Incorporating Travel Time Reliability into the Highway Capacity Manual (2014)

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80 C h a p t e r 6 This chapter discusses the enhancements that have been made to the FREEVAL and STREETVAL models during this project. It is divided into the following five sections: • Freeway facilities introduction; • Description of freeway facility enhancements; • FREEVAL-RL calibration; • Summary of freeway model enhancements; and • Urban streets enhancements. Freeway Facilities Introduction The FREEVAL (FREeway EVALuation) tool was first developed as a computational engine in 2000 for the HCM chapter on freeway facilities methodology. It has since gone through several improvements, and the most recent, FREEVAL 2010, is imple- mented in a Microsoft Excel and Visual Basic programming platform. FREEVAL 2010 is fully compatible with the HCM2010 and is distributed to HCM users via the Volume 4 website (TRB 2010b). It is designed for the analysis of freeway facilities but incorporates all methodological details for the analysis of basic freeway segments, merge and diverge sections, and freeway weaving segments. It is unique in the HCM2010 in that it can analyze both undersaturated and congested regimes and allows for the evaluation of multiple segments across multiple analysis time periods. Since the publication of HCM2010, FREEVAL 2010 has been customized to create a more user-friendly envi- ronment for analyzing work zones (NCDOT FREEVAL-WZ), as well as for managed lanes (FREEVAL-ML) through NCHRP Project 3-96 (Wang et al. 2012). The adaptation of the freeway facilities method for use in a reliability analysis required several changes and enhance- ments to FREEVAL. The objective of this section is to provide an overview of the recent reliability analysis enhancements to both the core computational engine and the user interface. The enhanced computational engine is named FREEVAL-RL (FREeway EVALuation–ReLiability). Incorporation of the Two-Capacity Phenomenon under Queue Discharge Conditions The HCM2010’s freeway facilities methodology does not consider the two-capacity phenomenon, namely the drop in throughput from theoretical capacity that occurs after break- down at a freeway bottleneck. The enhanced FREEVAL-RL accounts for this capacity reduction in the queue discharge based on a user-defined proportional drop in capacity, desig- nated as a. The default for a is set at 7% on the basis of a recent synthesis of the literature. Incorporation of Speed Adjustment Factor for Some Nonrecurring Congestion Sources In the HCM2010, operational impacts of nonrecurring con- gestion sources were addressed through a capacity adjustment factor (CAF), which reduces the basic segment capacity by a multiplicative factor. Using Equation 25-1 in the HCM2010, the methodology develops a new speed-flow curve between the free-flow speed and the new, user-defined capacity. In Project L08, the speed adjustment factor (SAF) amends Equation 25-1 by also reducing the free-flow speed (intercept of the speed- flow curve). This enhancement is critical for modeling weather impacts, which have been demonstrated to result in significant reductions in speed, even under low-volume conditions. Improved Modeling of CAF and SAF for Merge, Diverge, and Weaving Segments In the HCM2010, the application of Equation 25-1 does not distinguish between segment types. Specifically, when using a CAF or SAF, the analyst essentially assumed that the adjusted segment is a basic segment. In FREEVAL’s computations, the method bypasses weaving and ramp-segment speed calcula- tion procedures and uses Equation 25-1 instead. This approach Model Enhancements

81 sometimes results in unrealistic speed estimates and inconsis- tent results, as segment speeds may actually increase when add- ing a CAF. In Project L08, the enhancements directly incorporate SAF and CAF into the respective procedure for each segment type and thus consistently account for the particular segment characteristics. New Defaults for CAF and SAF for Incident and Weather Events on Freeways With the introduction of SAF and the increased use of CAF and SAF in evaluating nonrecurring sources of congestion in a reli- ability context, national defaults values should be offered to encourage a uniform and consistent application of the method- ology across agencies. Through an extensive literature review, the research team developed new default values for CAF and SAF, which have been incorporated in the methodology. Note that CAF inputs for work zones are adapted directly from HCM2010, pending the results of ongoing research in NCHRP Project 3-107, Work Zone Capacity Methods for the HCM. Enhanced Performance Measures for Congested Conditions To make the computational engine reliability analysis ready, two reliability performance measures were added to the engine’s output. The first of these performance measures is the travel time index (TTI), which is used for deriving the travel time dis- tribution. The augmented analysis also reports the denied entry vehicle queue length, which describes vehicles stored in a queue upstream of the first analysis segment. Computational Automation To generate a travel time distribution, FREEVAL needs to be executed multiple times, with a distinct FREEVAL run per- formed for each scenario, reflecting each scenario’s unique combination of FREEVAL input data. Running FREEVAL in a manual mode to generate travel time distributions is very time-consuming. Therefore, automating the scenario runs is a necessary addition to the computational engine. The revised FREEVAL-RL engine does so by automatically interacting with the freeway scenario generator (FSG) and directly receiv- ing scenario-specific input for performance measure compu- tation. FREEVAL-RL also provides automated generation of standardized reliability outputs. Travel Time Index Distribution Calibration In the next step, FREEVAL was calibrated for generating TTI distributions for HCM freeway reliability analysis. For this pur- pose, three calibration parameters were identified: the overall demand-level adjustment from the seed file, the percent drop in capacity during breakdown, and the jam density. The calibra- tion parameter effects on the TTI distribution were studied for a 12.5-mile facility (I-40 EB in Raleigh, North Carolina) for which segment and facility travel times for the calendar year 2010 were available from INRIX, the traffic data service. On the basis of the initial model runs and previous studies, three can- didate values for each calibration parameter were selected, resulting in 27 distinct combinations. To minimize calibration bias, the calibration analysis was limited to conditions in which no incidents or inclement weather events were evident. The results of a two-sample Kolmogorov–Smirnov (KS) test indicated that increasing the originally estimated demand levels in the seed file by 3% and selecting a value of 9% for the queue discharge capacity drop yielded estimated TTI distri- butions that were not significantly different from the empiri- cal INRIX distribution. Jam density values showed very little effect on the resulting TTI distribution. Description of Freeway Facility enhancements In this section, each of the enhancements is explained in more detail with the exception of travel time index distribution calibration. The section starts with the consideration of the two-capacity phenomenon and continues with SAF and CAF adjustments for basic segments, as well as merge, diverge, and weaving segments. New default values for CAF and SAF are presented followed by a discussion of recently added performance mea- sures. The section ends with a high-level explanation of the automation process. Incorporation of the Two-Capacity Phenomenon The HCM2010 freeway facilities methodology encompassed undersaturated and congested flow regimes over multiple time periods. However, the methodology was limited by its assumption of a fixed capacity threshold between the two flow regimes. The method did not consider the drop in throughput from theoretical capacity that has been observed after break- down has occurred at freeway bottlenecks. In other words, in the HCM2010 methodology, when demand exceeds capacity at a freeway bottleneck, queuing and congestion impacts are estimated, but the bottleneck discharges traffic at the prebreakdown capacity. However, strong evidence in the literature suggests that the freeway capacity at bottlenecks is measurably reduced after breakdown has occurred. Many studies have focused on the topic of queue discharge flow, and their results confirm that the capacity at a bottleneck drops by a factor ranging from 1% to 18%, with an average

82 reduction around 7%. This finding is often referred to as the two-capacity phenomenon. Past research has demonstrated that the incorporation of the freeway two-capacity phenomenon will result in non- trivial impacts on performance measures such as queue lengths, queue formation and dissipation times, speed and travel time, and facility levels of service. At first glance, a 5% to 7% reduction in capacity may seem trivial. Such a capacity reduction is equivalent to a drop of 120 vehicles per hour (veh/h) in capacity for a high-design free- way lane (2,400 passenger cars per hour per lane, or pcphpl). However, a closer investigation of shock wave theory for con- gested flow on freeways reveals that the drop in capacity of this magnitude will have significant impact on oversaturated traffic conditions. Figure 6.1 shows a shock wave diagram of traffic flow which is conceptually similar to the freeway facilities method adopted in the HCM2010. At density values below the density at capac- ity (Kcap), or demand values below the segment capacity (CN), the model uses the speed–flow relationship in the HCM2010 segment chapters for basic freeway segments, merge segments, diverge segments, or weaving segments. For densities above capacity (45 passenger cars per mile per lane, or pcpmpl), a linear flow–density model is assumed. The model is used to estimate the shock wave speed upstream of an active bottle- neck (Sb) with capacity less than the high upstream demand (CB < DH). The diagram also shows the speed of the accumu- lating shock wave (Sacc), and the dissipating shock wave (Sdis) after the upstream demand has dropped below the bottleneck capacity (CB > DL). When the bottleneck is activated, the maximum flow that is allowed to travel through the segment equals the down- stream bottleneck capacity CB in the current procedure. With consideration of the two-capacity regime, the actual through- put in the bottleneck after breakdown is assumed to drop by a%, where (1 - a) is the fraction of remaining bottleneck capacity. This is indicated in Figure 6.1 as a reduction in flow and an increase in density from KB to K′B. In Figure 6.1, the slope Sacc represents the speed of the forming queue (shock wave speed) under a demand flow DH. It can be computed by using Equation 6.1: 1 (6.1)accS D C K K H B H B ( ) = − − α − ′ where DH = demand flow rate upstream of the queue; CB = uninterrupted bottleneck capacity; KH = density upstream of the queue; K′B = density in the queue during queue discharge; and a = percent capacity drop (fraction). The shock wave speed is a critical variable in the oversatu- ration analysis. It helps predict the dimension of the queue, which greatly affects other freeway traffic characteristics and performance measures, such as density, speed, and travel time on the facility. To ascertain the impact caused by the capacity drop, expressing Sacc based on a is useful. Using the similar triangle rule, Equation 6.2 can be used to show the density during queue discharge. K K C C K KB B N ( )( )′ = − − α × × −1 (6.2)jam jam cap Substituting Equation 6.2 into Equation 6.1 gives the speed of the accumulating wave (Equation 6.3): 1 1 (6.3)acc jam jam cap S C F C C C K K C K K N H N B N H B( ) ( ) ( ) ( )= × − × − α × − + − α × × − When the peak period is over, demand is expected to decrease and eventually drop below the bottleneck capacity. At that time, the queue will start to dissipate. In Figure 6.1, the slope Sdis represents the speed of queue dissipation. Similarly, Equation 6.4 provides the speed of the dissipating wave, Sdis. 1 1 (6.4)dis jam jam cap S C F C C C K K C K K N L N B N L B( ) ( ) ( ) ( )= × − × − α × − + − α × × − Equations 6.3 and 6.4 make clear that the shock wave speeds (accumulating or dissipating) are sensitive to a num- ber of parameters, including the magnitude of capacity drop, bottleneck capacity, normal segment capacity and demand flow rate, and other segment attributes such as jam density and density at capacity. The impact from capacity drop would thus vary with the characteristics of the freeway segment of interest in a nonlinear fashion. In summary, the effect of capacity drop in queue discharge mode is not limited to decreasing the bottleneck capacity. It Source: Hu et al. (2012), Figure 1, p. 79. Reproduced with permission of the Transportation Research Board. Figure 6.1. Shock wave illustration with two-capacity approach.

