appendix E: On-Ramp Queue Spillback Analysis." National Academies of Sciences, Engineering, and Medicine. 2020.

*Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets*. Washington, DC: The National Academies Press. doi: 10.17226/25963.

**Suggested Citation:**"Appendix E: On-Ramp Queue Spillback Analysis." National Academies of Sciences, Engineering, and Medicine. 2020.

*Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets*. Washington, DC: The National Academies Press. doi: 10.17226/25963.

**Suggested Citation:**"Appendix E: On-Ramp Queue Spillback Analysis." National Academies of Sciences, Engineering, and Medicine. 2020.

*Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets*. Washington, DC: The National Academies Press. doi: 10.17226/25963.

**Suggested Citation:**"Appendix E: On-Ramp Queue Spillback Analysis." National Academies of Sciences, Engineering, and Medicine. 2020.

*Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets*. Washington, DC: The National Academies Press. doi: 10.17226/25963.

**Suggested Citation:**"Appendix E: On-Ramp Queue Spillback Analysis." National Academies of Sciences, Engineering, and Medicine. 2020.

*Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets*. Washington, DC: The National Academies Press. doi: 10.17226/25963.

**Suggested Citation:**"Appendix E: On-Ramp Queue Spillback Analysis." National Academies of Sciences, Engineering, and Medicine. 2020.

*Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets*. Washington, DC: The National Academies Press. doi: 10.17226/25963.

**Suggested Citation:**"Appendix E: On-Ramp Queue Spillback Analysis." National Academies of Sciences, Engineering, and Medicine. 2020.

*Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets*. Washington, DC: The National Academies Press. doi: 10.17226/25963.

**Suggested Citation:**"Appendix E: On-Ramp Queue Spillback Analysis." National Academies of Sciences, Engineering, and Medicine. 2020.

*Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets*. Washington, DC: The National Academies Press. doi: 10.17226/25963.

**Suggested Citation:**"Appendix E: On-Ramp Queue Spillback Analysis." National Academies of Sciences, Engineering, and Medicine. 2020.

*Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets*. Washington, DC: The National Academies Press. doi: 10.17226/25963.

**Suggested Citation:**"Appendix E: On-Ramp Queue Spillback Analysis." National Academies of Sciences, Engineering, and Medicine. 2020.

*Highway Capacity Manual Methodologies for Corridors Involving Freeways and Surface Streets*. Washington, DC: The National Academies Press. doi: 10.17226/25963.

Below is the uncorrected machine-read text of this chapter, intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text of each book. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

304 A P P E N D I X E On-Ramp Queue Spillback Analysis This document 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 Figure E-1 presents the 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.

305 Source: HCM 6th Ed. Exhibit 19-18 Figure E-1.Signalized intersections methodology with adjustments to address on-ramp queue spillback

306 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 Figure E-2, with three movements discharging into the on-ramp (SBL, EBT and NBR). Figure E-2. Typical signalized intersection ramp terminal in a diamond interchange The total throughput from the intersection into the on-ramp Î»ONR is the sum of the throughput from each of the contributing movements: ð ð ð ð (Equation E-1) The throughput for each movement i is the minimum value of its demand and capacity: ð ððð ð£ , ð (Equation E-2) Where: vi = demand flow rate for intersection movement i (veh/h) ci = capacity for intersection movement i (veh/h), as provided by HCM 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 (HCM Equation 19-8), with an adjustment factor for right turns fRT (Equation 19-13). If all movements at the intersection are undersaturated (vi â¤ ci for every i), then Equation E-1 is simplified and the total on-ramp demand throughput Î»ONR is: ð ð£ðð (Equation E- 3) 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:

307 â¢ Capacity of the on-ramp (Exhibit 14-12) â¢ Capacity at the merge segment, when oversaturated conditions occur at the freeway facility â¢ An active ramp metering RM The procedure to obtain cmerge is presented in Figure E-3. The freeway facility must be analyzed using the Freeway Facilities methodology (HCM Chapter 10) 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: ð = ðð ððð ð ð, ð¡,ð (Equation E- 4) 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. t = time step index

308 Figure E-3. Step 7B â Estimation of merging capacity in a freeway ramp 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. Figure E-4 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 Figure E-5. The cycle starts with the SBL green discharging into the on-ramp at a throughput rate Î»SBL, 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 (Î»SBL - 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 maintained and it is equal to LONR until the end of the green

