Update of Highway Capacity Manual: Merge, Diverge, and Weaving Methodologies (2023)

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47   Overview This chapter starts by presenting four research bundles prepared by the research team to address the knowledge gaps described in Chapter 1 and describing how they were prioritized to develop a Phase II work plan that could be accomplished within the time and budget allocated to NCHRP 07-26. The remainder of the chapter describes how this work plan was executed, starting with a summary of the team’s site identification process and data quality control proce- dure applied by the team. The data collection process is described, followed by the procedures for estimating segment capacity from the field data, cleaning the data, and selecting the sites for modeling. The chapter closes with the modeling framework used to develop recommended changes to the HCM’s merge, diverge, and weaving methodologies. Research Needs Prioritization The literature review described in Chapter 1 identified many gaps in knowledge and worth- while, high-value updates that could be made to HCM 6th Edition methods. The research team developed recommendations for the highest-value fixes that could be accomplished within the time and budget allocated to the project; these recommendations were subsequently reviewed and approved by the project oversight panel. It was not feasible to address all research gaps in this project. Consequently, the prioritization effort focused on the highest-value fixes, grouping them into four research bundles where one focused research effort could address several gaps simultaneously. The resulting recommended groupings and their prioritization are summarized in Table 12. The text below provides an addi- tional explanation of the research team’s reasoning for developing each bundle. • Bundle 1. Development of predictive model(s) for prebreakdown and breakdown capacities for weaving, merge, and diverge segments that use adjustment factors to pivot off the basic segment capacities. – Several papers in the literature identified issues with the HCM’s prediction of freeway weave, merge, and diverge capacities (as well as for basic segments). Observed capacities tended to be lower than predicted by the HCM methods. – This research effort, focused on capacity, offers the ability to address several gaps identified in the literature: ◾ The queue discharge capacity drop is not fixed at 7% but varies by site, ramp volumes, weaving, and speed. ◾ HCM merge capacities of 4,600 vph for the two right lanes are too high; 2,000 pc/h/ln may be better for prebreakdown. ◾ The HCM underestimates capacities at high-weave ratios. C H A P T E R 2 Research Approach

48 Update of Highway Capacity Manual : Merge, Diverge, and Weaving Methodologies ◾ Weaving methods for estimating freeway mainline capacity (HCM Chapter 13) do not converge to basic segment capacities at low ramp-volumes. – This research effort would involve identifying various weave, merge, and diverge sites around the United States and examining data already collected or collecting new data on 5-minute speeds and flow rates to identify breakdown. The sites will need to experience breakdowns regularly. A variety of geometric configurations and weaving volume ratios would be desired. – The research team ranked this effort #1 because accurately predicting how different design configurations affect capacity is a fundamental requirement for cost-effective design, and the literature indicates a strong need to improve the HCM’s capacity estimates for different freeway design options. The literature indicates this is a significant problem for the current methods. • Bundle 2. Investigation of the potential for and development of a unified speed prediction model for weave, merge, and diverge segments. This model would follow Rouphail et al.’s (2021) approach of modifying the speeds predicted by the basic segment model to reflect the turbulence of weaving, merging, and diverging activities. – The current weave, merge, and diverge speed prediction models were developed indepen- dently and consequently do not converge at the extremes, sometimes resulting in counter- intuitive results; for example, where taking away an auxiliary lane increases the predicted speed and lowers the density. – This research effort, building on recent work by Rouphail et al. (2021), provides the oppor- tunity to reconcile the weave, merge, and diverge methods in a manner that ensures con- sistent results when comparing different geometric design options. In essence, the speeds predicted by the basic segment equations are the starting point for the computation. Ranked Research Effort Bundle Description Rationale for Ranking Develop Prebreakdown and Postbreakdown Capacity Prediction Models (Bundle 1) Models would be sensitive to geometry, volumes, and traffic mix. They would extend the basic segment capacities to include the turbulence effects of weave, merge, and diverge situations. This bundle was ranked #1 by the team because accurately predicting how different design configurations affect capacity is a fundamental requirement for cost-effective design. In addition, the literature indicates a strong need for improving the HCM’s capacity estimates for different freeway design options. Develop Unified Weave, Merge, and Diverge Speed Prediction Model (Bundle 2) An integrated model covering weave, merge, and diverge following the approach of Rouphail et al. (2021), applying modification factors to the basic segment speed prediction model. This bundle was ranked #2 because an integrated model covering weave, merge, and diverge would solve the inconsistencies at the boundaries problem. It also gives the research team the opportunity to address several additional shortfalls in the current methods. Extend Speed and Capacity Prediction Methods to Additional Geometries (Bundle 3) The capacity and speed models developed in the first two bundles would be tested and extended as necessary on additional geometries. This bundle was ranked #3 because the ability to apply the HCM to a wider range of conditions will enhance its use in the evaluation of design alternatives. Develop Speed and CAFs for Freeway Management Strategies (Bundle 4) Freeway management strategy speed and CAFs would be developed for use with the models produced by the first two research bundles. This bundle was developed because there is strong interest in maximizing the productivity and lifetimes of our urban freeway system. HCM methods for predicting the operational benefits of these strategies will greatly facilitate their consideration in planning studies. Table 12. Prioritization of fixes and updates for HCM freeway merge/diverge/weave methods.

Research Approach 49   A turbulence factor (sensitive to geometry and flows) is applied to the basic segment speed to yield the predicted speed for a weave section. Other turbulence factors are applied for merge and diverge sections. The research team’s challenge and objective will be to ensure that the turbulence factors converge to each other as a weaving section is lengthened until it becomes separate merge and diverge sections. – This research effort will address the following weaknesses identified in Table 7: ◾ The HCM’s merge and diverge methods conflict with the fundamental speed–flow relationship. ◾ Acceleration lanes longer than 600 ft have little benefit. ◾ The HCM underestimates speeds, particularly in the 50 to 65 mph range. ◾ The HCM overpredicts densities at low flows and underpredicts densities at high flows. ◾ The HCM weave method does not converge to ramp merge/diverge operations at low ramp flows and/or long weave lengths. ◾ The HCM weave methods for estimating freeway mainline capacity, speed, and density (HCM Chapter 13) do not converge to basic segment operations at low ramp-volumes. ◾ Merge/diverge methods for estimating freeway speeds and densities (HCM Chapter 14) do not converge to basic segment operations at low ramp-volumes. – This research effort was ranked #2 because an integrated model covering weave, merge, and diverge segments would solve the boundary-inconsistency problem. It would also give the research team the opportunity to address several additional shortfalls in the current methods. • Bundle 3. Extend the speed and capacity prediction models to additional geometries. – This research effort would extend the previous work (Research Bundles #1 and #2) to cover additional geometries not covered well by current HCM methods. – The first priority would be the geometries lightly treated in the HCM: lane-add merge, lane-drop merge, multiple weaves within a single weave segment, two-lane on-ramps, two- lane off-ramps, major diverge, merge and diverge on five-lane freeways, left-hand on- and off-ramps, and HOV/HOT lane direct ramps. The second priority—to the extent that data, time, and resources permit—would be the rarer geometries not treated at all in the HCM at present: close merges (multiple on-ramps in series), close diverge (multiple off-ramps in series), major merge, merge and diverge on six-lane freeways, managed lane access points with buffer for acceleration/deceleration lanes, and collector–distributor road weaving. – This effort was ranked #3 because the ability to apply the HCM to a wider range of condi- tions would enhance its use in the evaluation of design alternatives. • Bundle 4. Develop speed and CAFs for the effects of freeway management strategies, including part-time shoulder use, CAV lanes, and ramp metering. – This research bundle would extend the previous work (Research Bundles #1 and #2) to cover a few selected freeway management strategies. – This bundle would focus initially on part-time shoulder use and on improving guidance on the capacity and operational effects of ramp metering. Other freeway management strate- gies (toll plazas, CAV lanes, truck-only lanes, interchange bypass lanes, reversible median lanes, VSL, and pavement markings controlling weaving) would be addressed only to the extent that data, time, and resources permit. – This research bundle was developed because there is strong interest in maximizing the productivity and lifetimes of our urban freeway system. HCM methods for predicting the operational benefits of these strategies would greatly facilitate their consideration in plan- ning studies. Addressing all four research bundles to a sufficient degree was determined to be infeasible within the Phase II scope. Therefore, the research team focused on the first three bundles, with only a high-level exploration of ramp metering sites as part of Bundle 4.