83 also increases queue formation shock wave speed and decreases the queue dissipation speed. In past research, even a 5% drop in capacity has been shown to result in an approximate 80% increase in queue length and 40% increase in travel time for a simulated test facility. In the proposed implementation for HCM2010, a default queue discharge drop of 7% is proposed on the basis of research. However, the user is given the flexi- bility in the FREEVAL-RL engine to set a within a range of 0% to 10%. The research team also expects a to emerge as a key calibration factor in the methodology, as described later in this section. Incorporation of Speed Adjustment Factor for Basic Segments The effects of weather and incidents on freeway facilities are modeled through a capacity adjustment factor (CAF) in the HCM2010. However, strong evidence in the literature sug- gests that weather and incidents also affect the free-flow speed, with especially severe weather events like heavy rain and snow resulting in significant speed drops even at very low volume lev- els. Therefore, another input was needed to account for free- flow speed adjustment as a result of the congestion source. This new adjustment factor is the speed adjustment factor (SAF). The research team explored various options for incorpo- rating SAF into the HCM2010 methodology and ultimately developed a modification to Equation 25-1. That equation dates back to the HCM2000 and uses a CAF to estimate a revised speed–flow relationship for work zones and incidents. Inputs to the equation are the base capacity (C), the free-flow speed (FFS), the CAF, and the prevailing flow rate (vp). The updated Equation 6.5, which adds SAF as a multiplier of the FFS, follows: FFS SAF 1 (6.5) ln FFS SAF 1 CAF 45 CAFS e C v C p ( )= × + − ( )( )× + − × × × where S = segment speed, mi/h; FFS = segment free-flow speed, mi/h; SAF = segment speed adjustment factor; C = original segment capacity, pcphpl; CAF = capacity adjustment factor; and vp = segment flow rate, pcphpl. With the revised Equation 25-1, the HCM2010 results remain unchanged for cases with SAF = 1.0, which may include some work zone configurations. The introduction of SAF results in internally consistent results and provides an additional calibration tool to enable better fitting to local conditions and driver culture. An example application of SAF and CAF for different base free-flow speeds and weather categories is shown in Figure 6.2. The defaults for SAF and CAF are based on a new research synthesis (presented in a later section). The graph shows the effects of medium rain (dashed) and heavy snow (dotted), rela- tive to clear weather conditions (solid line) for base free-flow speeds of 75 mph (blue), 65 mph (green), and 55 mph (red). Figure 6.2. Example application of SAF and CAF for different base FFS and weather categories.

84 Consideration of CAF and SAF for Other Segment Types The equation for CAF and SAF described in the previous sec- tion is ultimately intended for application to basic freeway segments. However, in the HCM2000 and HCM2010, it was also applied to the analysis of merge, diverge, and weaving segments with CAFs less than 1.0. As a further improvement, this section describes the adaptation of CAF and SAF to these other HCM2010 segment types. A challenge arises in both ramp (merge or diverge) and weaving segment analysis when considering CAF and SAF because the methodologies for both of these freeway segment categories do not use segment capacity as an input to the speed prediction equation. In essence, the HCM2010 procedures for these segment types violate the fundamental equation of traffic flow (speed = flow × density). Both methods first estimate seg- ment capacity and then perform a check to assure that traffic demands are below that capacity (otherwise, demand-to- capacity >1 and the oversaturated module is invoked). If the segment passes the capacity check, the segment speed is esti- mated from an independent regression equation. With the L08 enhancements, the base capacity is adjusted with the appropriate CAF before performing the demand-to-capacity check. Equa- tion 6.6 shows how the adjusted capacity is calculated: Adjusted Capacity Base Capacity CAF (6.6)= × where Adjusted Capacity = capacity used to perform the demand- to-capacity check to switch to the oversaturated procedure (if demand- to-capacity >1, then the oversatu- rated procedure is invoked); Base Capacity = segment capacity estimated from the appropriate HCM2010 chapter; and CAF = user input capacity adjustment factor. Given the current structure of the HCM methodology, the research team implemented CAF and SAF separately. Spe- cifically, CAF is used as a multiplicative factor of the segment base capacity in the initial checks, while SAF is subsequently used as a multiplier of FFS in the speed prediction equation (discussed for merge/diverge and weaving segments in the following subsection). Principally, the application of CAF and SAF is consistent with the basic segment procedure, with the caveat that the factors are applied in two (or more) sepa- rate steps. Merge and Diverge Segments Exhibit 13-11 in the HCM2010 gives equations for estimating the average speed of vehicles within the ramp influence area, as well as in outer lanes of the freeway. Those equations are updated by this research to incorporate the SAF. The updated equations are shown in Table 6.1. Exhibit 13-12 in the HCM2010 is used to estimate speed at off-ramp (diverge) junctions in a way that is similar to how Exhibit 13-11 is used to estimate speed at on-ramp segments. The updated equations are shown in Table 6.2. The variables in Table 6.1 and Table 6.2 are defined as follows: SR = average speed of vehicles within the ramp influence area, mph; for merge areas this includes all ramp and freeway vehicles in lanes 1 and 2; for diverge areas, this includes all vehicles in lanes 1 and 2; Table 6.1. Estimating Speed at Merge (On-Ramp) Junctions with SAF Consideration Average Speed in Equation Ramp influence area SR = (FFS × SAF) - ((FFS × SAF) - 42) MS MS = 0.321 + 0.0039e(vR12/1,000) - 0.002 (LASFR × SAF/1,000) Outer lanes of freeway SO = FFS × SAF SO = (FFS × SAF) - 0.0036(vOA - 500) SO = (FFS × SAF) - 6.53 - 0.006(vOA - 2,300) vOA < 500 pc/h 500 pc/h ≤ vOA ≤ 2,300 pc/h vOA > 2,300 pc/h Table 6.2. Estimating Speed at Diverge (Off-Ramp) Junctions with SAF Consideration Average Speed in Equation Ramp influence area SR = (FFS × SAF) - ((FFS × SAF) - 42)DS DS = 0.883 + 0.00009vR - 0.013(SFR × SAF) Outer lanes of freeway SO = 1.097(FFS × SAF) SO = 1.097(FFS × SAF) - 0.0039 (vOA - 1,000) vOA < 1,000 pc/h vOA ≥ 1,000 pc/h

85 SO = average speed of vehicles in outer lanes of the freeway, adjacent to the 1,500-ft ramp influence area, mph; S = average speed of all vehicles in all lanes within the 1,500-ft length covered by the ramp influence area, mph; FFS = free-flow speed of the freeway, mph; SAF = segment speed adjustment factor of the ramp segment; SFR = free-flow speed of the ramp, mph; LA = length of acceleration lane, ft; vR = demand flow rate on ramp, pcph; v12 = demand flow rate in lanes 1 and 2 of the freeway upstream of the ramp influence area; vR12 = total demand flow rate entering the on-ramp influence area, including v12 and vR, pcph; vOA = average per-lane demand flow in outer lanes adjacent to the ramp influence area (not including flow in lanes 1 and 2), pcphpl; Ms = speed index for on-ramps (merge areas); this is simply an intermediate computation that simplifies the equa- tions; and Ds = speed index for off-ramps (diverge areas); this is sim- ply an intermediate computation that simplifies the equations. By using Exhibit 13-13 in the HCM2010, the average speeds for merge and diverge (on-ramp and off-ramp) junc- tions are calculated. Similar to basic segments, a sensitivity analysis was performed for a typical merge (on-ramp) seg- ment. The default values used in this analysis are shown in Table 6.3. Figure 6.3 shows the impacts of various weather events, including medium rain (dashed) and heavy snow (dotted), relative to normal weather conditions (solid line) for base free-flow speeds of 75 mph (blue), 65 mph (green), and 55 mph (red) on a typical merge (on-ramp) segment. Each line in Figure 6.3 terminates at the capacity for the prevailing adjusted FFS and weather conditions. The flow rate on the x-axis is referenced to the segment immediately downstream of the on-ramp. Weaving Segments The capacity of a weaving segment is calculated using Equa- tion 12-3 in HCM2010. In the L08 enhancements, the weav- ing segment capacity is further adjusted by the appropriate CAF if necessary (Equation 6.6). Similar to ramp segments, Table 6.3. Default Values Used in Merge (On-Ramp) Segment Analysis FFS (mph) SFR (mph) LA (ft) Normal Medium Rain Heavy Snow SAF CAF SAF CAF SAF CAF 75 45 1,500 1 1 0.93 0.90 0.81 0.72 65 45 1,500 1 1 0.94 0.92 0.85 0.76 55 45 1,500 1 1 0.96 0.94 0.88 0.80 Figure 6.3. Example application of SAF and CAF for different base FFS and weather categories on merge (on-ramp) segments.