309 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 â Ramp Terminals and Alternative Intersections. Figure E-4. Sample intersection for calculation of a QAP for the on-ramp 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 Î»NBR, 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 Figure E-5, the adjusted capacity for the SBL movement cSBL,SP can be obtained from the QAP as the slope of the red line (cSBL,SP - cmerge) as follows: ð , â ð â ð ð â ð 0ð (Equation E-5)

310 Where: N(g1) = 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); g1 = effective green time for phase 1 Figure E-5. On-ramp queue accumulation polygon during queue spillback The adjusted capacity of the SBL movement cSBL,SP is then computed as: ð , = ð ð ð â ð 0ð (Equation E-6) 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: ð = ð£ð (Equation E-7) 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-

311 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 (Aakre & Aakre, 2017), during oversaturated conditions and when queue spillback occurs drivers show cooperative behavior, with higher priority vehicles often yielding to those with lower priority. The microsimulation package AIMSUN, which was used to simulate the study sites for this project, includes the feature Turn Cooperation Model to simulate this behavior, as illustrated in Figure E-6. In such cases, the gap acceptance model is no longer valid and a new approach must be used to evaluate the intersection performance. Figure E-6. Illustration of cooperative behavior in unsignalized intersections with queue spillback 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. Figure E-7 presents the 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.

312 Source: Adapted from HCM 6th Ed. Exhibit 20-6 Figure E-7. TWSC intersections core methodology with adjustments to address on-ramp queue spillback 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 (Figure E-1). The total throughput from the

313 intersection into the on-ramp Î»ONR is the sum of the throughput from each of the contributing movements. For each movement i discharging into the on-ramp, the throughput is the minimum value of its demand and its movement capacity: ð = ððð ð£ , ð , (Equation E-8) 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 (Figure E-1) 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 (Figure E-8). For a given time period of T minutes (typically T=15), the intersection yields throughput Î»ONR to the ramp (Step 5B), while the merge has capacity cmerge. If Î»ONR > 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. Figure E-8. On-ramp queue accumulation polygon â TWSC intersection From this relationship shown in Figure E-8 the spillback time TSB is defined as the amount of time within a time period when spillback is active: ð = ð â ð¿ â ð 0ð â ð (Equation E-9) Where:

314 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) Î»ONR = 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 capacity 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: ð , = ð Ã ð£â ð£ (Equation E-10) Where: cSB,i = capacity during spillback for movement i (veh/h) vi = demand flow rate for movement i (veh/h) cmerge = merging capacity of the on-ramp (veh/h) NSB = 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): ð , = ð , Ã ð + ðð,ð Ã (ð â ð ) ð (Equation E-11) Where: cEQ,i = adjusted capacity for movement i (veh/h) cSB,i = capacity during spillback for movement i (veh/h) vi = demand flow rate for movement i (veh/h) cmerge = 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 E- 3) becomes: ð , = ð , (Equation E-12) Step 11. Compute movement control delay

315 The average control delay is obtained using Equation 20-64 replacing the movement capacity cm,i by the adjusted capacity cEQ,i: ð = 3600ð , + 900ð â£â¢â¢ â¢â¡ ð£ð , â 1 + ð£ð , â 1 + 3600ð , Ã ðð ,450ð â¦â¥â¥ â¥â¤ + 5 (Equation E-13)

316 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 Figure E-9, 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. Source: Adapted from HCM 6th Ed. Exhibit 21-10 Figure E-9. AWSC intersections methodology with adjustments to address on-ramp queue spillback The only step in the methodology that differs from the TWSC (13D) is described below. Step 13D â 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:

317 â = 3600ð , (Equation E-14) Roundabout ramp terminals The methodology presented in Chapter 22 â Roundabouts is shown in Figure E-10. The additional steps proposed to the methodology are marked in blue. Each of the steps added and modified is discussed in the following paragraphs. This methodology is applicable only to single- lane roundabouts. Exhibit 22-9 and Table E-1 provide the required input data and potential data sources for roundabout motorized vehicle analysis.

318 Source: HCM 6th Ed. Exhibit 22-15 Figure E-10. Roundabouts methodology with adjustments to address on-ramp queue spillback

319 Table E-1. Required data and potential data sources â roundabout spillback evaluation 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 â 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 (Figure E-11) 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. Figure E-11. Priority order for a roundabout upstream of an on-ramp Next, the methodology calculates the capacity of the roundaboutâs exit lane into the on-ramp. Previous research (Robinson et al, 2006; Rodegerts & Blackwelder, 2005) 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 â 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 Î»SB-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: ð = min ð£ , ð Ã ð , 3,600â (Equation E-15) Where: Î»SB-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)