50 Update of Highway Capacity Manual : Merge, Diverge, and Weaving Methodologies The research team further recommended that the following HCM weaknesses identified from the literature review not be addressed in the Phase 2 effort because the team believed they are unlikely to significantly improve the HCM method results, adequate work-arounds already exist for them, or there are no U.S. data for them: • Right-lane FFS and percentage of heavy vehicles: averages across lanes are not reflective of the right-hand lane. – Uneven lane performance is already taken into partial consideration in merge and diverge methods focused on the right two lanes, although the current methods do not explicitly recognize speed and truck percentage differences in the right lane. This issue would become more critical if a lane-by-lane model such as that developed by NCHRP 15-57 were used. • Impacts of lower posted speeds for trucks are not included in the FFS estimate. – The Oregon DOT method may be sufficient, and operational performance may not be sig- nificantly affected. A 5-mph difference in FFS changes a basic segment’s predicted capacity by 50 pc/h/ln. • Influence area for ramp merge starts 400 ft upstream of the gore point. – Historic datasets based on the current definition of the influence area could no longer be used. In addition, moving the influence area upstream of the on-ramp may change the overall speed for the merge section (by including more queued vehicles on the mainline), thereby affecting the predicted density at capacity. However, this density will be different than within the merge area downstream of the on-ramp. The value of shifting the starting point of the influence area is unclear. • Manual/channelized mainline and ramp toll plazas. – Methods already exist among toll collection agencies for estimating plaza capacities. Since there are higher priority needs, the research team recommends that this item be deferred to other research efforts. • CAV lanes. – At the time of writing, there are no installations in the field where data can be collected. In addition, crucial information about the actual car-following and lane-changing algorithms and parameters that are being implemented or will be implemented in CAVs are in flux or considered proprietary and therefore unavailable to researchers. • Truck-only lanes. – The HCM currently appears to be readily extensible to truck-only lane analysis. The HCM already covers truck climbing lanes. Truck-only lanes in flat terrain are rare. • Interchange bypass lanes. – Interchange bypass lanes would appear to be readily evaluated using current HCM methods. • Reversible median lanes. – Reversible median lanes are relatively rare, and the current HCM methods for managed lanes may be close enough. • Variable speed limits. – This effort would require research into human behavior (driver compliance with advisory or enforceable speed limits). It is likely to depend more on enforcement and the protocol used to set and display the speeds than the design of the facility. In addition, there are rela- tively few U.S. installations for data collection at this time. • Pavement markings controlling locations of freeway-ramp and then ramp-freeway lane changes in weave sections. – There are no U.S. sites for data collection. Data Collection This section describes the process followed by the research team to select and screen the can- didate sites to be included in the analysis.

Research Approach 51   Data Sources The research team first conducted an in-depth inventory of the available sensor data that were publicly available on data-sharing platforms. These platforms included the University of Maryland Center for Advanced Transportation Technology Laboratory’s Regional Integrated Transportation Information System (RITIS), Caltrans’ Performance Measurement System (PeMS), the Washington State DOT DriveNet, and the Portland State University’s Intelligent Transportation System Lab’s PORTAL data archive. After evaluating candidate merge, diverge, and weaving sites available through these four platforms, additional sites were needed to reach the desired sample size of 120 sites. Therefore, the team obtained supplemental sensor data from NCHRP 15-57 and University of Kansas research teams. Figure 10 displays the location and number of the sites used for analysis in each state. As shown below, sites were obtained from nine states to maintain geographic diversity. However, a large proportion of the data was obtained from California, Florida, Utah, and Washington. At some sites, sensor data were only available for the mainline and lacked speed–flow data for the ramps. Because ramp volume was an important input during the speed–capacity–density model development process, the research team purchased StreetLight data for these sites. StreetLight provides anonymized location records from smartphones and navigation devices. These data were used to obtain the proportion of traffic (rather than actual volumes) staying on the mainline, as opposed to entering or exiting the freeway. Site Selection Process Candidate sites from DriveNet, PORTAL, and supplemental sources were identified from previous research using those sites. This subsection describes the five-step process followed by the research team to identify additional candidate sites from RITIS and PeMS. An example from one of the merge site studies in this research is provided next for illustration purposes. Step 1. Use Google Maps to Identify and Explore Congestion Patterns The “typical traffic” feature in Google Maps allowed the research team to identify candidate sites using their historical average performance prior to the COVID-19 pandemic. Figure 11 shows a simple merge segment in Tampa, Florida, on northbound I-75. Note that at the time of writing, Google Maps’ typical traffic feature no longer indicates congestion at this location, likely due to the effect of the pandemic. Step 2. Confirm Geometry Impacts That May Affect Capacity Google’s interface shows average performance without providing insights on the location of the actual bottleneck that results in low speeds. Therefore, the research team investigated potential road geometry impacts that might affect capacity and result in bottlenecks, such as lane drops, narrow lanes, or grades. In this example, the research team reviewed the site through Google Earth and observed that no lane drop or narrow lanes exist downstream of the on-ramp. This was especially important because the ramp is located approximately 2,500 ft upstream of a relatively long bridge. Step 3. Identify Target Sensor(s) Based on the observed congestion patterns, the team identified the relevant sensors for analysis. For this site, the RITIS platform was used. Figure 12 shows the locations of available sensors at this location in RITIS. Once a detector is selected in the RITIS, it shows up in blue to give visual feedback to what has been selected. The selected sensor in this example is located just downstream of the on-ramp. In addition to mainline sensors, the team evaluated ramp sensors,

Figure 10. Location and number of sites used for analysis by state.

Research Approach 53   Source: ©2020 Google Figure 11. Example analysis site in Tampa, Florida. Source: Screenshot from RITIS. Figure 12. Available sensor locations in RITIS for the example site.

54 Update of Highway Capacity Manual : Merge, Diverge, and Weaving Methodologies where available, to obtain ramp volumes. However, no ramp sensor was available for this loca- tion. When no ramp data were available, the team used StreetLight O-D percentages to estimate the ramp volumes by applying O-D percentages to upstream and downstream mainline sensors. Step 4. Verify Recurring Congestion Once the target sensors were identified, the research team explored the sensor data to ensure that recurring congestion occurred at the candidate site. Figure 13 shows a weekday speed pro- file from RITIS for Lane 1 (the rightmost lane) at the site over a 1-week period. The RITIS sensor data shows recurring congestion during the a.m. peak hour in which average speeds dropped below 45 mph on every weekday except Monday. Note that the research team only included speed data from the rightmost lane to make the graph easy to interpret. Sensor data used for all the analysis sites included lane-by-lane speed information, which was then aggregated to the approach level for the analysis, as explained in the “Field-Capacity Estimation Approach” subsection presented later. Step 5. Download and Extract Sensor Data In the final step, the team downloaded a full set of data from the identified sensors. The team typically downloaded at least 1 year of data. Downloaded data included lane-by-lane speeds, volumes, occupancy, and flow rate. Data Quality Control Procedure The step-by-step data quality control procedure applied to each site is described in the fol- lowing outline. 0. Data acquisition a. Obtain speed, volume, occupancy for each time entry b. Calculate occupancy and volume/occupancy ratio Source: Screenshot from RITIS. Figure 13. Sample RITIS speed profile for the example site.