86 the speed calculation procedure for weave segments is modi- fied to consider weather and incident reductions in free-flow speed, through the use of SAFs. The method separately esti- mates the speed of weaving and nonweaving vehicles, which are eventually combined to estimate a space mean speed of all vehicles in the segment. The equations for calculating the speed of weaving and nonweaving vehicles (Equations 12-19 and 12-20 in HCM2010) are modified by multiplying each occurrence of FFS by SAF (Equations 6.7, 6.8, and 6.9): 15 FFS SAF 15 1 (6.7)S W W ( )= + × −+ 0.226 LC (6.8) ALL 0.789 W LS =   FFS SAF 0.0072LC 0.0048 (6.9)NW MINS v N( )( )= × − − In the next step, the space mean speed of all vehicles in the weaving segment is computed by HCM2010 Equation 12-20, repeated here as Equation 6.10: (6.10) NW NW NW S v v v S v S W W W = +   +   The variables used in Equations 6.7 through 6.10 are as follows: SW = average speed of weaving vehicles within the weav- ing segment, mph; SNW = average speed of nonweaving vehicles within the weaving segment, mph; FFS = free-flow speed of the weaving segment, mph; SAF = speed adjustment factor of the weaving segment; W = weaving intensity factor; LS = length of the weaving segment, using the short length definition, ft (300 ft is the minimum value); LCALL = total lane-changing rate of all vehicles in the weaving segment, from HCM2010 Chapter 12, lane changes per hour; LCMIN = minimum rate of lane changing that must exist for all weaving vehicles to successfully complete their weaving maneuvers, from HCM2010 Chapter 12 (lane changes per hour); v = total demand flow rate in the weaving segment = vW + vNW, pcph; vW = weaving demand flow rate in the weaving segment, pcph; vNW = nonweaving demand flow rate in the weaving seg- ment, pcph; N = number of lanes within the weaving section; and S = space mean speed of all vehicles in the weaving segment. Example Problem 1 from HCM2010 Chapter 12 was selected as the basis for a speed versus flow rate sensitivity analysis. The SAFs and CAFs used in this analysis are shown in Figure 6.4. Note that under these particular sets of inputs, speed varies linearly with flow. Also note that the figure is truncated for flow rates below 1,200 pcphpl. Figure 6.4. Example application of SAF and CAF for different base FFS and weather categories on weaving segments.

87 New Defaults for CAF and SAF The research team performed an extensive literature review on the impacts of incidents and weather events on both seg- ment free-flow speed and capacity. Summaries are presented in Table 6.4 and Table 6.5. These tables show the new default values proposed for the HCM. Note that for incidents, the literature was inconclusive as to the effect on FFS, so a uni- form SAF of 1.0 is assumed for incidents. An experienced analyst may choose to override these defaults with the sup- port of local data or experience. Enhanced Performance Measures for Congested Conditions Because the focus of the L08 project is to incorporate nonrecur- ring congestion effects into the HCM2010, the procedure for Table 6.4. Literature Synthesis of Appropriate SAFs and CAFs for Different Weather Conditions Weather Type Capacity Adjustment Factors (CAF) Free-Flow Speed Adjustment Factors (SAF) Free-Flow Speed (mph) 55 mph 60 mph 65 mph 70 mph 75 mph 55 mph 60 mph 65 mph 70 mph 75 mph Clear Dry Pavement 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 Wet Pavement 0.99 0.98 0.98 0.97 0.97 0.97 0.96 0.96 0.95 0.94 Rain ≤0.10 in/h 0.99 0.98 0.98 0.97 0.97 0.97 0.96 0.96 0.95 0.94 ≤0.25 in/h 0.94 0.93 0.92 0.91 0.90 0.96 0.95 0.94 0.93 0.93 >0.25 in/h 0.89 0.88 0.86 0.84 0.82 0.94 0.93 0.93 0.92 0.91 Snow ≤0.05 in/h 0.97 0.96 0.96 0.95 0.94 0.94 0.92 0.89 0.87 0.84 ≤0.10 in/h 0.95 0.94 0.92 0.90 0.88 0.92 0.90 0.88 0.86 0.83 ≤0.50 in/h 0.93 0.91 0.90 0.88 0.87 0.90 0.88 0.86 0.84 0.82 >0.50 in/h 0.80 0.78 0.76 0.74 0.72 0.88 0.86 0.85 0.83 0.81 Temp <50 deg F 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.98 0.98 <34 deg F 0.99 0.99 0.99 0.98 0.98 0.99 0.98 0.98 0.98 0.97 <-4 deg F 0.93 0.92 0.92 0.91 0.90 0.95 0.95 0.94 0.93 0.92 Wind <10 mph 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 ≤20 mph 0.99 0.99 0.99 0.99 0.99 0.99 0.98 0.98 0.97 0.96 >20 mph 0.99 0.99 0.99 0.98 0.98 0.98 0.98 0.97 0.97 0.96 Visibility <1 mi 0.90 0.90 0.90 0.90 0.90 0.96 0.95 0.94 0.94 0.93 ≤0.50 mi 0.88 0.88 0.88 0.88 0.88 0.95 0.94 0.93 0.92 0.91 ≤0.25 mi 0.90 0.90 0.90 0.90 0.90 0.95 0.94 0.93 0.92 0.91 Table 6.5. Literature Synthesis of Appropriate CAFs for Different Incident Conditions Number of Lanes (one direction) No Incident Shoulder Closure One-Lane Closure Two-Lane Closure Three- Lane Closure Four-Lane Closure 2 1.00 0.81 0.70 0.00 0.00 0.00 3 1.00 0.83 0.74 0.51 0.00 0.00 4 1.00 0.85 0.77 0.50 0.52 0.00 5 1.00 0.87 0.81 0.67 0.50 0.50 6 1.00 0.89 0.85 0.75 0.52 0.52 7 1.00 0.91 0.88 0.80 0.63 0.63 8 1.00 0.93 0.89 0.84 0.66 0.66

88 doing so is expected to be used to model highly oversaturated conditions. To facilitate such cases, new performance mea- sures have been developed. These measures serve as addi- tional checks of reasonableness for the analyst, and some are derived from the travel time distribution. The estimated travel time distribution is expected to be the most critical output from this methodology. Denied Entry Queue Length A new output variable added in FREEVAL-RL is the denied entry queue length (DEQL). The motivation for adding this variable was to identify severely congested scenarios for fur- ther analysis. Another advantage of calculating the DEQL is that the analyst gets a sense of the validity of the reliability performance measures. In other words, the HCM2010 meth- odology is not designed to handle all congested conditions; in particular, it has not been validated for very severe congestion scenarios. Therefore, the procedure may generate unrealistic results under those conditions. The DEQL can serve as a flag for these types of scenarios. The DEQL informs the user of vehicle spillback out of the spatial domain of the coded facility in FREEVAL. Equation 6.11 is used to calculate DEQL at each analysis period inside the computational engine: Denied Entry Queue Length UV 5,280 (6.11) K KQ B = − × where Denied entry = denied entry queue length at the end of the queue length analysis period, ft; UV = number of unserved vehicles on the first segment of the facility at the end of the analysis period, veh; KQ = queue density, the vehicle density in the queue on the first segment of the facility at the end of the analysis period, veh/mi; calculated on the basis of a linear density– flow relationship in the congested regime inside the computational engine; and KB = background density, the first segment density over the analysis period assuming there is no queuing on the segment, veh/ mi/lane; this density is calculated using the expected demand on the segment in the corresponding undersaturated procedure in Chapters 11 through 13 of the HCM2010. Another advantage of representing DEQL is to give users a sense of how much they should expand the spatial scope of the coded facility. For example, the base scenario should preferably have no DEQL to ensure that the spatial extent of base congestion (no weather or incident effect) is fully contained within the facility. Similarly, the majority of sce- narios should preferably result in zero or low denied entry queues, with only rare and very severe scenarios having higher queue estimates. Travel Time Index for Entire Time-Space Domain The travel times for each segment at each analysis period (time-space domain) are available as outputs in the original HCM2010 methodology. Therefore, the facility’s travel time index (TTI) can simply be calculated by dividing individual travel times by the free-flow travel time. Equation 6.12 dem- onstrates this simple calculation: TTI TT FFTT (6.12)ij ij i= where TTIij = travel time index on segment i in analysis period j; TTij = travel time on segment i in analysis period j; and FFTTi = free-flow travel time on segment i. Also, the facility TTI in each analysis period is calculated simply by dividing facility travel time at a specific time period by its free-flow travel time (Equation 6.13): TTI TT FFTT (6.13)j j j= where TTIj = facility travel time index in analysis period j; TTj = facility travel time in analysis period j; and FFTTj = facility free-flow travel time in analysis period j. In applying the method to multiple scenarios, a separate TTI is generated for each 15-min analysis period in each sce- nario. These calculated TTIs, along with the corresponding probabilities produced by the freeway scenario generator, are used to develop a cumulative TTI distribution, as shown in Appendix A. The analyst may further decide to focus on the 50th, 85th, or 95th percentile TTI as a performance measure, as illustrated in Figure 6.5. The TTI distribution can further be segregated into recurring and nonrecurring scenarios, or it can be used to compare distributions based on different demand, weather, or incident conditions. Automation of Computations In order to evaluate multiple scenarios, some form of auto- mation is required. The HCM freeway facilities method has long relied on the use of computational engines like FREEVAL-2010 to conduct the analysis. With the introduc- tion of reliability analyses, FREEVAL needed to be adapted to run in batch mode. Essential information for reliability analysis is now saved from each run. Each run output is saved in a separate spreadsheet named according to the respective

89 scenario. The saved output from each run can be categorized as follows: • Scenario description; • Analysis period detailed performance measures; • Speed contour in the time–space domain; and • Overall result summary sheet. After the runs are completed, all scenario attributes are tabulated in a single spreadsheet for fast and efficient analy- sis. This summary report contains all the necessary infor- mation for each analysis period from all scenario runs. Each line represents a 15-min analysis period output for a given scenario. FreeVaL-rL Calibration Estimating the distribution of the travel time index (i.e., the ratio of average travel time to free-flow travel time) for a free- way facility involves using two computational engines. The first engine is the freeway scenario generator (FSG), which creates the different scenarios (unique combinations of demand patterns, weather conditions, incidents, work zones, and spe- cial events) that may be observed on a freeway facility, along with their individual probabilities. The second engine is FREEVAL-RL, which implements the HCM freeway facility methodology and calculates the travel time (and other per- formance measures) associated with each scenario. To fully calibrate the TTI distribution, several parameters in both the FSG and FREEVAL-RL can be adjusted to re-create observed operations in the field. This section describes the process of calibrating some of the key parameters available in FREEVAL-RL, without unduly complicating the calibration process. Traffic demand level is one of these parameters. Although traffic counts (or AADTs in data-poor environments) are used to calculate the entry traffic demand onto the facility, they are estimates of actual demand on the facility and can be significantly different from reality. An incorrect estimate of the traffic demand is likely to lead to an inaccurate estimate of the facility travel time. This point makes clear the importance of calibrating the traffic demand and determining the level at which the resulting travel time distribution is as close as possible to the field-observed distri- bution. In addition, the values assumed for (1) the percent drop in capacity during traffic breakdown (a) and (2) jam density can yield significant changes in the travel time esti- mate resulting from changes in bottleneck throughput queue lengths and the speeds at which queues accumulate and dis- sipate, respectively. Study Site and Data Sources The calibration methodology was applied to a 12.5-mile free- way facility on eastbound Interstate 40 between mile markers 278.5 (point A in Figure 6.6) and 291.0 (point B) near Raleigh, North Carolina. The case study facility has a speed limit of 65 mph and a free-flow speed of 70 mph. The reliability reporting period (RRP) over which the analysis was carried out included all weekdays of calendar year 2010, and a study period from 2:00 to 8:00 p.m. The facility is primarily a com- muter route that connects Durham to Raleigh, passing through the Research Triangle Park, a major employment center in the area. The two-way facility AADT was approximately 120,000 in 2010, and the eastbound facility experiences recurring congestion in the p.m. peak period. Traffic demand data were estimated from counts extracted from permanent side-fire radar sensors located along the facility mainline. Temporary tube counters placed at the Figure 6.5. Sample cumulative TTI distribution with key percentiles. CDF = cumulative distribution function.