320 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 â 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 Î»EB-ONR (veh/h) for this movement is given by: ð = min ð£ , ð Ã ð , 3,600â â ð (Equation E-16) Where: Î»EB-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 EB approach into the on-ramp Rank 3 â 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 (cNB), 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 (Î»NB-ONR) for this right-turn movement is given by: ð = min ð£ , ð Ã ð , 3,600â â ð â ð (Equation E-17) Where: Î»NB-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 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. Step 14 â Calculate the throughput into the on-ramp The maximum throughput from the roundabout to the on-ramp, ð is calculated as: ð = ð + ð + ð (Equation E-18) Step 15 â 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 (Figure E-1). 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, ð . If cmerge â¤ Î»ONR, then spillback is not expected to occur, and no adjustments are necessary in the procedure. If cmerge > Î»ONR, queues will develop along the on-ramp, and spillback may occur if

321 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 â Determine the on-ramp storage ratio and queue spillback length With the exit flow rate into the on-ramp (Î» ), the expected queue length QSP along the on- ramp during a 15-minute period analysis is: ð = ð â ð4 (Equation E-19) 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: ð , = ð , + ð , â ð ,4 (Equation E-20) The on-ramp storage ratio is calculated by dividing the available on-ramp storage LR (ft) by the average vehicle spacing , Lh (Equation 31-155): ð = ð¿ Ã ðð¿ (Equation E-21) 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 â 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: ð = ð â ð¿ Ã ð (Equation E-22) 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): ð , = ð Ã ð ð + ð , (Equation E-23) ð , = ð Ã ð ð + ð , (Equation E-24) ð , = ð Ã ð ð + ð , (Equation E-25) Where: Qsp,SB , Qsp,EB , Qsp,NB = queue due to the on-ramp spillback on SB, EB and NB approaches, respectively (veh) Î»SB-ONR, Î»EB-ONR, Î»NB-ONR = maximum throughput for SB, EB, and NB approaches into the on- ramp, respectively Q95,SB , Q95,EB , Q95,NB = 95th percentile queue on SB, EB, and NB approaches, respectively (veh))

322 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 (HCM Chapter 22). As indicated in HCM â 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, the HCM Chapter 22 â 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 (Kimber and Hollis, 1979). The additional delay (in sec/veh) due to the on-ramp spillback is calculated as follows: ð = 3600ð + 900ð â£â¢â¢ â¢â¡ ðð â 1 + ðð â 1 + 3600ð Ã ðð450ð â¦â¥â¥ â¥â¤ + 5 Ã ððð ðð , 1 (Equation E-26) Where cmerge = merging capacity of the on-ramp (veh/h) Î»ONR = exit flow rate into the on-ramp (veh/h) t = time period (h) (T = 0.25 h for a 15-min analysis)

323 Case Study: Evaluating Queue Spillback from Freeway On-Ramp 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: â¢ One freeway facility â¢ One arterial facility (Acadian Thruway), with four intersections: â¢ Perkins Rd. â¢ Acadian Center Rd. â¢ I-10 WB â¢ I-10 EB The subject freeway has three lanes and it connects to the arterial corridor (Acadian Thruway) through an interchange as illustrated in Figure E-1. Figure E-12. Illustration of study site 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.

324 Part 1 â Signalized Intersection Input data Signalized Intersection The geometry of the intersection connected to the I-10 EB on-ramp (I-10 EB) is shown in Figure E-13. There are three movements leading into the on-ramp: â¢ NBR: One channelized, unsignalized right-turn lane; â¢ SBL: One exclusive left turn lane with a protected phase; and â¢ EBT: One through lane. Figure E-13. Signalized intersection geometry â Acadian Thruway @ I-10 EB The phasing sequence of the subject intersection is presented in Figure E-14. 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). Figure E-14. Phasing sequence â I-10 EB intersection The demand volumes for each time period are presented in Table E-2. Additional input data are summarized in Table E-3.

325 Table E-2. Demand flow rates (veh/h) â I-10 EB intersection 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 Table E-3. Input data â I-10 EB intersection 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 1.0 1.0 - 1.0 - 1.0 1.0 Minimum Green (Gmin), s 5.0 5.0 - 15.0 - 5.0 15.0 Start-Up Lost Time (lt), s 2.0 2.0 - 2.0 - 2.0 2.0 Green Extension (e), s 2.0 2.0 - 2.0 - 2.0 2.0 Passage (PT), s 2.0 2.0 - 2.0 - 2.0 2.0 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 (Figure E-15), where segment 3 (diverge) and segment 5 (merge) connect to the subject signalized intersection (Acadian Thruway).