Research Approach 55   1. Check temporal segmentation error a. Cannot have both volume = 0 and occupancy > 0 b. Check for all hours of the day c. Error code 1 if corrected, no error if not d. Flag if occupancy is segmented wrongly between time stamps 2. Check “not enough data” error a. Dataset considered too small if fewer than 10 records b. Check for entire dataset c. If not enough, end here 3. Correct temporal segmentation error by shifting a. Occupancy next time stamp = occupancy now + occupancy previous b. Occupancy now = 0 4. Update volume/occupancy ratio a. Set 0 to volume/occupancy ratio whose value > 200 5. Check “volume over range” error a. Volume cannot be too large for 5-minute interval: threshold volume > 22 b. Check for all hours of the day c. Error code 2 6. Calculate moving standard deviation a. Window width = 12 b. Calculate standard deviation of volume in the moving window: Std_vol c. Calculate standard deviation of occupancy in the moving window: Std_occ 7. Check “stuck” error a. If either standard deviation is too small, then the loop detector is very likely stuck: Std_vol < 0.0001 or Std_occ < 0.0001 b. Check for 5 a.m. to 10 p.m. c. Previously no error reported rows d. Error code 3 8. Check “not reporting” error a. Volume or occupancy cannot be too small, or likely the detector is not reporting: volume = 0 or occupancy = 0 b. Check for 5 a.m. to 10 p.m. c. Previously no error reported rows d. Error code 5 9. Find observed volume/occupancy ratio and adjustment factors a. Observed volume/occupancy ratio = median (volume/occupancy ratio) b. For 10 p.m. to 5 a.m. c. Volume/occupancy > 0, not null d. Cases i. If observed volume/occupancy ratio is “nan” (not a number), error code 4, insufficient late-night data ii. If loop type is not “main,” error code 3, wrong loop detector type iii. If observed volume/occupancy ratio is within 10% to 50% of the free-flow volume/ occupancy ratio, correctable, factor = (free-flow volume/occupancy ratio)/(observed volume/occupancy ratio), error code 1 iv. If observed volume/occupancy ratio is more than 50% different from the free-flow volume/occupancy ratio, not correctable, error code 2 v. Not much difference between observed and free flow, no adjustment, error code 5 e. Adjust the volume/occupancy ratios by multiplying the values with their corresponding factors

56 Update of Highway Capacity Manual : Merge, Diverge, and Weaving Methodologies 10. Check “volume/occupancy ratio over threshold” error a. Cannot be too large: volume/occupancy ratio > 120 b. Check for all hours of day c. Previously no error reported rows d. Violating values set to “nan” 11. Average volume/occupancy ratio a. Volume/occupancy ratio = rolling median (window size = 7) 12. Check for “late-night zero volume/occupancy ratio” error a. Error description: (volume/occupancy ratio = 0) or (volume/occupancy ratio is null) b. Check for 10 p.m. to 5 a.m. c. Previously no error reported rows d. Error code 12 13. Proceed with analysis after all error checking completed The research team applied this 13-step procedure to each data collection site. The results of this process and a summary of the data collected for all sites is included in Appendix D of the this report’s companion, NCHRP Web-Only-Document 343. Operations Data Collection This subsection summarizes the operations data collected for the study sites. Geometric attri- butes, such as the number of lanes or the length of the acceleration or deceleration lane, are discussed in “Metadata Collection” presented later. Site Descriptions A total of 121 sites were included in the analysis. The number of sites representing different segment types included in the dataset is shown in Table 13. The geometry types were listed in Chapter 1, while the research bundles were described earlier in this chapter in the “Research Needs Prioritization” section. Summary of Collected Data For each site, speed, volume, and occupancy data were obtained in 5-minute intervals across each lane. Speed and volume data were used to estimate capacity and speed–flow relationships, as described later, while occupancy data were used to assess data quality, as discussed previ- ously. Typically, 1 year of data were collected from each site to be able to obtain a large number of breakdown events and to obtain reasonable capacity estimates. Sensor data were typically collected from the mainline (shown as #1 in Figure 14) to obtain bottleneck capacity (that is, Research Bundle Geometry Sample Size Cumulative Sample Size Percent Sites 1 and 2 Simple merge 26 26 21.3% Simple ramp weave 15 41 12.3% Simple diverge 23 64 18.9% 3 Collector–Distributor (C-D) weave 8 72 6.6% Close merge 6 78 4.9% Complex weave 12 90 9.8% Lane-drop diverge 6 96 5.7% Two-lane on-ramp 5 101 4.1% Two-lane off-ramp 9 110 7.4% Close diverge 7 117 5.7% 4 Ramp metering sites 4 121 3.3% Table 13. Distribution of segment types in the analysis dataset.

Research Approach 57   downstream of an on-ramp as shown below for a simple merge site and upstream of an o-ramp for simple diverge sites). Where sensors were available, on- and o-ramp volumes were also collected (shown as #2 below for a simple merge site). For weaving segments, missing data were supplemented with StreetLight data as discussed in the “Supplemental Data for Operational Analysis” presented next. For the C-D weave sites, sensors were only available on the mainline instead of on the collector– distributor road. As a result, while the team decided to keep the C-D weave sites to investigate mainline capacity, these sites were not included in the speed–capacity–density model develop- ment process. Supplemental Data for Operational Analysis In addition to the speed and ow data, supplemental data were collected to support the opera- tions analysis. is subsection describes these data sources and explains how they were incor- porated into the analysis. Heavy Vehicle Data Heavy vehicle data were collected for each site to help develop heavy vehicle adjustment factors for use in calculating capacities using the HCM 6th Edition procedure. Heavy vehicle per- centages were obtained using the FHWA’s Highway Performance Monitoring System (HPMS) database. e research team recognized that the HPMS’s daily average truck percentages are not representative of all hours of the day. Specically, many freeways have higher truck percentages at night when the amount of passenger car travel is lower. However, the use of HPMS data was deemed acceptable for this eort for the following reasons: 1. Most breakdown events occur during daytime under recurring congestion rather than at night. As such, the team has condence that the average heavy vehicle percentages from HPMS are adequate and appropriate to use as estimate capacities in the speed–ow model development. 2. e HPMS data are commensurate with the kind of data that agencies applying the method would have available. Few agencies have 24-hour volume sensors with heavy vehicle per- centages broken out. As such, the data used in this study match what analysts will have avail- able when applying the study’s method. 3. Nighttime breakdown events (with higher truck percentages) would already be excluded from the analysis as they would likely be due to an incident, weather, or work zone events, rather than recurring congestion. Grade and Elevation Data Grade data are also needed to develop heavy vehicle adjustment factors for use in calculating capacities using the HCM 6th Edition procedure. Grade data were obtained from DriveNet. In a previous FHWA-funded project (Wang et al. 2017), the University of Washington’s STAR Lab and its collaborators produced elevation data for all Interstate highways in the United States. Figure 14. Ideal sensor locations for simple merge sites to obtain bottleneck capacity (#1) and ramp volumes (#2).