90 on- and off-ramps for a 2-week period were used to supplement the data because the ramps have no permanent sensors. Side- fire sensor data were collected for all of 2010 at the 15-min level; daily per-lane volumes were calculated at each sensor to deter- mine combinations of days and months that operated similarly. Figure 6.7 shows trends in average daily traffic (ADT) per lane for 2010. Monday through Wednesday experience similar demand levels, while Thursday is more elevated and Friday has the highest demand. Although seasonal variation was not as significant, four seasons encompassing three months each (December–January–February; March–April–May; June–July– August; and September–October–November) were selected to group months with similar demands and similar weather conditions. This process resulted in 12 separate demand groups, or pat- terns. Daily and monthly demand factors were calculated from the ratio of ADT for each combination of month and day for 2010 to the AADT. These values were then averaged for each of the 12 demand patterns emerging from the data. These patterns are depicted in Table 6.6 for each collection of con- tiguous cells with the same background color and border. As part of the calibration, the overall demand levels were adjusted to determine the best demand level that recreates the observed operations. Fifteen-minute segment travel times were downloaded from the Regional Integrated Transporta- tion Information System based on INRIX probe data that were collected across the facility during the RRP. The facility travel time was estimated from the segment travel times using a pseudotrajectory method based on the concept of “stitch- ing” or “walking” the travel time. To identify typical opera- tions with only recurring congestion effects, each 15-min period of the year was compared with weather and incident logs to confirm which time periods had no weather events or incidents. Inclusion Thresholds Theoretically, the reliability procedure can generate up to 22,932 detailed scenarios for the subject facility. Many of these may have exceptionally low or near-zero probability. In addition, some may be infeasible—for example, a two- or three-lane closure on a two-lane freeway segment. In this Source: © 2013 Google. Figure 6.6. I-40 facility location.

91 Table 6.6. Demand Factors: Ratio of ADT to AADT by Month and Day of Week Month Sunday Monday Tuesday Wednesday Thursday Friday Saturday January 0.617609 0.999005 1.030232 1.042881 1.055117 1.084198 0.662407 February 0.763747 0.941499 1.013144 1.041699 1.094640 1.142797 0.837179 March 0.794913 1.045799 1.071891 1.066066 1.113577 1.173921 0.940873 April 0.817347 1.076144 1.090055 1.100863 1.164751 1.217906 0.911421 May 0.815670 1.078904 1.108827 1.116618 1.160484 1.213328 0.933496 June 0.805796 1.080620 1.088449 1.070022 1.141443 1.183148 0.942226 July 0.764001 1.085168 1.073553 1.105148 1.150022 1.187813 0.933042 August 0.801063 1.048545 1.054661 1.062905 1.095856 1.167686 0.911527 September 0.768024 1.018452 1.026499 1.026072 1.077352 1.155702 0.893950 October 0.825240 1.051489 1.048223 1.069537 1.109691 1.163729 0.924886 November 0.756585 0.976373 1.002337 1.043700 1.084126 1.072912 0.829501 December 0.586780 0.977116 0.958762 0.989379 0.918297 1.010103 0.744283 Figure 6.7. Facility average ADT per lane by month and day of the week.

92 case, the improbable and zero-probability detailed scenar- ios were removed from the reliability analysis. That trans- lates to an inclusion threshold of near zero, meaning all scenarios with probability greater than zero were included in the analysis. Thus 2,058 scenarios were used in evaluat- ing travel time reliability for the I-40 facility, as shown in Table 6.7. In general, the scenarios with extremely low probability are not expected to be observed in the field in a single year; how- ever, they are included in the predicted TTI distribution when an inclusion threshold of zero is used. As a result, a comparison of the predicted and observed distributions is hard to interpret: the predicted distributions include the low-probability sce- narios, while the observed distribution may not include any of them. In addition, the low-probability scenarios tend to have exceptionally large TTI values that significantly shift the tail of the cumulative distribution to the right (i.e., toward higher TTI values). These scenarios may also result in demand shifts in the real world that are not directly accounted for in the freeway reliability method. Therefore, the procedure allows the user to specify an inclusion threshold and include only scenarios with probabil- ity larger than a specified threshold. For instance, an inclu- sion threshold of 1.0% means that only the scenarios with probability larger than 0.01 are considered in the analysis. Figure 6.8 presents the TTI cumulative distributions for four different inclusion threshold values for the subject facility, as well as the observed TTI distribution obtained from the INRIX data warehouse. For the subject facility, including all the scenarios with a nonzero probability in the analysis (i.e., inclusion threshold = zero) resulted in a general overestima- tion in the TTI cumulative distribution. Increasing the thresh- old to 1.0% brought the TTI distribution much closer to the observed distribution. An inclusion threshold of 1.2% resulted in matching planning time index (PTI) values for the pre- dicted and observed TTI distributions. Inclusion thresh- olds larger than 1.2% yielded a general underestimation in the TTI distribution. Increasing the value of the inclusion threshold reduces the number of scenarios and consequently the computational engine run time; however, at the same time, it reduces the per- centage of the coverage of feasible scenarios (Table 6.8). In other words, the larger the value of the inclusion threshold, then the greater the number of scenarios excluded from the analysis. As a result, fewer feasible scenarios are covered in the analysis. As shown in Table 6.8, the number of scenarios signifi- cantly drops as the value of the inclusion threshold is increased. Going from an inclusion threshold of 0.00% to 0.01% elimi- nates half of the scenarios and decreases the coverage of the distribution by only 0.29%. This means that more than 1,000 of the scenarios contributed to only 0.29% of the TTI distribution. Table 6.7. I-40 Facility: Final Scenario Categorization Scenario Type Number of Scenarios Percent of Total No incidents and nonsevere weather 12 0.6 No incidents and severe weather 66 3.2 Incidents and nonsevere weather 528 25.7 Incidents and severe weather 1,452 70.6 Total 2,058 100.0 Figure 6.8. I-40 facility: Travel time distribution results for different inclusion thresholds. Table 6.8. I-40 Facility: Number of Scenarios and Coverage of Feasible Scenarios Inclusion Threshold (%) Number of Scenarios Coverage of the Distribution (%) 0.00 2,058 100.00 0.01 1,004 99.71 0.10 496 97.46 1.00 264 89.63 1.20 210 85.07 1.30 174 82.55 2.00 84 75.91 3.00 81 67.04 4.00 4 37.32

93 Summary of Freeway Model enhancements The enhancements to the FREEVAL-RL computational engine include the following: • Incorporating the two-capacity phenomenon under queue discharge conditions; • Incorporating SAFs for certain nonrecurring congestion sources; • Improving modeling of CAFs and SAFs for merge, diverge, and weaving segments; • Adding new defaults for CAFs and SAFs for incidents and weather events on freeways; • Extending performance measures for congested conditions; and • Automating computation. The output of the enhanced computational engine is consis- tent with the HCM. Moreover, this section documents the calibration process for generating a cumulative TTI distribution for freeway travel time reliability purposes (to be applied before incor- porating any weather or incident effects), using the expanded HCM2010 approach to estimate facility reliability. In this process, three calibration parameters were tested: the traffic demand-level adjustment, the percent capacity drop during breakdown (a), and the facility jam density. Three values for each calibration parameter were evaluated, resulting in a total of 27 parameter combinations. Cumulative TTI distri- butions for each parameter combination were compared with the observed cumulative TTI generated from INRIX travel time data. The distributions were generated for a 12.5-mile freeway facility (eastbound I-40 near Raleigh, North Carolina). The statistical analysis revealed that increasing the overall base demand level in the seed file by 3.0% and using a value of 9% for a resulted in cumulative TTI distributions that were not statistically different from the observed cumulative TTI distributions. This conclusion applied to all jam density values because the results indicated that the estimated distri- bution was not sensitive to jam density over the range of parameter values investigated. In addition, increasing the traf- fic demand adjustment factor and the breakdown capacity reduction factor (a) resulted in increased TTI values and a shift in the TTI distribution toward the right, as expected. The large difference in some TTI distributions between HCM2010 and INRIX at higher percentiles could be attrib- uted to unreported events that may have affected demand and capacity over the course of the year. The travel time effects of unreported events would still be present in the INRIX data set. Urban Streets enhancements This section describes the enhancements made to the urban street segment methodology described in Chapter 17 of the HCM2010. The methodology is used to evaluate the opera- tion of undersaturated street segments. The enhancements described in this section extend the HCM2010 methodology to the evaluation of the operation of urban street facilities with one or more oversaturated segments. Three enhancements are described in this section. The first is a procedure for adjusting the discharge rate from a signal- ized intersection when a downstream incident or work zone blocks one or more lanes on the segment. The second is a procedure for computing the effective average vehicle spacing on a segment with spillback. The third is a process for using the HCM2010 methodology to evaluate urban street facilities with spillback in one or both travel directions on one or more segments. Mid-Segment Lane Restriction When one or more lanes on an urban street segment are closed, the flow in the lanes remaining open will be adversely affected. Occasionally, this blockage can have an adverse effect on the performance of movements entering the seg- ment at the upstream signalized intersection and on those exiting the segment at the downstream signalized intersec- tion. The nature of these impacts is shown in Figure 6.9 for a work-zone-related lane blockage. The impacts are similar for mid-segment incidents. In Figure 6.9, the mid-segment work zone is shown to influence the saturation flow rate of movements at both the upstream and downstream signalized intersections. Logically, the magnitude of the effect will increase as the distance between the intersection and work zone decreases. The mid-segment work zone can also influence segment travel time, especially if the demand exceeds the work zone capacity during a por- tion (or all) of the signal cycle. These influences are shown for one direction of travel; however, the work zone can be located in the middle of the street such that it influences both direc- tions of travel. Three areas of impact are identified in Figure 6.9. The effect on the upstream intersection saturation flow rate is the sub- ject of discussion in this section. The effect on segment travel time and capacity is addressed in the Chapter 5 section Urban Street Scenario Development. The effect on the downstream intersection saturation flow rate is described in Appendix J. Procedure The methodology described in HCM2010 Chapter 17 is shown in the flowchart in Figure 6.10. It consists of five main