326 Figure E-15. Freeway facility segmentationâ I-10 EB The geometric features of the freeway facility are summarized in Table E-4. Table E-4. Freeway facility (I-10 EB) - geometric features 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 â 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 average green times for these movements vary by time period as they are computed as function of the demands on each intersection approach. 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. If there were no conflicting movements discharging into the on-ramp, the NBR capacity would be 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

327 throughput of the unsignalized turning movement is also assumed to be equal to its saturation flow rate. Therefore: ð , = ð , Ã ð Ã ð where sNBR,FF = saturation flow rate of NBR movement at free-flow conditions (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: ð = 1ð¸ = 11.18 where 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: ð = 100 â 0.78ð â 0.31ð100 = 100 â 0.78 Ã 5 â 0.31 Ã 0100 = 0.961 where PHV = percentage heavy vehicles in the corresponding movement group (5%) Pg = approach grade for the corresponding movement group (0%) Therefore, the saturation flow rate ð , = 1,900 Ã 11.18 Ã 0.961 = 1,547 ð£ðâ/â 1.18 0.961 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: ð = ð£ ð / ,1 â ð / , 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) 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 HCM Chapter 31 (Signalized Intersections Supplemental):

328 â¢ During the queue service time (gs) portion of the conflicting phase green, the opposing movement flow rate is equal to its saturation flow rate; â¢ During the green extension time (ge), the opposing movement flow rate is equal to its arrival flow rate during the effective green (qg); Table E-5 illustrates the calculation of the NBR potential 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 during each phase as the product of the NBR saturation flow rate and the phase duration. Transition times between consecutive phases are also taken into consideration assuming that they have no conflicting flow rate to the on-ramp. Table E-5. Calculation of NBR potential capacity for a single cycle â Time Period 2 Active phase Conflicting flow Duration (s) Conflicting flow rate (veh/h) NBR saturation flow rate sNBR (veh/h) NBR discharge volume (veh) Ï1 (SBL) - gs,SBL sSBL 40.2 1739 282 3.1 Ï1 (SBL) -ge,SBL qg,SBL 3.7 128 1282 1.3 Transition time 1 - 5.7 - 1547 2.5 Ï2 (NBT) - 50.7 - 1547 21.8 Transition time 2 - 5.7 - 1547 2.5 Ï7 (EBT) - gs,EBT sEBT 6.3 1811 263 0.5 Ï7 (EBT) - ge,EBT qg,EBT 2.0 97.2 1319 0.8 Transition time 7 - 5.7 - 1547 2.5 Total 120.0 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: ð = 34.8 Ã 3600120 = 1045 ð£ðâ/â Because of the actuated control operation, the discharging rates to the on-ramp are different during each time period since they depend on effective green times and flow profiles. Therefore, this procedure must be repeated for every time period to compute the capacity of the NBR unsignalized movement cNBR (Table E-6). Table E-6. NBR capacity, computed for each time period Time Period NBR capacity (veh/h) 1 1213 2 1045 3 978 4 1182

329 Table E-7 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. Table E-7. Calculation of the on-ramp demand (vR) based on the intersection operation. 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 (Table E-8). As shown, the ramp flow rates for the merge segment (segment 5) are obtained from Table E-7, and highlighted in bold. Table E-8. Freeway facility (I-10 EB) â demand inputs Segment ID Time Period 1 Time Period 2 Time Period 3 Time Period 4 Mainline flow rate (veh/h) Ramp flow rate (veh/h) Mainline flow rate (veh/h) Ramp flow rate (veh/h) Mainline flow rate (veh/h) Ramp flow rate (veh/h) Mainline 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 Table E-9. Oversaturated conditions occur during time periods 2 and 3, therefore queueing may occur along the on-ramp.

330 Table E-9. Performance measures for the freeway facility (I-10 EB) Seg 1 Seg 2 Seg 3 Seg 4 Seg 5 Seg 6 Seg 7 (Basic) (Diverge) (Diverge) (Basic) (Merge) (Basic) (Basic) TP 1 D C D C D D D TP 2 E F F F F F E TP 3 D D F F F E E TP 4 D C C B C C C 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. Table E-10 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. Table E-10. Spillback check â I-10 EB on-ramp 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 (Figure E-1). 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 â 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 Table E-7. Step 7B â 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

331 Oversaturated Segment Evaluation procedure (HCM 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. Figure E-16 shows the values of ONRQ and ONRO over the analysis period (60 minutes), converted to hourly flow rates. Figure E-16a 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. Figure E-16b 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. Table E-11 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.