58 Update of Highway Capacity Manual : Merge, Diverge, and Weaving Methodologies That work developed a point-featured geodatabase with geographic coordinates and elevation data for freeway centerlines. The elevation product used by NCHRP 07-26 consisted of 10-ft elevation data—that is, points are spaced at 10-ft intervals along highway centerlines. However, instead of computing grade for every 10-ft link along the study freeways, grades were estimated every 100 ft (one station). More specifically, a particular query point was first located on a cor- responding freeway segment by referencing it with segment endpoints. Next, a 100-ft-long grade query segment was constructed by finding the related geopoints. Finally, the grade was com- puted linearly for the 100-ft segment by dividing the vertical elevation difference by the horizontal milepost distance. Grades obtained by this method are smoother and thus more reasonable than those computed at 10-ft intervals. After computing, the roadway direction used to develop the grade estimate was aligned with the traffic sensor monitoring direction to determine whether the grade in the study direction was uphill (positive sign) or downhill (negative sign). StreetLight Origin-Destination Data Some analysis sites only had sensors on the mainline. While the research team was able to estimate mainline capacity using the speed–flow data, detailed information on ramp or weaving demands was unavailable. As a result, the team would not have been able to include those sites in model development because ramp volumes and weaving intensity were among the primary inputs into the project’s models. To overcome this data limitation, the research team purchased StreetLight data to estimate ramp demands and weaving intensity. StreetLight data were utilized to obtain proportions of freeway demand and ramp demand. The estimated proportions were then applied to the mainline sensor data to obtain freeway-to- ramp demand for diverge sites; ramp-to-freeway demand for merge sites; and ramp-to-freeway, freeway-to-ramp, and ramp-to-ramp demand for weave sites. Thus, the estimated ramp volumes were consistent with the mainline sensor data that was utilized to estimate freeway mainline capacity. StreetLight data are purchased by zone, and the team purchased a total of 60 zones with 5 years of data from 2016 to 2020. The analysis of a merge or diverge site requires two zones per site, while a weaving site requires four zones for estimating the relative volume proportions. A sample diagram showing this process for Simple Ramp Weave Site 1 and the resulting StreetLight outputs are shown in Figure 15. The left side of the figure shows a screenshot of the weave site; four analysis zones (marked by the blue and yellow dots in the illustration) are placed on the mainline upstream of the weave, on the mainline downstream of the weave, on the on-ramp, and on the off-ramp. The analysis zones are placed far enough upstream on the ramps to assure that volume proportions are accurately estimated even for tight ramp weaving areas. On the right side of the figure, the output data of an O-D analysis of StreetLight Index are summarized in a pivot table to show the O-D trip index for each zone pair. The StreetLight Index represents a relative volume of trip activity but is not an estimated count of trips or vehicles. The StreetLight Index is a normalized value that accounts for variations in sample size across space and time. The index data are used to get the volume V proportions of freeway-to-ramp (Vfr), ramp-to-freeway (Vrf), and ramp-to-ramp (Vrr) movements for a weave site. These values can also be used to compute the volume ratio (VR), defined as the proportion of vehicles completing a weaving maneuver divided by the total segment volume. StreetLight data were collected for the same time periods used by the freeway sensor data. However, if the freeway sensor data were collected earlier than 2016, StreetLight data from 2016 were used to provide the closest estimation of O-D flows. Additionally, hour-by-hour StreetLight data were used to capture time-of-day variations of freeway and ramp proportions. Table 14 shows an example of how the volume proportions change by time of day for Simple Ramp Weave Site 1.

Research Approach 59   StreetLight data processing for merge and diverge sites followed a similar process. For each site, a zone activity analysis was applied to get the StreetLight Index outputs for the two zones set on the mainline upstream and the on- or o-ramp. Based on the two index outputs, the propor- tions of Vff and Vrf are calculated for a merge site and the proportions of Vff and Vrf are calculated for a diverge site. Using 60 zones, the research team was able to estimate O-D percentages for 19 sites that otherwise could not have been included in the analysis. Table 15 lists the sites that were included in the supplemental StreetLight data collection. Day Type 0: Weekday (Tu-Th) Sum of Average Daily O-D Traffic (StL Index) Column Labels Row Labels 1-3 Mainline Downstream 1-4 Off-ramp Grand Total 1-1 Mainline Upstream 61,978 6,774 68,752 0: All Day (12am-12am) 42,018 4,604 46,622 1: 5am (5am-6am) 1,700 150 1,850 2: 6am (6am-7am) 2,852 345 3,197 3: 7am (7am-8am) 2,891 284 3,175 4: 8am (8am-9am) 2,735 335 3,070 5: 2pm (2pm-3pm) 2,635 242 2,877 6: 3pm (3pm-4pm) 2,515 256 2,771 7: 4pm (4pm-5pm) 2,238 272 2,510 8: 5pm (5pm-6pm) 2,394 286 2,680 1-2 On-ramp 10,113 2,710 12,823 0: All Day (12am-12am) 6,750 1,802 8,552 1: 5am (5am-6am) 255 20 275 2: 6am (6am-7am) 527 141 668 3: 7am (7am-8am) 666 181 847 4: 8am (8am-9am) 584 152 736 5: 2pm (2pm-3pm) 351 96 447 6: 3pm (3pm-4pm) 334 118 452 7: 4pm (4pm-5pm) 306 111 417 8: 5pm (5pm-6pm) 340 89 429 Grand Total 72,091 9,484 81,575 Source: Screenshot from StreetLight user interface (left), research team spreadsheet (right). Figure 15. Example of StreetLight data processing for weave sites. Time Period StreetLight Volumes Total Volume Vtotal Estimated Proportions Vff Vfr Vrf Vrr Vff% Vfr% Vrf% Vrr% 5 a.m. – 6 a.m. 1,700 150 255 20 2,125 80.0% 7.1% 12.0% 0.9% 6 a.m. – 7 a.m. 2,852 345 527 141 3,865 73.8% 8.9% 13.6% 3.6% 7 a.m. – 8 a.m. 2,891 284 666 181 4,022 71.9% 7.1% 16.6% 4.5% 8 a.m. – 9 a.m. 2,735 335 584 152 3,806 71.9% 8.8% 15.3% 4.0% 2 p.m. – 3 p.m. 2,635 242 351 96 3,324 79.3% 7.3% 10.6% 2.9% 3 p.m. – 4 p.m. 2,515 256 334 118 3,223 78.0% 7.9% 10.4% 3.7% 4 p.m. – 5 p.m. 2,238 272 306 111 2,927 76.5% 9.3% 10.5% 3.8% 5 p.m. – 6 p.m. 2,394 286 340 89 3,109 77.0% 9.2% 10.9% 2.9% Table 14. Example hour-by-hour variations in freeway and ramp demand proportions.

60 Update of Highway Capacity Manual : Merge, Diverge, and Weaving Methodologies Metadata Collection The metadata were used to create structured and consistent information to enable the research team to describe and analyze site characteristics for each study site. Appendix A of the NCHRP Web-Only Document 343 provides a data dictionary with detailed information related to the variables used, along with a brief definition and applicable segment type (for example, weave only, all segments) for each variable. Field-Capacity Estimation Approach The research team followed the methodology described in HCM Chapter 26, “Freeway and Highway Segments: Supplemental,” to estimate capacity from the sensor data. This section describes the steps involved in this process. Speed and Flow Rate Aggregation The HCM’s capacity estimation methodology requires 15-minute flow rates, while the sensor data obtained from each site typically provided speeds and flow rates in 5-minute intervals. There- fore, the research team aggregated 5-minute speeds s and flow rates v to 15-minute intervals for use in the analysis. The speed aggregation was performed using a simple weighted average for each lane as follows: ( ) ( ) ( )= × + × + × + + Speed S v s v s v s v v v i i t i t i t i t i t i t i t i t i t , (1), 1 , 1 , 2 , 2 , 3 , 3 , 1 , 2 , 3 where t1, t2, and t3 are the successive 5-minute intervals and i is the subject lane (i = 1 to the total number of lanes n). The 5-minute volume data were converted to 15-minute values by summing each 5-minute interval for each lane as follows: = + +Volume V v v vi i t i t i t, (2), 1 , 2 , 3 Lane-to-Approach Aggregation The application of per-lane capacity estimates to the analysis sites showed that lane flows were imbalanced at some sites, resulting in unreasonable capacity estimates in some cases. Further, the HCM 6th Edition generally does not support lane-by-lane analysis for merge, diverge, and weaving segments but rather analysis across all lanes. As a result, the research team analyzed the Weaving Sites Bundle 3 Merge/Diverge Sites Simple Ramp Weave_1 Simple Ramp Weave_2 Simple Ramp Weave_3 Simple Ramp Weave_4 Simple Ramp Weave_7 Simple Ramp Weave_8 Simple Ramp Weave_10 Simple Ramp Weave_12 Simple Ramp Weave_13 Simple Ramp Weave_14 Simple Ramp Weave_15 Two Lane On Ramp_2 Two Lane Off Ramp_6 Two Lane Off Ramp_9 Close Diverge_1 Close Diverge_4 Close Merge_3 Lane Drop Diverge_3 Close Merge_1 Table 15. Study sites using StreetLight data.