94 Figure 6.9. Mid-segment work zone impacts. Saturation flow rate reduced by... 1. downstream work zone presence 2. downstream queue at work zone Segment travel time increased by... 1. slow speed through work zone 2. time in queue, if oversaturated Segment capacity based on... 1. number of open lanes 2. other geometric factors Saturation flow rate reduced by... 1. underutilized lanes 2. upstream work zone presence Segment length, L Work zone length, Lwz Figure 6.10. Methodology flowchart. Input volume and geometry Setup Module Report delay, queue storage ratio, volume-to-capacity ratio. Signalized Intersection Module Initial Queue Present? YesNo Set demand flow = capacity Reset demand flow = input flow rate Segment Evaluation Module Initial Queue Delay Module Performance Measures Module Another analysis period? Yes Finish No modules that are completed in sequence to produce a reliable estimate of street segment performance. In application, the methodology is repeated for each segment of the facility. The results of each application are aggregated to produce an esti- mate of facility performance. The HCM2010 provides more detail about these modules. The procedure described in this section is used to adjust the saturation flow rate of the movements entering a seg- ment when one or more downstream lanes are blocked. The procedure was developed for incorporation within the HCM Chapter 17 methodology, specifically, the segment evalua- tion module. The sequence of calculations in the segment

95 evaluation module is shown in Figure 6.11. The module com- prises eight procedures. As shown in the figure, the module is implemented in an iterative loop which repeats until conver- gence on the estimated phase duration is achieved. The relevant procedure is implemented in the sixth compu- tational routine, “ComputeMidSegmentCapacity,” outlined by a thick bold line. It compares the estimate of movement capacity (computed in the previous procedure) with the down- stream lane capacity. If the movement capacity exceeds the downstream lane capacity, then the movement saturation flow rate is reduced accordingly. This can occur when one or more downstream lanes are blocked because of a work zone or an incident. A new saturation flow rate adjustment factor is introduced by the procedure. This factor is computed for each movement entering the subject segment. Equations 6.14 and 6.15 are used to compute the factor value: If or 1.0 then: 0.1 otherwise: 1.0 (6.14) ms ms, 1 ms, ms, 1 ms ms, c c f f f c c f i i i i i i < < = × ≥ = − − with 0.25 1,800 (6.15)msc k N S Nj f= ≤ where fms,I = adjustment factor for downstream lane blockage during iteration i; cms = mid-segment capacity, veh/h; ci = movement capacity during iteration i, veh/h; kj = jam density (= 5,280/Lh), veh/mi/lane; Lh = average vehicle spacing in stationary queue, ft/veh; Sf = free-flow speed, mph; and N = number of lanes. The number of lanes used in Equation 6.15 equals the num- ber of unblocked lanes (i.e., the open lanes) while the blockage is present. The variable i in the adjustment factor subscript indicates that its value is incrementally revised with each subsequent iteration. Ultimately, it converges to a value that results in a movement capacity that matches the available mid-segment capacity. For the first iteration, the factor value is set to 1.0 for all movements. The factor value is also set to 1.0 if the seg- ment is experiencing spillback. In that situation, a saturation flow rate adjustment factor for spillback (which incorporates the downstream lane blockage effect) is computed for the movement. The calculation of the factor for spillback is described in a subsequent subsection. Equation 6.15 indicates that the factor is less than 1.0 when the mid-segment capacity is smaller than the movement Figure 6.11. Segment evaluation methodology. Check intersection volume balance and adjust if needed (VolumeCheck) Determine origin–destination volumes for segment (DefineODMatrix) Compute spillback time for flows internal to segment (SpillbackCheck) Compute projected arrival flow profile for internal movements (SegmentAnalysisModule) Finish Start Compute signalized intersection phase duration and uniform delay (SignalizedIntersectionModule) Compute delay due to turns from the major street (DelayDueToTurnsModule) Final phase duration = initial phase duration? YesNo Compute baseline uniform delay and first-term back-of-queue (ComputeAveragePhaseDuration) Adjust saturation flow rate when downstream lane blocked (ComputeMidSegmentCapacity)

96 capacity. If the factor has been set to a value less than 1.0 in a previous iteration, then the factor continues to be adjusted with each subsequent iteration until convergence is achieved. A minimum factor value of 0.1 is imposed as a practical lower limit. Equation 6.15 is based on the linear speed-density rela- tionship developed by Greenshields (1934) and the funda- mental relationships among flow, speed, and density. These relationships underlie the vehicle-proximity adjustment factor used in the HCM2010 Chapter 17 methodology (i.e., Equation 17-5) to compute segment running speed. When the average vehicle spacing Lh is 25 ft/veh, the mid-segment capacity is computed as cm = 52.8 N Sf. The saturation flow rate adjustment factor for downstream lane blockage is applicable to all signalized intersection move- ments that enter the urban street segment of interest. It is used to adjust the saturation flow rate of these movements. If implemented in the HCM2010, it would be added to Equa- tion 18-5 in Chapter 18. It would also be multiplied by the result obtained from Equations 31-59, 31-61, 31-62, 31-63, 31-101, 31-102, 31-104, 31-105, 31-106, 31-107, and 31-116 in HCM2010 Chapter 31. For those entry movements that have permissive or protected-permissive left-turn operation, the adjustment factor is also used to adjust the number of left-turn sneak- ers per cycle. This adjustment is shown in Equation 6.16: n n f n P f s a s s a L( ) = = + If exclusive left-turn lane then: If shared left-turn lane then: 1 (6.16) , ms , ms where ns,a = adjusted number of sneakers per cycle (= 2.0), veh; ns = number of sneakers per cycle, veh; and PL = proportion of left-turning vehicles in the shared lane. The change suggested by Equation 6.16 requires multiplying the factor fms by the result obtained from Equation 31-60 in Chapter 31 of the HCM2010. This factor should also be multi- plied by the ns term in Equations 31-113, 31-118, and 31-119, and by the (1 + PL) term in Equations 31-115 and 31-120. Effective Average Vehicle Spacing When an urban street segment experiences spillback, traffic movements at the upstream signalized intersection will be severely limited in the ability to serve traffic demand. Specifi- cally, the upstream movements that are destined for entry into the segment may be blocked by queued vehicles for some or all of the green indication (green traffic light). Thus, spill- back effectively reduces the capacity of these movements. Segment spillback falls into two categories. One type is called sustained spillback. It represents a condition in which the volume entering the segment exceeds the capacity of the downstream intersection for sufficient time to allow queued vehicles to extend for the length of the segment. Sustained spillback is a consequence of inadequate capacity. The period of sustained spillback starts the first time that vehicles stop on the segment because of the downstream signal and then block (or slow) the departure of one or more upstream movements desiring to enter the segment. A second type of segment spillback is called cyclic spill- back. It represents a condition in which the volume entering the segment does not exceed the capacity of the downstream intersection, but the signal timing (i.e., phase duration and offset) relationship between the upstream and downstream intersections is such that a queue of stopped vehicles can extend for the length of the segment for a portion of the sig- nal cycle. Random cycle-to-cycle variation in demand and capacity can increase the frequency and extent of this type of spillback. Cyclic spillback is more likely to occur at signalized interchanges and closely spaced signalized intersections. The remainder of the discussion in this subsection addresses sustained spillback because it is associated with large delays caused by congested conditions. Note that the interchange ramp terminals methodology in Chapter 22 of the HCM2010 addresses cyclic spillback. Chapter 30 of the HCM2010 describes a procedure for computing the time that spillback occurs on a segment, rela- tive to the start of a specified analysis period (and given any initial queue present at that time). One step in this procedure requires the calculation of the maximum queue storage on the segment. This calculation is based on the average vehicle spacing in a stationary queue Lh. Specifically, the maximum queue storage value is computed by dividing the length of segment available for storage by Lh. This calculation can overestimate the actual number of queued vehicles needed to precipitate segment spillback. The bias stems from the assumption that all vehicles on the segment will always be stationary when spillback occurs. This is a weak assumption because the downstream signal operation creates backward- traveling waves of starting and stopping. Between the start- ing wave and the stopping wave, vehicles are moving at the saturation headway and its associated speed. This behavior is illustrated in Figure 6.12. Figure 6.12 illustrates the position of vehicles during one point in time on a segment with spillback. Specifically, it indi- cates vehicle positions a few seconds after the onset of the red signal indication. The first four vehicles are shown to be stopped in the queue. The next five vehicles are moving at the saturation headway. The remaining vehicles are shown to be stopped. Those remaining vehicles will begin moving forward in a few seconds. The point of this figure is that the maximum queue storage value is less than that computed using the HCM2010 method because the spacing of the moving vehicles is larger

