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

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75   Overview This chapter presents the results of the modeling performed on the data collected at the study sites. The first three subsections present results for speed estimation, density-at-capacity estima- tion, and capacity estimation, each of which include results for weaving, simple merge, and simple diverge sites. The next two subsections discuss the validation of the speed and capacity models and the results of small-scale data collection at three sites where before-and-after ramp meter- ing data were available. The models that were initially developed by NCHRP 07-26 (referred to as the original models in this chapter) were tested at two practitioner workshops hosted by the Pennsylvania and Wisconsin DOTs. Workshop preparations and outcomes are presented in the next-to-last subsection. Based on the results of the workshops, the original weaving models were recalibrated to include complex weaving sites; the resulting models are referred to as proposed models, and their results are provided immediately following the discussions of the original weaving model results in the first three subsections. No refinements were found to be needed to the original simple merge and simple diverge models as a result of the workshop testing. The chapter concludes with recommended changes to the HCM 6th Edition chapters that address freeway weaving segments and freeway merge and diverge segments. Model Results for Speed Estimation Weaving Sites The NCHRP 07-26 team initially calibrated a weaving model for just simple weaving sites. This original model was used in the pilot implementation phase with agencies. After receiving feedback from the pilot testing, as well as the NCHRP 07-26 panel, the team recalibrated the model to also include complex weaving sites. This proposed model is the one ultimately recom- mended by the project and is the one that is included in the draft HCM chapters produced by the project. This section documents the development of both the original and proposed model. Table 17 summarizes basic information for the simple weave study sites included in the analysis for testing and calibration of the original model. Table 18 shows the additional data for complex weave sites that were added to the simple sites when developing the proposed model. In total, the weave model was calibrated from a sample size of 57,548 data points, each representing a 15-minute speed–flow observation. For each site, the volume ratio VR was calculated for each hour using either StreetLight data or ramp sensor data. The mainline volume and speed data were collected for 15-minute intervals, consistent with the HCM. The sample size for each site not only depends on the data collection duration (for example, some sites have 1 year of data while others have 3 months of data) but also on the selection criteria C H A P T E R 3 Findings and Applications

76 Update of Highway Capacity Manual : Merge, Diverge, and Weaving Methodologies that were used to determine the 15-minute-interval speeds included in the model development. The selection criteria for including 15-minute-interval speeds were as follows: • Observed speed ≥ 0.7 × FFS, as speeds less than 70% of the FFS generally fall within the con- gested flow regime and should not be part of the speed–flow model development. • Observed speed < calculated HCM basic segment speed, as speed observations that exceed the HCM basic segment speed (for example, 90 mph on a 70-mph FFS facility) are likely outlier events that should not be included in the model. • Observed volume > 500 pc/h/ln, as flow rates below 500 pc/h/ln are defined as “free-flow” in the HCM framework and generally are not associated with a notable drop in operating speed. • Valid (non-zero) mainline and ramp observations for the associated time interval, as missing data are likely to skew the modeling results. In other words, only observations with completed speed–flow pairs were used in the analysis. HCM Model Results Figure 23 compares speeds estimated by the HCM methodology with the observed speeds. The RMSE was calculated to investigate how well each model fits the observed field data. The HCM methodology tended to underestimate travel speeds for the study’s simple weaving seg- ments, with an overall RMSE of 12.92 mph. Simple Ramp Weave_3a Tigard, OR OR-217 1,165 487 Simple Ramp Weave_4a Tigard, OR OR-217 2,600 571 Simple Ramp Weave_6a, b Vallejo, CA I-80 1,000 1,904 Simple Ramp Weave_7 Seattle, WA I-5 1,886 3,181 Simple Ramp Weave_8 Everett, WA I-5 1,425 4,292 Simple Ramp Weave_9b Stockton, CA CA-99 650 6,678 Simple Ramp Weave_10 Stockton, CA CA-4 630 8,617 Simple Ramp Weave_12 Everett, WA I-5 2,020 6,377 Simple Ramp Weave_13a Bellevue, WA WA-520 1,000 1,873 Simple Ramp Weave_14 Seattle, WA I-5 1,013 3,078 Simple Ramp Weave_15 Seattle, WA I-5 3,422 3,949 Total 43,744 Notes:a Sites used only for speed estimation and not capacity estimation, as these sites were not the source of congestion, which affected their capacity but not speeds during the undersaturated flow regime. b Sites where on- and off-ramp volumes were used to estimate the VR by assuming Vrr = 2% of the on-ramp volume. This assumption was needed because no reliable data for the ramp-to-ramp flow were available. Analysis Weaving Site Location Highway Segment Short Length (ft) Sample Size Simple Ramp Weave_1 Solana Beach, CA I-5 4,562 152 Simple Ramp Weave_2 Jacksonville, FL I-95 4,653 2,585 Table 17. Summary of analysis datasets for simple weave sites. Site Location Highway Weave Short Length (ft) Sample Size Complex Weave_5 West Valley City, UT UT-201 1,633 1,798 Complex Weave_6 San Jose, CA I-680 1,000 4,667 Complex Weave_7 Salt Lake City, UT UT -201 1,230 4,372 Complex Weave_8 Oakland, CA I-880 2,730 2,967 Total 13,804 Table 18. Summary of analysis datasets for complex weave sites.