Research Approach 61   approach capacity across all lanes by aggregating approach speeds and flow rates. The approach speed for each 15-minute interval was calculated using a weighted average as follows: ( ) ( ) ( )= × + × + + × + + + Approach Speed S V S V S V S V V V approach n n n , . . . . . . (3) 1 1 2 2 1 2 Similarly, the approach volume aggregation for each 15-minute interval was conducted as follows: = + + + ApproachVolume V V V V n approach n, . . . (4)1 2 The approach speed is expressed in units of miles per hour and therefore directly usable in the HCM capacity estimation methodology. However, approach-level 15-minute volumes needed to be converted to hourly flow rates using the following equation: = ×Flow Rate Vapproach 4 (5) Capacity Estimation The following steps were used to estimate capacity from field data, consistent with the HCM Chapter 26 methodology. 1. FFS Estimation a. The FFS is estimated by calculating the average speed for volumes below 500 vph/ln. b. For some sites, this estimation methodology resulted in artificially low speeds. This situ- ation occurred when sites had frequent low-speed and low-volume periods, likely due to high nighttime truck percentages, nighttime work zones, or inclement weather days. At some other sites, traffic volumes rarely dropped below the 500 vph/ln threshold. In both instances, the research team followed the HCM’s guidance of estimating the FFS as the posted speed limit + 5 mph. c. The team visually confirmed the FFS estimate with the observed speed–flow data plot for each site (see Appendix C of NCHRP Web-Only Document 343) before using the estimate in any modeling efforts. 2. Breakdown Event and Corresponding Volume Identification a. A breakdown event is not simply identified as any 15-minute interval whose speed drops at least 25% below the FFS. Instead, consistent with the HCM, the methodology considered flow recovery. As demonstrated in Figure 16, only the first drop of the speed curve below 75% of FFS in Region 3 was considered a breakdown event. The second is not a break- down event because the prevailing speed has only returned to approximately 42 mph and therefore has not yet recovered to within 10% of FFS for at least 15 minutes. Following the numbering scheme in Figure 16, approach speeds were classified into four regions: Region 1 is “free flow,” Region 2 is “dropping,” Region 3 is “congested,” and Region 4 is “recovering.” In a sequence of 15-minute speeds, only the first interval in Region 3 following a Region 1 or Region 2 interval is identified as a breakdown event. b. Every other volume measurement is classified as uncongested volume, and these events were not used for capacity estimation. However, all uncongested observations were used to estimate the speed–flow model. 3. Bins for Uncongested Volumes a. The uncongested volumes are put into n ranges of 100 vph/ln. 4. Average Flowrate a. The average uncongested flow rate for each range is calculated.

62 Update of Highway Capacity Manual : Merge, Diverge, and Weaving Methodologies 5. Prebreakdown Volume a. Using the same process described in Step 2, a prebreakdown volume was selected as the volume that occurred 15 minutes immediately prior to the interval where a breakdown started. In other words, only the last volume in Region 1 or Region 2 immediately prior to a Region 3 interval was identied as a prebreakdown volume. 6. Bins for Prebreakdown Volumes a. Similar to Step 3, the prebreakdown volumes are put into n bins of 100 vph/ln. 7. Breakdown Probability a. Once the uncongested volume bins (Step 3) and prebreakdown bins (Step 6) were iden- tied, the probability of prebreakdown for each range was calculated as follows: Breakdown Probability P Prebreakdown Counts Uncongested Counts B i i i =, (6), where i is the subject range. 8. Weibull Function a. e Weibull distribution is obtained using the average ow rate across bins from Step 4 and breakdown probability from Step 7. e estimation of the Weibull parameters is described in detail in the next subsection. 9. Estimated Capacity a. Using the Weibull parameters α and β, capacity is estimated as follows: ln 1 (7)a lb ( )= × − −Capacity where λ is the acceptance rate of breakdown and takes the HCM’s recommended value of 15%. is nine-step procedure was applied to each site aer the data cleaning had been completed. A summary of all data for each study site is included in Appendix D of NCHRP Web-Only Document 343, with a summary of just the relevant capacity, speed, and density data provided in Appendix B in the same document. Figure 16. Example of a typical breakdown event, including speed drop and recovery from 15:00 (3 p.m.) to 19:00 (7 p.m.).

Research Approach 63   Weibull Parameter Estimation The average uncongested flow rate from each range and the breakdown probability for each range are needed to estimate the Weibull distribution parameters. Only breakdown flow rates that exceeded 1,000 vph/ln were considered, because breakdowns at lower volumes are typically due to work zones, incidents, or other nonrecurring events. The 1,000 vph/ln threshold was selected based on previous research (Geistefeldt 2007) and discussions between the research team and international experts. The cumulative distribution function (CDF) for the Weibull distribution is provided by the following function (F): 1 exp (8) g a b ( ) ( )= − − −    F x x where x is the average uncongested flow rate per range, α is the scale parameter, β is the shape parameter, and γ is the location parameter. For the two-parameter estimation suggested by the HCM, γ = 0. To be able to fit the data manually, it is desirable to transform the CDF into a format that is easily solvable. Therefore, the research team applied the log transformation to the CDF to allow for linear regression as shown below: ln (9)bw b a( )= −y where ln (10)w ( )= x [ ]( )( )= − −y F xln ln 1 (11) Fitting a linear regression on Equation 9, the following is obtained. This transformation allowed the research team to readily estimate the shape and scale parameters for the Weibull distribution, consistent with HCM Chapter 26. (12)b = Slope ln (13)b a( )− = Intercept The Weibull parameter estimation was applied to each study site. Additional data quality checks conducted on the estimates were conducted before using the capacity values for model development. In some instances, the Weibull approach resulted in unrealistic capacity estimates, typically whenever the underlying sample size of breakdown events was too low. Based on a visual comparison of the capacity estimate against the speed–flow data, the team made a final determination of each site’s viability. This process is described in more detail in the next section. Data Cleaning This section discusses the data cleaning activities that were undertaken by the research team prior to model development. These consisted of two main activities: (1) replacing the Weibull distribution capacity estimation methodology under certain conditions with an approach directly using the speed–flow curve and (2) excluding certain sites during model development due to observed anomalies (for example, downstream bottleneck).