97 than Lh. This observation will always be true when the seg- ment length is sufficiently long that the stopping wave does not reach the upstream signal before the onset of the next green indication. The procedure described in this section is used to estimate the effective average vehicle spacing (L*h) on a segment with spillback. The derivation of this new variable is based on the vehicle trajectories shown in Figure 6.13. The segment of interest is shown on the left side of the figure. Spillback is pres- ent for all of the cycles shown; however, trajectories are shown for only two cycles. The solid trajectories coincide with vehi- cles that enter the segment as a through movement at the upstream intersection. The dashed lines coincide with vehicles that enter the segment as a turn movement. A vehicle that enters the segment traveling north as a through vehicle is shown to experience four cycles before exiting the segment. The trajectories show that the vehicles move forward at a satu- ration headway of 3,600/s seconds per vehicle (where s is the saturation flow rate in vehicles per hour) and a speed of Va ft/s. The lines that slope downward from the upper left to lower right represent the waves of reaction time. They have a slope of tpr seconds per vehicle. The starting wave originates at the onset of the green indication and the stopping wave origi- nates at the onset of the red indication. The average vehicle spacing when vehicles are stopped is Lh feet per vehicle. The relationship between the trajectories of the moving vehicles in Figure 6.13 defines the following relationship between speed, saturation headway, vehicle length, and driver starting response time tpr (Equation 6.17). 3,600 (6.17)prt s L V h a = − where tpr = driver starting response time, s/veh; and s = saturation flow rate, veh/h; Lh = average vehicle spacing in stationary queue, ft/veh; and Va = average speed of moving queue, ft/s. Driver starting response time and the distance between vehicles in a stopped queue at signalized intersections have been the subject of several previous studies. Messer and Fambro (1977) found that driver response was fairly constant at 1.0 s, regardless of queue position. The only exception was the driver in the first queue position who had an additional Vehicles moving up in queue. Signal indication has been red for several seconds. Figure 6.12. Vehicle position seconds after onset of red indication. Figure 6.13. Vehicle trajectories during spillback conditions. r Lh g Lh tpr 1 VaL t x 0 3,600/s C Vehicle Source Through movement at upstream intersection Turn movement at upstream intersection

98 delay of 2.0 s. The shorter response time of the second and subsequent queued drivers is likely due to their ability to anticipate the time to initiate motion by seeing the signal change and/or the movement of vehicles ahead. Messer and Fambro also found that the average length of roadway occu- pied by each queue position is about 25 ft. Another study of driver response time was conducted by George and Heroy (1966). They found driver response to be relatively constant at about 1.3 s for all queue positions. How- ever, further examination of their data suggests that the first driver’s response time was slightly longer, at about 1.5 s to 2.0 s. Response times in the preceding studies were all measured at the start of vehicle motion. A study found that driver response to disturbance (including the start of motion) remained fairly constant as the platoon of queued vehicles increased its speed (Herman et al. 1971). In particular, they found that the speed of propagation of the response wave was relatively constant at about 26 ft/s up to platoon speeds of 30 ft/s. By using an average distance between stopped vehicles of 25 ft, the starting response time for this wave speed can be calculated as 1.0 s (= 25/26). Bonneson (1992) evaluated discharge headway data by using a regression model based on Equation 6.17. He found that a starting response value of 1.34 s/veh provided the best fit to headway data at signalized intersections. On the basis of the relationships shown in Figure 6.13, the following procedure can be used to estimate the effective average vehicle spacing. Step 1: Compute Wave Travel Time The time required for the driver reaction wave to propagate backward to the upstream intersection is computed using Equation 6.18: (6.18)max , thru pr t L t L a h = × where tmax = wave travel time, s; La,thru = available queue storage distance for the through movement, ft; and tpr = driver starting response time (= 1.3), s/veh. The available queue storage distance for the through move- ment La,thru equals the segment length less the width of the upstream intersection. A value of 1.3 seconds per vehicle is recommended for the driver starting response time tpr. This value is based on the findings from past research summarized in the previous subsection. The average vehicle spacing in a stationary queue can be estimated using Equation 31-149 from Chapter 31 of the HCM2010. This equation estimates spacing for traffic streams composed of passenger cars and trucks. The discussion in Chapter 31 indicates that a value of 25 ft/veh can be used for the average spacing of passenger-car-only traffic streams. Step 2: Compute Speed of Moving Queue The average speed of the moving queue is computed using Equation 6.19. This equation was derived from Equation 6.17. 3,600 (6.19) pr V L s t a h ( )= − When the average vehicle spacing is 25 ft/veh, the satura- tion flow rate is 1,800 veh/h, and the driver starting response time is 1.3 s/veh, then the average speed of the moving queue is computed as 35.7 ft/s. Step 3: Compute Effective Average Vehicle Spacing The relationship between the trajectories of the moving vehicles defines the following relationships among speed, saturation flow rate, signal timing, and vehicle spacing (Equation 6.20): t r L L r t C L rs L s V r t C L L t g C s h h h a a h h ( )( ) ≤ < ∗ = ≤ < ∗ = +  ≤ < ∗ = − − If 0.0 then: If then: 3,600 If then: 1.0 3,600 (6.20) max max ,thru 1 max pr where L*h = effective average vehicle spacing in stationary queue, ft/veh; r = effective red time (= C - g), s; g = effective green time, s; and C = cycle length, s. Equation 6.20 has three component equations. Which com- ponent equation is used for a given segment and analysis period depends on the values of tmax, r, and C. The value of average vehicle spacing from the first component equation represents the smallest value that can be obtained from Equa- tion 6.20. The value from the last component equation repre- sents the largest value that can be obtained. The value obtained from the middle component equation varies between those two extreme values, depending on the value of tmax. The procedure described in this section is used to estimate the effective average vehicle spacing L*h on a segment with spillback. This estimate is intended for use with the spillback check procedure documented in Chapter 30 of HCM2010. The spillback check procedure is used to estimate the time until spillback. The variable L*h should be substituted for Lh in

99 Chapter 30. The result will be a more reliable estimate of the time until spillback. Sustained Spillback This subsection describes a methodology for using the HCM2010 urban streets methodology to evaluate a facility with spillback in one or more travel directions on one or more segments. This discussion addresses sustained spillback, as already defined. The effect of spillback on traffic flow is modeled through an iterative process that repeatedly applies the HCM2010 methodology to the subject urban street facility. If spillback occurs on a segment, then the discharge rate of the traffic movements entering the segment are reduced such that (1) the number of vehicles entering the segment equals the number of vehicles exiting the segment and (2) the residual queue length equals the available queue storage distance. A conceptual overview of the spillback methodology fol- lows. The approach used to model spillback effects is similar to the multiple-time-period analysis procedure described in Chapter 18 of HCM2010. However, in this application, a single analysis period is divided into subperiods for separate evalua- tion. Each subperiod is defined using the following rules: • The first subperiod starts with the start of the analysis period. • The current subperiod ends (and a new subperiod starts) with each new occurrence of spillback on the facility. • The total of all subperiod durations must equal the origi- nal analysis period duration. As with the multiple-time-period analysis procedure, the residual queue from one subperiod becomes the initial queue for the next subperiod. When all subperiods have been evalu- ated using the HCM2010 methodology, the performance measures for each subperiod are aggregated for the analysis period using a weighted-average technique, in which the weight is the volume associated with the subperiod. The spillback modeling approach is described by applying it to a simple two-segment urban street facility. It supports travel in both directions, so four occurrences of spillback are possible. The analysis period is 0.25 h, which coincides with the time interval 0.0 h to 0.25 h. The facility is shown in Figure 6.14 along with the initial queue at the start of the analysis period. The HCM2010 methodology is used to evaluate the facil- ity. The results indicate that spillback occurs on segment 2–3 in the eastbound travel direction (i.e., EB 2-3). This condition is shown in Figure 6.15. The time until spillback is 0.10 h, which is before the end of the analysis period. As a result, the predicted travel time for the eastbound direction is not cor- rect. Therefore, additional evaluation is needed. The HCM2010 methodology is used again to evaluate the facility, but this time the analysis period is reduced to 0.10 h, which coincides with the time interval 0.0 h to 0.10 h. The initial queue for EB 2-3 is still 1.0 vehicle. The results from the evaluation again indicate that the time until spillback is 0.10 h. However, the predicted travel time for this subperiod is correct because the time until spillback does not exceed the analysis period. At this point, the results reflect only the time period 0.0 h to 0.10 h. Additional evaluation is needed to estimate the facility performance for the time period 0.10 h to 0.25 h. N 1 2 3 Figure 6.14. Example facility at start of analysis period. 1 2 3 Spillback at Ts = 0.1 h Evaluation 1a Analysis Period T = 0.25 h Initial Queue = 1.0 veh Figure 6.15. Example facility at time 0.10 hours.

100 Therefore, the HCM2010 methodology is again used to eval- uate the facility. The analysis period is 0.15 h (= 0.25 - 0.10), which coincides with the time interval 0.10 h to 0.25 h. The facility is shown in Figure 6.16. For this subperiod, the initial queue for EB 2-3 is 4.0 vehicles. Also, the saturation flow rate of each movement entering EB 2-3 is reduced to ensure that the residual queue on EB 2-3 does not exceed the available queue storage distance in subsequent time intervals. The results indicate that spillback occurs on segment 1–2 in the eastbound travel direction (i.e., EB 1-2). This condition is shown in Figure 6.16. The time until spillback is 0.05 h, which is before the end of the analysis period. As a result, the predicted travel time for the eastbound direction is not cor- rect. Once again, additional evaluation is needed. The HCM2010 methodology is used to evaluate the facil- ity, but this time the analysis period is reduced to 0.05 h, which coincides with the time interval 0.10 h to 0.15 h. The initial queue for EB 2-3 is still 4.0 vehicles. The results from the evaluation again indicate that the time until spillback is 0.05 h. However, the predicted travel time for this subperiod is correct because the time until spillback does not exceed the analysis period. At this point, the results reflect only the time periods 0.0 h to 0.10 h and 0.10 h to 0.15 h. Additional evaluation is needed to estimate the facility performance for the time period 0.15 h to 0.25 h. The HCM2010 methodology is again used to evalu- ate the facility. The analysis period is 0.10 h (= 0.25 - 0.15), which coincides with the time interval 0.15 h to 0.25 h. The facility is shown in Figure 6.16. For this subperiod, the initial queue for EB 2-3 is 4.0 vehicles and that for EB 1-2 is also 4.0 vehicles. The saturation flow rate of each movement enter- ing EB 1-2 and EB 2-3 is reduced to ensure that the residual queue on EB 1-2 and on EB 2-3 does not exceed the available queue storage distance in subsequent time intervals. The results of this evaluation indicate that no new spill- back occurs. So, the predicted travel time for this subperiod is correct. The average travel time for the facility is computed as a weighted-average travel time for each of the three subperiods, in which the weight used is the subperiod volume. The sequence of calculations in the spillback methodology is shown in Figure 6.17. It consists of several routines and two loops, one of which is an iterative loop with a convergence criterion. The HCM2010 urban streets methodology is imple- mented at three separate points in the flowchart. Following the logic flow from the Start box, the HCM2010 methodology is initially implemented and the presence of spillback is checked. If spillback does not occur, then the results are reported and the process is concluded. If spillback occurs on a segment, then a subperiod is defined and the HCM2010 methodology is reimplemented using an analysis period that is shortened to equal the time until spillback. The iterative loop shown on the right side of Figure 6.17 is called to quantify a saturation flow rate adjustment factor for each movement entering the segment with spillback. The value of this factor is determined to be the value needed to limit the entry movement volume such that the residual queue on the segment does not exceed the available queue storage distance. The following subsections describe the spillback method- ology as a sequence of computational steps that culminate in the calculation of facility performance for a specified analysis period. The input data requirements for this meth- odology are the same as for the HCM2010 urban streets methodology. Step 1: Initialize Variables Set the original analysis period variable To equal to the analy- sis period T input by the analyst. Set the total time variable Ttotal, 0 equal to zero and the subperiod counter k to 0. Step 2: Implement the HCM2010 Methodology The HCM2010 methodology is implemented in this step to evaluate the facility described by the input data. The analysis period duration is computed as T = To - Ttotal,k. Increase the value of the subperiod counter k by 1.0. Step 3: Check for Spillback During this step, the results from Step 2 are examined to deter- mine if new spillback has occurred. One direction of travel on Figure 6.16. Example facility at time 0.15 hours. 1 2 3 Evaluation 2a Analysis Period T = 0.15 h (= 0.25 - 0.10) Initial Queue = 4.0 veh Spillback at Ts = 0.05 h