332 Figure E-16. Freeway facility, segment 5 (merge) performance: (a) merge capacities and (b) queue lengths Table E-11. Freeway performance during time period 4 â with and without the queue storage constraint 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

333 Step 7C â 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. Figure E-17 presents the queue accumulation profiles for (a) the on-ramp and (b) for the NBR movement. Figure E-17. Estimated queue lengths and merge capacities â time period 2 The cycle starts with a permitted left-turn movement (Î¦1: 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 HCM Chapter 31 â 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:

334 ð , = ð ð / ,1 â ð / , Where: sNBR,perm = saturation flow rate of the NBR movement (veh/h/ln) Î»SBL = 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 Î¦1 are determined next. During the SBL queue service time: ð = ð = 1,739 veh/h/ln â ð , = 282 veh/h/ln 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: ð , = ððð ð , , ð£ = ððð(282, 521) = 282 ð£ðâ/â Where: Î»NBR,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 Î»SBL is equal to the arrival flow rate during the effective green (qg,SBL, from Equation 19-32): ð = ð , = ð Ã ð£3600 Ã ð¶ð ð = 0.08 Ã 5863600 Ã 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) gSBL = SBL effective green time (s) For this conflicting flow, therefore, the NBR saturation flow rate sNBR,perm2 is obtained using Equation 31-100: ð , = ð ð / ,1 â ð / , ð , = 128ð Ã . / ,1 â ð Ã . / , = 1282 ð£ðâ/â/ðð

335 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: ð , = ð , = 1282 ð£ðâ/â Where: Î»NBR,2 = throughput for the NBR movement during the SBL green 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 Î¦1 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: ð = ð + ð , = 1,739 + 282 = 2,021 veh/h or 0.561 veh/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: ð â ð = 2,021 â 1,142 = 879 ð£ðâ/â ðð 0.244 ð£ðâ/ð 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 (Figure E-17a). This process is then repeated for all phases throughout the cycle. The results for a single cycle (120 sec) are presented in Table E-12, 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 Table E-12 describes a portion of the cycle, as follows: â¢ gs1: queue service time for SBL (Î¦1), as previously discussed â¢ ge1: green extension time for SBL (Î¦1). 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 â¢ r1: effective red time for SBL (Î¦1). 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 â¢ g2*: effective green for NBT (Î¦2), 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 â¢ g2**: remaining effective green for NBT (Î¦2). 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 â¢ r2: effective red time for NBT (Î¦2). 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 â¢ gs7: queue service time for EBT (Î¦7). The EBT discharges into the on-ramp at the saturation flow rate. The throughput of the NBR movement is 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 â¢ ge7*: green extension time for EBT (Î¦7). 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

336 â¢ ge7**: remaining extension time for EBT (Î¦7). 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 â¢ r7: effective red time for EBT (Î¦7). 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. Table E-12. Discharge flow rates into the on-ramp for each phase throughout the cycle â time period 2 Active phase t (s) Duration (s) Protected movement Permitted movement On-ramp analysis Î»prot (veh/s) vNBR (veh/s) Î»NBR (veh/s) NBR queue (veh) Î»ONR (veh/s) Î»ONR - cmerge (veh/s) On-ramp queue (veh) gs1 0.00 40.16 0.483 0.145 0.078 0.00 0.56 0.24 0.00 ge1 40.16 3.74 0.036 0.145 0.356 2.66 0.39 0.07 9.80 r1 43.90 5.70 0.000 0.145 0.430 1.87 0.43 0.11 10.08 g2* 49.60 0.88 0.000 0.145 0.430 0.25 0.43 0.11 10.72 g2** 50.48 49.82 0.000 0.145 0.145 0.00 0.14 -0.17 10.82 r2 100.30 5.70 0.000 0.145 0.145 0.00 0.14 -0.17 2.22 gs7 106.00 6.25 0.503 0.145 0.073 0.00 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 0.00 0.17 -0.15 3.01 r7 114.3 5.7 0.000 0.145 0.145 0.00 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 â Calculate equivalent capacities for the affected movements Since spillback does not occur during time period 2, no adjustment to the intersection capacity is necessary. 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 â 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 Table E-7.