64 Update of Highway Capacity Manual : Merge, Diverge, and Weaving Methodologies Using the Speed–Flow Curve Instead of the Weibull Distribution to Estimate Capacity The previously described field-capacity estimation process using the Weibull distribution is generally a robust method for estimating freeway capacities and is consistent with the HCM’s recommended approach. It accounts for the highly stochastic nature of breakdown events and provides a valid estimate of capacity under consideration of that stochasticity. However, when there are limited data or a small number of breakdown events, the fitting of the Weibull curve can lead to unrealistic capacity estimates. To address this issue, the research team developed speed–flow curves for each site and investigated the results of the Weibull dis- tribution fitting for capacity estimation. These speed–flow curves are included in the data sum- mary in Appendix C of NCHRP Web-Only Document 343. For sites where the Weibull distribution resulted in unreasonable capacity estimates, the research team estimated capacity directly from the speed–flow curves by taking the 85th percentile of the prebreakdown volumes. Note: Chart = graphical estimation of capacity; Weibull = capacity estimation from Weibull distribution. Figure 17(a) shows an example from a simple diverge site where the fitted Weibull distribu- tion indicates very high capacity using the 15% acceptance of the breakdown events (approxi- mately 2,400 vph/ln). However, the speed–flow curve shows that the flow rate rarely exceeded 2,000 vph/ln and that most prebreakdown events occurred in the range of 1,500 to 2,000 vph/ln (Figure 18b). The dashed green line in Figure 17(b) shows the capacity estimate using the speed–flow curve. The capacity estimate using the Weibull distribution is not displayed in Figure 17(a) because there are no observed flow rate data in that range. This characteristic helped the research team identify sites where capacity should be estimated directly from the speed–flow curve. As a result, the team estimated capacity for this site by calculating the 85th percentile of the prebreakdown volumes from the speed–flow curve (Figure 18). In the cases where the Weibull distribution and speed–flow curve produced relatively similar capacity estimates, the research team used the Weibull distribution for consistency with the HCM. Figure 18 shows an example of a site where the Weibull distribution and the speed–flow curve resulted in generally the same capacity estimate. Removal of Sites from Model Development The site selection process described earlier in this chapter screened out many sites where con- gestion was due to a downstream bottleneck. In addition, further investigation of the analysis results and the speed–flow curves determined that breakdown events at some additional sites were likely due to a downstream bottleneck. Therefore, those sites were not included in the model development. Figure 19 shows an example from a simple merge site where most breakdowns occurred at very low flow rates, and the curve sharply ends around 1,200 vph/ln. This pattern is likely due to breakdowns not being caused by the subject segment itself but instead, due to queue spillback from a downstream bottleneck. The site depicted in Figure 19 was not included in the model development. The criteria for the removal of sites from model development primarily relied on a visual inspection of the speed– flow curves, an assessment of the site geometry (for example, proximity to adjacent interchanges and the type of the interchange), and engineering judgment.

Research Approach 65   (a) Capacity Estimated from Weibull Distribution (approximately 2,400 vph/ln) (b) Capacity Estimated from the Speed–Flow Curve (approximately 2,000 vph/ln) NOTE: Chart = graphical estimation of capacity; Weibull = capacity estimation from Weibull distribution. 0 500 1,5001,000 2,5002,000 3,000 1.0 0.8 0.6 0.4 0.2 0.0 0 500 1,5001,000 2,5002,000 3,000 100 80 60 40 20 0 Figure 17. Comparison of field-capacity estimates for a diverge site using the Weibull distribution and the speed–flow curve. 0 500 1,5001,000 2,5002,000 3,000 100 80 60 40 20 0 NOTE: Chart = graphical estimation of capacity; Weibull = capacity estimation from Weibull distribution. Figure 18. Example of site with consistent capacity estimates from the Weibull distribution and the speed–flow curve.

66 Update of Highway Capacity Manual : Merge, Diverge, and Weaving Methodologies Final Sites The team gathered data for a total of 121 sites, along with before-and-after data for four additional sites with ramp meters. Of the 121 sites, 17 were not used for capacity estimation due to concerns of downstream spillback. Appendix D of NCHRP Web-Only Document 343 sum- marizes the data for each of these sites, while Appendix C provides speed–flow data for all sites. Modeling Framework This section describes the modeling framework used in the operational analysis of freeway merge, diverge, and weaving segments. It discusses the modeling concepts included in Chap- ters 13 and 14 of the HCM 6th Edition as well as an alternative approach that was proposed and field-verified in the STRIDE University Transportation Center (UTC) (University of Florida Transportation Institute) project titled “Assessing and Addressing Deficiencies in the HCM Weaving Segment Analyses” (Rouphail et al. 2021). The team also considered a hybrid approach employing elements from both methods. The overarching principles during model development included • A model form that can be applied to merge, diverge, and weaving segments to enable con- sistency across freeway segment analyses and address the HCM’s discontinuity between the merge/diverge and weaving methods; • Methods that do not violate the fundamental relationship between flow, density, and speed; • A model form that is sensitive to key parameters influencing speed and capacity, such as seg- ment short length for weaving segments or acceleration lane length for merge segments; and • Simplification of the methods and analysis methodology to increase the use of HCM among practitioners. Weaving Analysis in the HCM 6th Edition The HCM weaving methodology estimates segment capacity and average segment speed. Capacity is estimated using by HCM Equation 13-5, as shown below: ( ) [ ] [ ]= − +  + +c c VR L NIWL IFL S WL438.2 1 0.0765 119.8 (14) 1.6 0 500 1,5001,000 2,5002,000 3,000 100 80 60 40 20 0 NOTE: Chart = graphical estimation of capacity; Weibull = capacity estimation from Weibull distribution. Figure 19. Speed–flow curve indicating a likely downstream bottleneck.

Research Approach 67   where cIWL = per-lane capacity of the weaving segment under equivalent ideal conditions (pc/h/ln); cIFL = per-lane capacity of a basic freeway segment with the same FFS as the weaving segment under equivalent ideal conditions (pc/h/ln); VR = volume ratio, the fraction of overall demand volume that is weaving; Ls = short length of the weaving segment (ft); and NWL = number of weaving lanes, a function of the segment configuration, which includes ramp weaves, major weaves, and two-sided weaves. Under high-volume ratios, capacity becomes constrained by the intensive lane changing in the segment, and an alternative capacity equation is used, depending on the value of NWL. This capacity is expressed by HCM Equation 13-7 as shown below, where cIW represents the capacity of the entire segment rather than the average of each lane. The lower of the two calculated capacities is applied in the method. = = =       c VR N VR N IW WL WL 2,400 for 2 lanes 3,500 for 3 lanes (15) Prior to determining capacity, the HCM first determines whether the segment is short enough to operate as a weaving segment. If the threshold distance LMAX is exceeded, the segment is analyzed instead as a sequence of merge, basic, and diverge segments. The threshold distance is calculated as follows from HCM Equation 13-4: [ ]( )= × +  − ×L VR NMAX WL5,728 1 1,566 (16) 1.6 The threshold length is derived from the density-based capacity model by setting the weaving segment capacity cIWL to be equal to the basic segment capacity cIFL and solving for Ls. The HCM’s weaving segment speed model is a density-weighted value of weaving and non- weaving vehicle speeds. It is expressed in HCM Equation 13-22 as follows, where v represents demand flow rate and S represents average speeds for the component movements consisting of weaving (W) and nonweaving (NW) flows. = +     +     S v v v s v S W NW W W NW NW (17) While the speed S is seemingly derived from a simple calculation, the process of getting to the value S is rather complex, involving multiple steps. Each step inevitably incorporates some modeling error, which is likely to be compounded as the number of models increases. In summary, applying HCM weaving method requires • Checking that the segment will operate as a weaving segment (that is, Ls < LMAX); • Checking that the segment operates at a v/c ratio < 1.0; • Estimating the lane-changing rates for both weaving vehicles (both required and optional lane changes) and nonweaving vehicles (all optional lane changes), which in turn requires several additional intermediate model calculations; • Estimating the average speeds of weaving and nonweaving vehicles based on their lane- changing rates and other configuration variables; and • Estimating the overall segment speed and density.