101 one segment is considered a site. Each site is checked in this step. Any site that has experienced spillback during a previous subperiod is not considered in this step. The predicted controlling time until spillback is recorded in this step. If several sites experience spillback, then the time of spillback that is recorded is based on the site experiencing spillback first. The site that experiences spillback first is flagged as having spilled back. The controlling time until spillback for the subperiod Tcs, k is set equal to the time until spillback for this site. The total time variable is computed using Equation 6.21, which represents a cumulative total time for the current, and all previous, subperiods. (6.21)total, total, 1 cs,T T Tk k k= +− where Ttotal,k is equal to the total analysis time for subperiods 0 to k, in hours, and Tcs,k is equal to the controlling time until spillback for the subperiod k, in hours. If spillback does not occur, then the performance measures from Step 2 are saved using the procedure described in a sub- sequent subsection. The analyst then proceeds to Step 10 to determine the aggregate performance measures for the analysis period. Step 4: Implement the HCM2010 Methodology to Evaluate a Subperiod At the start of this step, the analysis period is set equal to the controlling time determined in Step 3 (i.e., T = Tcs,k). All other Start Evaluate facility using HCM methodology (EvaluateStreetSystem) Check for first segment to spillback during analysis period (SetupToSecondRun) Has spillback occurred for the first time on a given segment and before the end of the analysis period? Yes No Set analysis period (T) = time to spillback Evaluate facility using HCM methodology (EvaluateStreetSystem) Set initial queue for next subperiod = residual queue (AdjustResidualQueue) Compute the spillback sat. flow adj. factor of upstream movements (ComputeAdjustedCapacity) Evaluate facility using HCM methodology (EvaluateStreetSystem) Compute queue length prediction error for spillback segments (ComputeQueueError) Prediction error = 0? No Yes Save performance measures for current analysis period (SavePerformanceMeasures) Aggregate delay and travel time for all subperiods. Report for analysis period. Finish Increase total time by time to spillback Set analysis period (T) = original analysis period duration, Set total time = 0.0 Save performance measures for current analysis period (SavePerformanceMeasures) Is total time original analysis period? Yes No Set analysis period (T) = original analysis time minus total time Figure 6.17. Spillback methodology flowchart.

102 input variables remain unchanged. Then, the HCM2010 meth- odology is implemented to evaluate the facility. The perfor- mance measures from this evaluation are saved using the procedure described in a subsequent subsection. Step 5: Prepare for the Next Subperiod by Determining the Initial Queue During this step, the input data are modified by updating the initial queue values for all movement groups at each intersec- tion. This modification is necessary to prepare for a new evalu- ation of the facility for the next subperiod. The initial queue for each movement group is set to the estimated residual queue from the previous evaluation. The initial queue values for the movement groups at the downstream intersection that exit each segment are checked by comparing them with the available queue storage distance. The storage distance for the left-turn movement group is computed using Equation 6.22. The storage distance for the right-turn movement group is computed using a variation of this equation. N L L N L n k a a h k ( ) = + − ∗ 1 (6.22)qx,lt, , ,thru ,lt lt , where Nqx,lt,n,k = maximum queue storage for left-turn movement group during subperiod k, veh; La,thru = available queue storage distance for the through movement, ft; La,lt = available queue storage distance for the left-turn movement, ft; Nlt = number of lanes in the left-turn bay, lanes; and L*h,k = effective average vehicle spacing in stationary queue during subperiod k, ft/veh. The available queue storage distance for the through move- ment equals the segment length less the width of the upstream intersection. For turn movements served from a turn bay, this length equals the length of the turn bay. For turn movements served from a lane equal in length to that of the segment, the queue storage length equals the segment length less the width of the upstream intersection. The maximum queue storage for the through movement group is computed using Equation 6.23: N L L N L n k a a h k ( ) = + − ∗ 1 (6.23)qx,lt, , ,thru ,lt lt , where Nqx,thru,n,k equals the maximum queue storage for through movement group during subperiod k, in vehicles, and Nth equals the number of through lanes (shared or exclusive), in lanes. The initial queue for each movement group exiting a seg- ment is compared with the maximum queue storage values. Any initial queue that exceeds the maximum value is set to equal the maximum value. Step 6: Prepare for the Next Subperiod by Determining the Saturation Flow Rate Adjustment During this step, the saturation flow rate is recomputed for movement groups entering the site identified in Step 3 as having spillback. This modification is necessary to pre- pare for a new evaluation of the facility during the next subperiod. The process of recomputing the saturation flow rate uses an iterative loop. The loop converges when the saturation flow rate computed for each upstream movement is suffi- ciently small that the number of vehicles entering the spill- back segment just equals the number that leaves it. To produce this result, a spillback saturation flow rate adjustment factor fsp is computed for each movement. Its value is set to 1.0 at the start of the first loop (i.e., fsp,0 = 1.0). The process begins by setting the analysis time to equal the time remaining in the original analysis period (i.e., T = To - Ttotal,k). The next task is to compute the estimated volume arriving to each movement exiting the segment at the downstream sig- nalized intersection (i.e., the adjusted destination volume). This calculation is based on the origin–destination matrix and discharge volume for each movement entering the segment. These quantities are obtained from the variables calculated using the HCM2010 methodology, as described in Section 1 in Chapter 30 of HCM2010. The adjusted destination volume is computed using Equation 6.24: (6.24), , od, , , 1 4 D va j k i j k i ∑= = where Da,j,k = adjusted volume for destination j (j = 1, 2, 3, 4) for subperiod k, veh/h; and vod,i,j,k = volume entering from origin i and exiting at desti- nation j for subperiod k, veh/h. The letters j and i in Equation 6.24 denote the following four movements: 1 = left turn, 2 = through, 3 = right turn, and 4 = combined mid-segment access points. The next task is to compute the proportion of Da, j, k that originates from upstream origin i. These proportions are computed using Equation 6.25: (6.25), , od, , , 1 4 D va j k i j k i ∑= = where bi,j,k is the proportion of volume at destination j that came from origin i for subperiod k, in veh/h.

103 intersection. The movements of interest are those that enter the subject segment. Equation 6.28 is used for this purpose: dv (6.28)sp, , , , , , , 0.5 ms, , sp, , , 1f c f fi k l u i k u i k i k i k l=   × × − where fsp,i,k,l = adjustment factor for spillback for upstream move- ment i for iteration l in subperiod k; cu,i,k = capacity at the upstream intersection for move- ment i for subperiod k, veh/h; and fms,i,k = adjustment factor for downstream lane blockage for movement i for subperiod k. The adjustment factor is shown to have a subscript l, indi- cating that the factor value is refined through an iterative pro- cess in which the factor computed in a previous iteration is updated using Equation 6.28. In theory, the exponent associated with the ratio in paren- theses should be 1.0. However, an exponent of 0.5 was found to provide for a smoother convergence to the correct factor value. The adjustment factor for downstream lane blockage was described in an earlier section of this chapter. The discus- sion following Equation 6.14 noted that this adjustment factor is incorporated into the spillback factor (as shown in Equation 6.28) for segments with spillback. The last task of this step is to adjust the access point entry volumes. Equation 6.29 is used for this purpose. One factor is computed for each access point movement that departs from the access point and enters the direction of travel with spillback. fx (6.29)ap, , , , , ,4, 0.5 ap, , , , , 1f fm n i k p i k m n i k p( )= × − where fap,m,n,i,k,p equals the access point volume adjustment factor for movement i at access point n of site m for iteration p in subperiod k. The access point volume adjustment factors are used to adjust the volume entering the segment at each access point. Step 7: Implement the HCM2010 Methodology to Evaluate the Remaining Time The HCM2010 methodology is implemented in this step to evaluate the facility described by the input data. The analysis period was set in Step 6 to equal the time remaining in the original analysis period. The saturation flow rate of each move- ment influenced by spillback is adjusted using the factors quantified in Step 6. Step 8: Compute the Queue Prediction Error During this step, the predicted residual queue for each move- ment group is compared with the maximum queue storage. The next task is to estimate the maximum discharge rate for each upstream movement. This estimate is based on con- sideration of the capacities of the downstream movements exiting the segment, and their volumes. When the segment has incurred spillback, the capacity of one or more of these exiting movements is inadequate relative to the discharge rates of the upstream movements entering the segment. The com- puted maximum discharge rate is intended to indicate the amount by which each upstream movement’s discharge needs to be limited to maintain a balance between the number of vehicles entering and exiting the segment. Equation 6.26 is used for this purpose. They are applied to each of the four upstream entry movements i. dv min , fx min , fx fx (6.26) , , ,2, ,2, ,1, ,1, ,2, od, ,1, ,3, ,3, ,2, od, ,3, ,2, od, ,4, b c b c v b c v v u i k i k d k i k d k i k i k i k d k i k i k i k i k ( ) ( ) = × + × × + × × + × with fx (6.27),2, ,2, ,2, od, ,2, b c v i k i k d k i k = × where dvu,i,k = maximum discharge rate for upstream movement i for subperiod k, veh/h; cd,j,k = capacity at the downstream intersection for move- ment j for subperiod k, veh/h; and fxi,2,k = volume adjustment factor for origin i for sub- period k. The factor fx represents the ratio of two quantities. The numerator represents the downstream through capacity that is available to the upstream through movement. The denomi- nator represents the volume entering the segment as a through movement and exiting as a through movement. The ratio is used to adjust the exiting turn movement and access point volumes such that they are reduced by the same proportion as is the volume for the exiting through movement. The product bi, j, k × cd, j, k represents the maximum discharge rate for entry movement i that can be destined for exit move- ment j such that the origin–destination volume balance is maintained and the exit movement’s capacity is not exceeded. It represents the allocation of a downstream movement’s capacity to each of the upstream movements that use that capacity when the allocation is proportional to the upstream movement’s vol- ume contribution to the downstream movement volume. The capacity for the combined set of access points is unknown and is unlikely to be the source of spillback. Hence, that capacity is not considered in Equation 6.26. The next task is to estimate the saturation flow rate adjust- ment factor for the movements at the upstream signalized