337 Step 7B â 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 (Figure E-16a). The merging capacity for time period 3 is 1,142 veh/h. Step 7C â 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. Figure E-18 illustrates the queue accumulation polygon for both the on-ramp and the NBR movement. Figure E-18. Estimated queue lengths and merge capacities â time period 3 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 =

338 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: ð â ð = (0.483 + 0.078) â 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: ðððð ð¡ð ð ðððððððð = 35.5 â 27.90.244 = 31.2ð 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: â¢ gs1* (31.2s): discharging at saturation flow rate â¢ 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 Î²1,sp, defined as the ratio between the maximum on-ramp capacity during queue spillback and the throughput from the intersection movements (SBL and NBR): ð½ , = ðð + ð = 0.317(0.483 + 0.078) = ð.ððð A capacity reduction factor Î²1,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: ð , = ð Ã ð½ , = 0.483 Ã 0.565 = 0.273 ð£ðâ/ð ð , = ð Ã ð½ , = 0.078 Ã 0.565 = 0.044 ð£ðâ/ð The procedure is then repeated for the remaining movements of the cycle, as shown in Table E-13. 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 Î»ONR is greater than the merge capacity cmerge. Therefore, the maximum allowed throughput Î»ONR,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 Î»ONR,ajd and Î»ONR. 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.

339 Table E-13. Discharge flow rates into the on-ramp for each phase throughout the cycle â time period 3 Active phase t (s) Duration (s) On- ramp queue (veh) Protected movement Permitted movement On-ramp analysis Capacity reduction adjustment Î»prot (veh/s) vNBR (veh/s) Î»NBR (veh/s) Q(NBR) (veh) Î»ONR (veh/s) Î»ONR,adj (veh/s) Î»ONR,adj - cmerge (veh/s) Î²sp gs1* 0.0 31.2 27.92 0.483 0.175 0.078 0.00 0.561 0.561 0.244 1.000 gs1,sp 31.2 16.1 35.54 0.483 0.175 0.078 3.01 0.561 0.317 0.000 0.565 r1 47.3 5.7 35.54 0.000 0.175 0.430 5.12 0.430 0.317 0.000 0.739 g2* 53.0 30.3 35.54 0.000 0.175 0.430 4.31 0.430 0.317 0.000 0.739 g2** 83.3 17.0 35.54 0.000 0.175 0.175 0.00 0.175 0.175 -0.142 1.000 r2 100.3 5.7 33.11 0.000 0.175 0.175 0.00 0.175 0.175 -0.142 1.000 gs7 106.0 6.3 32.30 0.503 0.175 0.073 0.00 0.576 0.576 0.259 1.000 ge7 112.3 2.0 33.92 0.027 0.175 0.366 0.64 0.393 0.393 0.076 1.000 r7* 114.3 1.0 34.08 0.000 0.175 0.430 0.25 0.430 0.430 0.113 1.000 r7** 115.3 4.7 34.18 0.000 0.175 0.175 0.00 0.175 0.175 -0.142 1.000 Cycle end 120 0 33.51 - - - - - - Step 7D â 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. Table E-14 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 Î»ONR and the actual throughput Î»ONR,adj are computed. Next, the capacity reduction factor Î²sp is computed as the ratio of Î»ONR and Î»ONR,adj. A value of Î²sp < 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 Î»ONR and Î»ONR,adj, respectively, by their duration. At the end of the table, the expected and actual volumes are aggregated and a capacity reduction factor Î²sp,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 (Table E-7). The adjusted capacity is calculated by applying the spillback capacity reduction factor Î²sp, calculated in Table E-14: ð , = ð Ã Î² , = 685 Ã 0.704 = ððð.ð ð¯ðð¡/ð¡ 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 Figure E-18, the on-ramp queue during the EBT green does not reach the maximum storage length of 35.5 veh.

340 Table E-14. Calculation of spillback capacity reduction factor for the SBL movement for time period 3 Cycle Active phase Duration (s) On-ramp analysis Spillback adjustment Î»ONR (veh/s) Î»ONR,adj (veh/s) Î²sp On-ramp expected discharge volume (veh) On-ramp actual discharge volume (veh) 2 gs1 47.3 0.561 0.561 1.000 26.56 26.56 3 gs1* 31.2 0.561 0.561 1.000 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 1.000 4.67 4.67 4 gs1,sp 39.0 0.561 0.317 0.565 21.89 12.37 5 gs1 5.1 0.561 0.561 1.000 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 1.000 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 1.000 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 1.000 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 (Î²sp,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 â 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 Table E-7. Step 7B â Obtain merging capacity with Freeway Facilities method The merge capacity for time period 4 has been previously determined, as shown in Figure E- 16a. 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 â 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 Figure E-19. 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.