68 Update of Highway Capacity Manual : Merge, Diverge, and Weaving Methodologies The literature review and method assessment described in Chapter 1 identified a number of issues with the HCM weaving method. In addition to its complexity, its estimates of speeds and capacity do not always match well with field observations. In general, the HCM’s capacity pre- dictions appear to be on the high side, while its speed predictions appear to be on the low side. One issue with the HCM method is its relative lack of sensitivity to the segment short length. For example, increasing the short length from 500 to 2,000 ft increases capacity by a little over 100 pc/h/ln, assuming other variables are kept constant. This trend is likely to discourage designers from improving the design of the weaving segment as apparently it would have no measurable effect on capacity and quality of service. In contrast, recent research (Rouphail et al. 2021) found that the segment short length had a significant impact on speed and capacity. Another issue with the HCM method is the discontinuity between the capacity and speed esti- mates. Because the HCM considers capacity to occur at a density of 43 pc/mi/ln, one would expect (or require) that speed at capacity would be equal to CIWL/43. However, this constraint cannot be met in the current procedure, thus creating an inconsistency in defining the LOS criteria. Weaving Analysis in NCHRP 07-26 Recent research by the STRIDE UTC (Rouphail et al. 2021) that focused on simple ramp weaves proposed a different and simplified framework for evaluating weaving segments. The research team tested this new approach, along with other alternatives, and ultimately decided to follow the model form proposed by the new approach. However, given the more extensive dataset assembled by NCHRP 07-26, an expanded set of parameters was considered to improve the model fit. Furthermore, the NCHRP 07-26 approach expanded the methodology to include speed and capacity models for simple merge and diverge segments along with more complex geometries for segments. The proposed modeling framework for merge, diverge, and weaving segments meets the fundamental equation of traffic flow and avoids the need for many of the submodels used to calculate average segment speed. The intent of this approach was to provide the best fit to field observations of the segment speed and then use the same model to estimate capacity. In addition, the framework allows segments that have insignificant weaving volumes to converge operationally to a basic segment. In other words, while geometry is important, the amount of weaving traffic also dictates the extent to which the segment will operate as a weaving segment. The form of the proposed speed model is as follows: = −S S SIWo b (18) where So is the average weaving segment speed, and Sb is the average speed of an equivalent basic segment with the same total volume, number of lanes, and FFS. The term SIW stands for Speed Impedance due to Weaving. This formulation ensures (a) that under near-ideal conditions (that is, near zero weaving), SIW approaches zero and the speed approaches that which is observed for a basic segment; and (b) capacity can be computed in a manner consistent with speed, as explained below. Developed using combinations of drone videos and road sensor data for simple ramp weaves, the STRIDE model (Rouphail et al. 2021) uses the following form, where Vrf and Vfr are the weav- ing volumes from the ramp and the freeway, respectively: = − × × +    × −   ×    S S V V N V N L o b rf fr l l S 0.025 17.3 500 1 (19) 3 0.344 0.369

Research Approach 69   Figure 20 compares the HCM (Figure 20a) and STRIDE (Figure 20b) speed models against eld data. e results illustrate the issue of the HCM model underestimating speed, with most of the data lying above the equal-speed line. e RMSE value for the HCM model was 9.18 mph, compared to 3.98 mph for the STRIDE model. e next step in the modeling approach is to ensure consistency between speed and the density- based capacity estimation. Following the HCM’s guidance that weaving segment capacity occurs at a density of 43 pc/mi/lane (which was revisited in NCHRP 07-26 as discussed in Chapter 3 herein), the speed equation can be rearranged for capacity estimation. In Equations 20 and 21, Cw is the weaving segment capacity, CB the equivalent basic freeway segment capacity, and Nl the number of lanes in the segment. ( )( )= − × × +    × − ×    c S C V V N C L W b w rf fr l w S43 0.025 17.3 500 1 (20) 3 0.344 0.369 Equation 20 is quadratic in Cw, which yields a closed-form solution for capacity as a function of the FFS and breakpoint (BP) of the speed-ow curve. From HCM Chapter 12, the model for Sb(Cw) is: 45 or if (21) 2 2 ( ) ( ) ( ) ( )= − −    − − = <S C FFS FFS C C BP C BP S C FFS C BPb w B w w b w w e HCM’s second capacity model, based on the weaving demand volumes, is retained in this framework. e NCHRP 07-26 model framework that was tested proceeds as follows: • Convert all demand volumes to 15-minute ow rates in pc/h units. • Calculate the segment capacity using both the proposed density-based equation and the HCM’s weaving demand volume model and select the lower of the two capacities. • Calculate the segment’s v/c ratio; if v/c exceeds 1.0, the analysis stops as this case requires a facility-based analysis as described in HCM Chapter 10. • Calculate the overall segment speed using the proposed speed model for So. • Calculate segment density D = V/So and determine the corresponding LOS. (a) HCM model (b) STRIDE model Source: Rouphail et al. (2021), Figure 5-1. Figure 20. Comparison of predicted and eld-observed speeds for simple ramp weave sites for the HCM and STRIDE models.

70 Update of Highway Capacity Manual : Merge, Diverge, and Weaving Methodologies Merge and Diverge Analysis in the HCM 6th Edition The HCM’s modeling concepts for merge and diverge segments have evolved over time. The 1985 HCM focused on estimating demand volumes in Lane 1 (rightmost lane) and used overall volumes and FFS to estimate LOS. In the more recent editions, the focus shifted to consider the two rightmost lanes (in the case of right-hand ramps) along with the acceleration and decelera- tion lanes that form the RIA. The RIA length is assumed to occur 1,500 ft downstream/upstream of on-/off-ramps. Another important consideration is that prior to the development of the free- way facility methodology in HCM 2000, the operational analysis focused on the two rightmost lanes only, both in terms of volume and density estimation leading to LOS determination. The effect of nearby on- and off-ramp locations and volumes was accounted for as well in some cases. To accommodate the new facility analysis in 2000, the original procedure was appended to include a speed estimation model for the outer lanes, the aggregation of speeds across all lanes, and an overall density estimation for the entire merge or diverge segment. The HCM’s methodology suffers from both theoretical and practical limitations. From a prac- tical standpoint, volume estimation in Lanes 1 and 2 requires a significant number of inputs, including demand volumes and locations of nearby ramps, even though in many cases such data are not readily available from freeway sensors nor are they directly used in the procedure. An example of the data elements required to estimate Lane 1 and 2 flows is shown in HCM Exhibit 14-8, reproduced below as Figure 21. In addition, because those estimates are based on regression models, users have noticed very often that the method may predict unrealistic volumes in either the RIA or on the outer lanes, especially at the boundary conditions. This issue neces- sitated the addition of a section in HCM Chapter 14, “Checking the Reasonableness of the Lane Distribution Prediction,” to adjust the lane volume estimates when evaluating 6- and 8-lane freeway merge and diverge segments. Source: HCM 6th Edition, Exhibit 14-8 No. of Freeway Lanesa Model(s) for Determining PFM 4 6 8 Selecting Equations for PFM for Six-Lane Freeways Adjacent Upstream Ramp Subject Ramp Adjacent Downstream Ramp Equation(s) Used None None None On Off On On Off Off On On On On On On On On On None On Off None None On Off On Off Equation 14-3 Equation 14-3 Equation 14-5 or 14-3 Equation 14-3 Equation 14-4 or 14-3 Equation 14-3 Equation 14-5 or 14-3 Equation 14-4 or 14-3 Equation 14-5 or 14-4 or 14-3 Notes: If an adjacent diverge on a six-lane freeway is not a one-lane, right-side off-ramp, use Equation 14-3. a 4 lanes = two lanes in each direction; 6 lanes = three lanes in each direction; 8 lanes = four lanes in each direction. Equation 14-3 Equation 14-4 Equation 14-5 Figure 21. Example of HCM merge/diverge method complexity.