Findings and Applications 77   STRIDE Model Results As discussed in Chapter 2, an alternative speed estimation model for simple weaving seg- ments was developed by a STRIDE research project (Rouphail et al. 2021). Figure 24 compares the speeds estimated using the STRIDE model (Equation 19) to the observed speeds. The STRIDE model had a lower RMSE (7.15 mph) compared to the HCM model, indicating better speed estimation. NCHRP 07-26 Original Model Results The speed estimation results presented above showed that the STRIDE model outperformed the HCM method for the simple weaving sites. However, for certain sites, the STRIDE model still resulted in considerable speed differences compared to field-observed speeds. To provide a better model fit, the research team investigated recalibrating the STRIDE model parameters, while maintaining the model form provided in Equation 19. The general form of the equation for this original NCHRP 07-26 model that was tested for calibration is as follows: 500 1 (29) 1 e a b g d = − × × +    × −   ×     − − S S V V N V N L W b rf fr l GP l GP s where SW = average weaving segment speed (mph), Sb = HCM-calculated average speed of an equivalent basic segment (mph), Vrf = on-ramp volume (pc/h/ln), Vfr = off-ramp volume (pc/h/ln), Nl–GP = number of general-purpose lanes in the weaving segment (ln), V = total weaving segment volume (pc/h/ln), and Ls = weaving segment short distance (ft), the distance between the end points of any pave- ment markings that discourage or prohibit lane changing. Figure 23. Comparison of HCM-estimated and field-observed speeds for simple weave sites.

78 Update of Highway Capacity Manual : Merge, Diverge, and Weaving Methodologies The effect of the presence of a managed lane on weaving segment speed was found to be not significant. Two optimization algorithms were applied for the model testing and recalibration. The Levenberg-Marquardt algorithm was used to find the optimal unconstrained parameters that can best estimate the observed speeds. The Trust Region Reflective algorithm was applied for optimizing constrained parameters. A variety of bounds for constrained parameters were tested. Based on the analysis findings and the sensitivity results (discussed later in this chapter), the research team selected the model parameters shown in Table 19. The model parameters for the original STRIDE model are also provided for comparison. With the recalibrated parameters, the RMSE was reduced substantially from 7.15 mph to 2.82 mph. Figure 25 compares the NCHRP 07-26 original model’s estimated speeds with the observed speeds. As shown, while the recalibrated model greatly improved speed predictions, the model does not perform as well for a few sites (for example, the green scatters for the Simple Ramp Weave_15 site show the estimated speeds are generally higher than the observed speeds when the observed speeds are less than 50 mph). NCHRP 07-26 Revised Model Results The pilot implementation testing of the original model for weaving segments resulted in the team revisiting the weaving model formulation to consider the geometry of complex weaving segments more explicitly. In response to the implementation testing results, three new model Figure 24. Comparison of STRIDE-estimated and field-observed speeds for simple weave sites. Model RMSE (mph) Original STRIDE Model 0.025 17.302 0.344 0.369 3.000 7.15 Recalibrated NCHRP 07-26 Model 0.060 0.088 0.131 0.423 2.861 2.82 Table 19. Recalibration of the STRIDE model parameters for simple weave sites.

Findings and Applications 79   forms were considered to explicitly consider the required lane changes needed to complete the weaving maneuvers. These additional models added multipliers to the Vrf and Vfr parameters to account for weaving segment configuration. The three new model forms considered for the proposed model are given below in Equations 30 through 32. The differences in the models are related to the number and type of configuration parameters involved. Proposed Model Form 1 1 1 1 1 500 1 (30) 1 e a b q g d ( ) ( ) ( ) ( ) = − × × + + + × + +           × −   ×     − S S LC NW V LC NW V N V N L o b rf rf rf fr fr fr l GP l s Proposed Model Form 2 1 1 500 1 (31) 1 e a b q g d( ) ( ) = − × × + + × +    × −   ×     − S S LC V LC V N V N L o b rf rf fr fr l GP l s Proposed Model Form 3 1 1 1 1 500 1 (32) 1 e a q g dβ ( ) ( ) = − × × + + × +           × −   ×     − S S NW V NW V N V N L o b rf rf fr fr l GP l s where So = estimated average speed in the weaving segment (mph), Sb = average speed of an equivalent freeway basic segment (per the HCM) (mph), LCrf = minimum number of lane changes for ramp-to-freeway weaving traffic, LCfr = minimum number of lane changes for freeway-to-ramp weaving traffic, Figure 25. Comparison of original NCHRP 07-26 estimated and field-observed speeds for simple weave sites.