104 This distance is computed using the equations described in Step 5. Any difference between the predicted and maximum queues is considered a prediction error. If the sum of the abso- lute errors for all movements is not equal to a small value, then the analysis returns to Step 6. Step 9: Check the Total Time of Analysis During this step, the total time of analysis Ttotal,k is compared with the original analysis period To. If they are equal, then the analysis continues with Step 10. If the two times are not in agreement, the access point volumes are restored to their original value and then multiplied by the most current access point volume adjustment factor. The analysis then returns to Step 2. Step 10: Compute the Performance Measure Summary During this step, the average value of each performance mea- sure is computed. The value is a representation of the average condition for the analysis period. For uniform delay at one intersection, it is computed using Equation 6.30. (6.30)1, , 1,agg, , ,all , d d T v i j i j o i j = × where d1,i,j = uniform delay for lane group j at intersection i, s/veh; d1,agg,i,j,all = aggregated uniform delay for lane group j at intersection i for all subperiods, s/veh; and vi,j = demand flow rate for lane group j at intersection i, veh/h. A variation of Equation 6.30 is used to compute the aver- age value for the other intersection performance measures of interest. Equation 6.31 is used to compute the average running time for one site, when a site is one direction of travel on one segment. (6.31), ,agg, ,all thru, , 1 t t w R m R m m k k n ∑ = = where tR,m = segment running time for site m, s; tR,agg,m,all = aggregated segment running time for site m for all n subperiods, s; and wthru,m,k = weighting factor for site m for subperiod k, veh. A variation of Equation 6.31 is used to compute the average value for the other intersection performance measures of interest. The term in the denominator of Equation 6.31 equals the total through volume during the analysis period. Procedure for Saving Performance Measures The performance measures are computed using the HCM2010 methodology and saved at selected points in the spillback methodology. These measures typically correspond to a spe- cific subperiod of the analysis period. Each measure is saved by accumulating its value for each subperiod. The sum is then used to compute an average performance measure value dur- ing the last step of the methodology. Equation 6.32 is used to save the computed uniform delay for one intersection lane group. The computed delay repre- sents a cumulative total time for the current, and all previous, subperiods. (6.32)1,agg, , , 1,agg, , , 1 1, , , , ,d d d wi j k i j k i j k i j k= + ×− with (6.33), , , ,w T vi j k i j k= × where d1,agg,i,j,k = aggregated uniform delay for lane group j at intersection i for subperiods 0 to k, s/veh; d1,i,j,k = uniform delay for lane group j at intersection i for subperiod k, s/veh; wi,j,k = weighting factor for lane group j at intersection i for subperiod k, veh; and vi,j,k = demand flow rate for lane group j at intersection i for subperiod k, veh/h. The weighting factor represents the number of vehicles arriving during the analysis period for the specified lane group. A variation of Equation 6.32 is also used to compute the aggregated values of the following performance measures at each intersection: • Incremental delay; • Initial queue delay; • Uniform stop rate; • Incremental stop rate based on second-term back-of-queue size; and • Initial queue stop rate based on third-term back-of-queue size. Equation 6.34 is used to save the computed running time for one site, when a site is one direction of travel on one segment. (6.34),agg, , ,agg, , 1 , , thru, ,t t t wR m k R m k R m k m k= + ×−

105 Table 6.9. Segment Description Segment Location Street Class Segment Length (ft) Speed Limit (mph) Aviation Parkway Tucson, Arizona High-speed principal arterial 2,800 55 SW Barbur Boulevard Portland, Oregon Suburban principal arterial 2,937 35 SE Powell Boulevard Portland, Oregon Suburban minor arterial 1,405 35 with 1 1 (6.35)thru, , , , , , , sl , , , , , , sr, , , , , , w T v N v P v P m k t i j k t i j i j k L i j k i j k R i j k ( ) ( )= × + − + −   where tR,agg,m,k = aggregated segment running time for site m for subperiods 0 to k, s; tR,m,k = segment running time for site m for subperiod k, s; wthru,m,k = weighting factor for site m for subperiod k, veh; and vt,i,j,k = demand flow rate in exclusive through lane group j at intersection i for subperiod k, veh/h/lane; Nt,i,j = number of lanes in exclusive through lane group j at intersection i, lanes; vsl,i,j,k = demand flow rate in shared left-turn and through lane group j at intersection i for subperiod k, veh/h; vsr,i,j,k = demand flow rate in shared right-turn and through lane group j at intersection i for sub- period k, veh/h; PL,i,j,k = proportion of left-turning vehicles in the shared lane group j at intersection i for subperiod k, and PR,i,j,k = proportion of right-turning vehicles in the shared lane group j at intersection i for subperiod k. When applying Equations 6.34 and 6.35, the lane group j and intersection i are located at the downstream end of the subject site m. The weighting factor represents the number of through vehicles arriving at the downstream intersection as a through movement during the analysis period. A variation of Equation 6.34 is also used to compute the aggregated values of the following performance measures at each intersection: • Through movement delay; • Through movement stop rate; • Travel time at free-flow speed; and • Travel time at base free-flow speed. The methodology described in this section is new to the urban streets methodology in Chapter 17 of the HCM2010. Incorporation of this methodology into the HCM requires its adoption by TRB’s Highway Capacity and Quality of Service Committee. The saturation flow rate adjustment factor for spillback is applicable to all signalized intersection movements that enter the urban street segment of interest. It is used to adjust the saturation flow rate of these movements. It would be added to Equation 18-5 in Chapter 18 of the HCM2010. Its imple- mentation approach is the same as that described for the saturation flow rate adjustment factor for downstream lane blockage, as described earlier. Validation of Urban Streets Model This subsection describes the activities undertaken to validate the accuracy of the three enhancements described in this section. The objective of the validation process is to demonstrate the ability of the methodology to accurately predict urban street performance for a wide range of conditions. To facilitate the validation, the three enhancements were implemented in a test version of the computational engine that automates the urban streets methodology in Chapter 17 of the HCM2010. The validation was based on a comparison of performance estimates from the engine with those obtained from a traffic simulation model. Three urban street segments were selected for the evaluation. The evaluation activities included the initial coding of a data file for each segment and the subsequent com- parison of estimates from the engine and simulation model. Table 6.9 describes the three segments. All three have coor- dinated-actuated control, and they offer a range in speed limit, access point density, median type, and segment length. All seg- ments have four through lanes, two lanes in each direction. Table 6.10 summarizes the traffic characteristics and signal- ization at each of the segments. The evaluation was based on a comparison of performance measures obtained from the enhanced HCM2010 methodol- ogy with those obtained from a simulation model. CORSIM (version 5.1) was determined to be a suitable simulation model for this purpose. For each segment, spillback was created for one travel direc- tion by reducing the number of through lanes by one. This direction is referred to as the spillback direction. Through movement delay was used to assess the level of agreement between the simulated and predicted segment

106 Table 6.10. Segment Traffic and Signalization Characteristics Segment Travel Direction Average Volumea (veh/h) Base Free- Flow Speedb (mph) Signal Timinga Left-Turn Phasinga Cycle Length (s) Major-Street Split (s) Major Street Minor Street Aviation Parkway NB 1,200 47 80 54 Protected Protected SB 1,300 47 54 Permissive Permissive SW Barbur Boulevard NB 530 40 100 52 Protected Split SB 1,700 40 54 Protected Protected– Permissive SE Powell Boulevard EB 1,130 38 120 93 Protected Permissive WB 1,147 38 99 Permissive Permissive Note: NB = northbound; SB = southbound; EB = eastbound; WB = westbound. a Data apply to the downstream intersection. b Base free-flow speed is computed using the procedure in Chapter 17 of the HCM2010 (TRB 2010a). operation. Delay data were collected for the signalized inter- section serving vehicles exiting the segment in the spillback direction. Thus, the delay to the four through movements at that signalized intersection was collected for each of three segments, yielding 12 observations. Turn movement delay was not collected because the HCM2010 methodology does not explicitly address the effect of turn bay blockage on turn movement delay. The delay time estimate from CORSIM was compared with the HCM2010 control delay estimate. Delay time is computed as the difference between the total travel time and the travel time at the free-flow speed. This delay was determined to be the most appropriate delay variation for comparison with HCM2010 control delay for congested conditions. The analysis period used with the HCM2010 methodology, and the total run time used with the simulation model, were both set at 1 hour. This approach was used because the delay incurred by oversaturated movements is time-dependent. Seven replications were used for the simulation of each seg- ment. The average delay for the replications was compared with the results from the enhanced HCM2010 methodology. The delay data obtained from the two sources are com- pared in Figure 6.18. The three data points shown in the “congested” region of the figure correspond to the through movement for the spillback direction at each of the three segments. The other data points correspond to the through movements that are crossing the segment or traveling in the nonspillback direction. The thin line shown in the figure represents an x = y line. A data point that falls on this line indicates the engine value equals the simulation value. In general, the data tend to cluster around the x = y line, suggesting that the engine prediction is in good agreement with that obtained from CORSIM. Figure 6.18. Control delay comparison for three segments. 0 50 100 150 200 250 300 350 0 100 200 300 400 500 Control Delay Predicted by Revised Method, s/veh D el ay T im e Pr ed ic te d by C O R SI M , s /v eh Through-Vehicle Delay 1 1 Not congested Congested