Research Approach 71   Merge and diverge areas have widely been considered by system operators to be freeway bottle necks. HCM Chapter 14, however, assumes that there is no drop in capacity at those loca- tions, which appears to conflict with recent research findings. The only capacity checks in the procedure are related to whether the adjoining basic segments can either deliver or receive flow rates limited by their capacity. In addition, the HCM methodology “establishes a maximum desirable rate of flow entering the ramp influence area, exceeding this value does not cause a failure when other capacity values are not exceeded. Instead, it means that operations may be less desirable than indicated by the methodology.” The use of maximum desirable flow rate seems to be redundant, as it has no bearing on capacity, speed, or density estimation in the current methodology. The HCM procedure is unclear on the relationship between capacity and density at capacity. A density-at-capacity value of 45 pc/mi/ln is well documented for basic freeway segments. While the HCM recommends a value of 43 pc/mi/ln for weaving segments, no such clarity exists for merge and diverge segments. In fact, HCM Exhibit 14-3 (reproduced below as Table 16) perhaps defines a capacity density above 35 pc/mi/ln based on the tabulation, although the adjoining chapter text remains silent on the issue. If that is the case, then a density at capacity of 45 pc/mi/ln should also be adopted in the HCM chapter since the HCM’s merge/diverge segment capacity is the same as that of a basic freeway segment. By far the most theoretically egregious problem in the HCM merge and diverge methodology is that it violates the fundamental equation of traffic (volume = speed × density). This is because the procedure provides separate regression models for density and speed estimation in the RIA, as shown below for merge areas (HCM Equation 14-22 for density, reproduced here as Equa- tion 22, and HCM Exhibit 14-13 for speeds, reproduced as here Figure 22). = + + −D v v LR R A5.5475 0.00734 0.0078 0.00627 (22)12 where DR = Destiny in ramp segment; vR = Volume in ramp segment; v12 = Volume in two rightmost lanes in ramp segment; and LA = Length of acceleration lane. As a simple example, consider a merge segment on a four-lane freeway, with vf = 3,000 pc/h, vR = 1,000 pc/h, LA = 1,000 ft, FFS = 60 mph, and SFR = 45 mph, where vf is volume on the freeway entering the segment and SFR is the ramp speed. The flow rate in the RIA is simply vR12 = 3,000 + 1,000 = 4,000 pc/h since PFM = 1.0 (see Figure 22), where PFM is the proportion of mainline flow in the ramp influence area. HCM Equation 14-22 gives a density of 30 pc/mi/ln, and HCM Exhibit 14-13 predicts a speed in the RIA of 52 mph. The total flow rate in the RIA based on those LOS Density (pc/mi/ln) A ≤ 10 B > 10–20 C > 20–28 D > 28–35 E > 35 F Demand exceeds capacity SOURCE: HCM 6th Edition, Exhibit 14-3. Table 16. HCM 6th Edition merge/ diverge LOS density thresholds.

72 Update of Highway Capacity Manual : Merge, Diverge, and Weaving Methodologies estimates is 2 ln × 30 pc/mi/ln × 52 mph = 3,120 pc/h. This value is much lower than the actual flow in the RIA, which is 4,000 pc/h. In fact, if the density equation is assumed to be correct, the corresponding speed should be 4,000/(2 × 30) = 66.6 mph, which is higher than the FFS. Conversely, if the speed equation is the correct one, then the density should have been 4,000/(2 × 52) = 38.5 pc/mi/ln. It appears, based on these calculations, that speed estimation should be the calculation that is retained, with density predicted from the fundamental equation. Interestingly, the HCM method correctly applies the fundamental equation for estimating the density and LOS of the entire segment. In essence, the method aggregates speeds across all lanes [Lanes 1 and 2, and outer lane(s)] to come up with an average segment speed S per HCM Exhibit 14-15, and an overall segment density that is based on the total segment volume V and the number of lanes N per HCM Equation 14-24, reproduced here as Equation 23: = × D V N S (23) Merge and Diverge Analysis in NCHRP 07-26 The NCHRP 07-26 modeling approach used the same general framework for merge and diverge segments that was introduced above for weaving segments. The approach stipulates that an upper bound for the overall speed in the merge (SM) or diverge (SD) segment is the speed on a companion basic segment (SB) that services the same demand flows, same FFS, and same number of lanes. A speed reduction term is applied that accounts for impedances due to the merge (SIM) or diverge (SID) maneuvers. Thus: = − = −S S SIM S S SIDM B D Band (24) Two of the complicating factors present in the HCM methodology were not initially consid- ered in the first stage of model development. These include the estimation of Lane 1 and 2 vol- umes, which in turn may require the estimation of volumes at and locations of nearby on- and off-ramps. The motivation for this approach was that if the isolated ramp model, which excludes those variables, produced a good fit to the field speed observations, the team would recommend its use to make the speed estimation simpler for practitioners. Otherwise, the team would incor- porate those effects one at a time to ascertain their predictive value for speed estimation. The form of the initial proposed speed model for a merge segment SM is given as follows: 500 1 (25)a b g d ( )= − −       S S V V N L M B R a Average Speed in Equation Ramp influence area Outer lanes of freeway Source: HCM 6th Edition, Exhibit 14-13. Figure 22. HCM speed models for merge areas.

Research Approach 73   where VR = on-ramp flow rate, V = total flow rate on the segment = VF + VR, N = number of lanes, La = effective length of the acceleration lane, and α, β, γ, δ = model parameters to be optimized. The above model also incorporates the effect of FFS, which is included in the estimation of the basic segment speed SB. A second model was also considered to test the effect of variables from nearby on- and off-ramps in the following form: 500 1 (26)b g d e q ( )= − ∝ −               S S V V N L v L v L M B R a u u d d where vu, vd = volumes at the upstream and downstream ramps, respectively; Lu, Ld = distances from the subject ramp gore point to the upstream and downstream ramp gore points, respectively; ε, θ = additional model parameters to be optimized; and other variables as previously defined. The capacity estimation method developed by NCHRP 07-26 for merge and diverge segments follows the same path as the method developed for weaving segments. If one followed the HCM modeling assumption that merge/diverge density at capacity is the same as that of a basic seg- ment, then one can estimate the capacity of a merge CM or diverge CD segment using Equation 27 for the isolated merge case. A similar model can be derived for the isolated diverge case, using an assumed density at capacity of 45 pc/mi/ln. The same approach works for other density-at-capacity values, which proved necessary based on the project’s field data. 45 500 1 (27)b g d ( )( )= − ∝ −        C S C V C N L M B M R M a Equation 27 requires solving the quadratic equation in CM, where 45 or if (28) 2 2 ( ) ( ) ( ) ( )= − −    − − = <S C FFS FFS C C BP C BP S C FFS C BPB M B M B b M M Summary In summary, the methodologies in HCM Chapters 13 (weaving segments) and 14 (merge and diverge segments) technically boil down to two principal estimations, that of capacity and average speed (or density), regardless of how many intermediate calculations are needed to obtain those values. While the proposed NCHRP 07-26 model forms offer a way to significantly simplify the HCM methods, they will continue to rely on some elements of the current HCM methodology to characterize either speed or capacity. With respect to the weaving segment analysis, the proposed approach initially retained the alternative capacity model in HCM Equation 13-6, which is based on the relative magnitude of weaving traffic VR. In addition, the team considered retaining the current capacity model in

74 Update of Highway Capacity Manual : Merge, Diverge, and Weaving Methodologies HCM Equation 13-5. However, this approach would require that density at capacity for weaving segments remain at a constant value of 43 pc/mi/ln as Chapter 13 stipulates (or 45 pc/mi/ln for merge and diverge segments). As will be discussed in Chapter 3, the field data collected by NCHRP 07-26 provides clear evidence that the current HCM assumption of capacity occurring at these (high) density values may not be reasonable but that breakdown in fact occurs at sig- nificantly lower capacities. The modeling approach was further refined after feedback from the pilot implementation testing, as described in the next chapter.