341 Figure E-19. Estimated queue lengths and merge capacities â time period 4 Step 7D â 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 Table E-15. 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. Table E-15. Calculation of spillback capacity reduction factor for the SBL movement during time period 4 Cycle Active phase Duration (s) On-ramp queue (veh) On-ramp analysis Spillback adjustment Î»ONR (veh/s) Î»ONR,adj (veh/s) Î²sp On-ramp expected throughput (veh) On-ramp actual throughput (veh) 1 gs1 6.0 34.42 0.505 0.505 1.000 3.02 3.02 1 gs1,sp 29.9 35.54 0.505 0.317 0.628 15.12 9.50 1 ge1 0.0 35.54 0.388 0.317 0.818 0.00 0.00 2 gs1 31.2 13.20 0.505 0.505 1.000 15.79 15.79 2 ge1 4.7 19.07 0.095 0.095 1.000 0.44 0.44 3 gs1 31.2 0.00 0.505 0.505 1.000 15.79 15.79 3 ge1 4.7 5.87 0.058 0.058 1.000 0.27 0.27 4 gs1 40.2 0.00 0.561 0.561 1.000 22.55 22.55 4 ge1 3.7 9.80 0.392 0.392 1.000 1.46 1.46 5 gs1 40.2 0.00 0.561 0.561 1.000 22.55 22.55 5 ge1 3.7 1.31 0.392 0.392 1.000 1.46 1.46

342 6 gs1 40.2 0.00 0.561 0.561 1.000 22.55 22.55 6 ge1 3.7 1.31 0.392 0.392 1.000 1.46 1.46 7 gs1 40.2 0.00 0.561 0.561 1.000 22.55 22.55 7 ge1 3.7 1.31 0.392 0.392 1.000 1.46 1.46 8 gs1 40.2 0.00 0.561 0.561 1.000 22.55 22.55 8 ge1 3.7 1.31 0.392 0.392 1.000 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 Î²sp, calculated in Table E-15: ð , = ð Ã ð½ , = 746 Ã 0.967 = ððð.ð ð¯ðð¡/ð¡ 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). Table E-20 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. Table E-16. Comparison of performance measures â with and without consideration of spillback effects 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 Part 2 â Two-Way Stop Control (TWSC) Intersection Input Data Figure E-20 shows the geometry of the TWSC intersection.

343 Figure E-20. TWSC intersection geometry â Acadian Thruway @ I-10 EB Spillback check â 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): ð = ð , Ã ð Ã ð ð = 1,900 Ã 11.18 Ã 0.961 = 1,547 ð£ðâ/â In this case 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. Table E-17 summarizes the calculations for this step.

344 Table E-17. Calculation of the on-ramp demand (vR) based on the TWSC intersection operation Time Period Parameter Movements EBT NBR SBL 1 Demand (veh/h) 8 315 652 v/c 0.06 - 0.96 c (veh/h) 125 1547 677 min (v, c) 8 315 652 Merge demand vR (veh/h) 975 2 Demand (veh/h) 4 608 591 v/c 0.10 - 0.48 c (veh/h) 42 1547 1222 min (v, c) 4 608 591 Merge demand vR (veh/h) 1203 3 Demand (veh/h) 18 708 685 v/c 0.64 - 0.56 c (veh/h) 28 1547 1222 min (v, c) 18 708 685 Merge demand vR (veh/h) 1411 4 Demand (veh/h) 24 80 463 v/c 1.00 - 0.60 c (veh/h) 24 1547 768 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 Part 1, it is already known that spillback will occur during time period 3 (Table E-1). Evaluation of queue spillback impacts The evaluation of queue spillback impacts on the TWSC intersection follows the procedure detailed in Figure E-7. Since this is a multiperiod analysis, the procedure must be applied for each time period as discussed in Part 1. 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 Table E-17. 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 from Part 1, the same values are used: â¢ Time periods 2 and 3: 1,142 veh â¢ Time period 4: 1,142 veh/h during 4 time steps (60 seconds), then 1,903 veh/h. 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. Table E-18 shows the calculations for plotting the on-ramp queue. For each time period, the difference between the on-ramp throughput Î»ÎÎR and the merge capacity cmerge is

345 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 â 4.55 = 10.45 minutes. Table E-18. Queue accumulation plot calculations for on-ramp â TWSC intersection Time Period Duration (min) On-ramp demand (vR) (veh/h) On-ramp queue growth rate (Î»ÎÎR - 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 - - - Figure E-21 illustrates the queue accumulation polygon for the on-ramp, based on the table results. Figure E-21. Queue accumulation polygon for the on-ramp â TWSC intersection 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: ð , + ð , + ð , = ð = 1,142 ð£ðâ/â

346 The capacities during spillback conditions are then obtained proportionally to their demand flow rates (Equation E-10): ð , = ð Ã ð£ð£ + ð£ + ð£ = 1,142 Ã 685685 + 708 + 18 = 554.4 ð£ðâ/â ð , = ð Ã ð£ð£ + ð£ + ð£ = 1,142 Ã 708685 + 708 + 18 = 573.0 ð£ðâ/â ð , = ð Ã ð£ð£ + ð£ + ð£ = 1,142 Ã 18685 + 708 + 18 = 14.6 ð£ðâ/â The equivalent capacities cEQ,i for each movement i, aggregated for the 15-min time period, are obtained proportionately to the spillback time TSB (Equation E-11): ð , = , Ã Ã( ) = . Ã . Ã . = 757 ð£ðâ/â ð , = , Ã Ã( ) = Ã . Ã . = 869 ð£ðâ/â ð , = , Ã Ã( ) = Ã . . Ã . = 24 ð£ðâ/â 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). Table E-23 compares the performance measures of the affected intersection movements for the cases with and without consideration of spillback effects during time period 3. All three movements discharging to the on-ramp have significantly higher delays when considering spillback effects. Table E-19. Comparison of performance measures in a TWSC intersection â time period 3 - with and without spillback effects Movement Demand (veh/h) Capacity (veh/h) Control delay (s/veh) Without spillback With spillback Without spillback With spillback EBT 18 28.0 18.7 166.5 479.8 NBR 708 1547.0 868.9 0 24.5 SBL 685 1222.0 757.2 9.4 37.2 Part 3 â All-Way Stop Control (AWSC) Intersection with Input Data Figure E-20 shows the geometry of the study intersection.

347 Figure E-22. AWSC intersection geometry â Acadian Thruway @ I-10 EB Spillback check â 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.Table E-20 summarizes the calculations for this step. 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 Table E- 21.

348 Table E-20. Calculation of the on-ramp demand (vR) based on the AWSC intersection operation. Time Period Parameter Movements EBT NBR SBL 1 Demand (veh/h) 54 467 313 Adjusted demand (veh/h) 54 467 313 v/c 0.143 - 0.672 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 Adjusted demand (veh/h) 40 512 432 v/c 0.114 - 0.984 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 Adjusted demand (veh/h) 19 539 546 v/c 0.048 - 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 Adjusted demand (veh/h) 28 160 316 v/c 0.062 - 0.618 c (veh/h) 455 619 511 min (v, c) 28 160 316 Merge demand vR (veh/h) 504 Table E-21. Check for spillback occurrence â AWSC intersection Time period vR (veh/h) Ramp queue (veh) Ramp queue (ft) Ramp storage ratio (RQ) Spillback expected? 1 834 0.0 0.0 0.00 No 2 984 14.9 21.9 0.62 No 3 1020 82.1 53.4 1.50 Yes 4 504 0.0 0.0 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 Figure E-9. 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.

349 Step 13A - Determine intersection throughput to on-ramp The intersection throughput to the on-ramp was previously determined at the spillback check (Table E-20). 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 Table E-22. Table E-22. Queue accumulation plot calculations for on-ramp â AWSC intersection Time Period Duration (min) On-ramp demand (vR) (veh/h) On-ramp queue growth rate (Î»ÎÎR - cmerge) (veh/s) Initial ONR queue (veh) Time to spillback (min) Spillback time (TsB) (min) Final ONR queue (veh) 2 15 984 0.023 0.0 - - 21.0 3 15 1020 0.033 15.2 7.25 7.75 35.5 4 15 504 -0.110 35.5 - - 0.0 Figure E-21 illustrates the queue accumulation polygon for the on-ramp, based on the table results. Figure E-23. Queue accumulation polygon for the on-ramp â AWSC intersection 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 Table E-23.

350 Table E-23. Equivalent capacities and headways for on-ramp â Time Period 3 â AWSC intersection Movement Capacity during spillback (csp) (veh/h) Regular Capacity (c) (veh/h) Equivalent Capacity (cEQ) (veh/h) Spillback departure headway (hsp) (s) EBT 15 396.0 212.1 17.0 NBR 439 550.0 496.5 7.3 SBL 445 462.0 453.7 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). Table E-24Table E-20 compares the performance measures of the intersection movements for the cases with and without consideration of 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 the same performance measures. Table E-24. Comparison of performance measures â time period 3 - with and without spillback effects 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 10.0 10.0 EBT 19 396 212 12.6 21.7 9.1 17.0 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 546 462 454 128.0 136.5 7.8 7.9 SBT 220 494 494 16.0 16.0 7.3 7.3