80 Update of Highway Capacity Manual : Merge, Diverge, and Weaving Methodologies NWrf = number of lanes from which a weaving maneuver from the on-ramp to the freeway can be made with one or no lane changes, NWfr = number of lanes from which a weaving maneuver from the freeway to the off-ramp can be made with one or no lane changes, Nl-GP = number of general-purpose lanes on the weaving segment (the impact of a managed lane on the weaving speed is not considered), V/Nl = overall weaving segment volume (pc/h/ln), Ls = short distance, the distance (ft) between the end points of any barrier markings that prohibit or discourage lane changing, Vrf = on-ramp weaving flow rate (pc/h), and Vfr = freeway mainline weaving flow rate (pc/h). The same optimization methodology described for the original model was followed for testing the proposed models. The research team developed unconstrained, constrained, and iteration- based models. The Vproposed-1 model (Equation 30) was calibrated first, and the initial calibration results are shown below in Table 20. In the unconstrained approach, all model parameters (α, β, θ, γ, δ, and ε) are positive but unbounded to be able to take on any value. In the constrained model, parameters α, β, θ, and γ are still unbounded, but parameters δ and ε were bounded to be greater or equal to 0.4 and less than or equal to 3, respectively. In the third approach, parameter estima- tion was achieved through 7,500 or more iterations until the model converged. Based on the results given in Table 20, the research team decided to proceed with the con- strained technique, which uses the Trust Region Reflective algorithm, as the value of the cali- brated ε value (reflecting the effect of the number of lanes) was very high in other techniques. Initially, model Vproposed-1 was used to test various constrained scenarios using major weave data; θ values as low as 0.001 means that Vfr has virtually no impact on So. This result led the team to the conclusion that the most logical results for the model parameters are obtained when β and θ are set to 1. This decision was bolstered by the fact that the current weights based on configu- ration were deemed to be sufficient to characterize the differential effect in the two weaving volumes. The constrained estimation results using the three proposed model forms are given below in Table 21. Technique Description RMSE (mph) Unconstrained are positive and unbounded 1.531 11.978 0.000 0.039 0.00 101.096 3.86 Constrained are positive and unbounded, 0.060 3.680 0.001 0.302 0.40 3.000 4.31 Iterations 7,500 iterations or greater 0.114 8.833 0.000 0.011 0.53 439.041 3.79 Table 20. Initial calibration results from unconstrained, constrained, and iteration-based techniques. Model Description RMSE (mph) Vproposed-1 is positive and unbounded, and and 0.056 1 1 0.3 0.4 3.0 4.86 Vproposed-2 0.045 1 1 0.3 0.4 3.0 4.83 Vproposed-3 0.068 1 1 0.3 0.4 3.0 4.81 Table 21. Parameter and RMSE values for proposed model forms.

Findings and Applications 81   The research team ultimately converged on model Vproposed-1 as it provided the optimal results (despite a slight increase in RMSE). The model form was most intuitive and was preferred for practical applications as it added both configuration weights (LC and NW) to both Vrf and Vfr, according to the type of weave segment being analyzed. Because β and θ were set to 1, these parameters were removed from the model and the final model form is given below in Equation 33. 1 1 1 1 500 1 (33) 1 e a g d ( ) ( ) ( ) ( ) = − × + + + + +           × −   ×     − S S LC NW V LC NW V N V N L o b rf rf rf fr fr fr l GP l s This model form was also tested with simple weave data, where all LCs and NWs are equal to one. This results in a simplification of the model form to Equation 34: 500 1 (34) 1 e a g d = − × +    × −   ×     − S S V V N V N L o b rf fr l GP l s The final set of model parameters for both simple and complex weaves are given in Table 22. The dataset did not contain two-sided weaving segments, but the team recommends using the Simple Weave model for that application, with customization of the LC and NW values as applicable. Simple Merge Sites Nine simple merge sites were used to calibrate the speed estimation model for merge sites, as shown in Table 23. The mainline and on-ramp volume and speed data were collected in 15-minute intervals. The selection criteria for including a 15-minute-interval speed were the same as described in the previous subsection for the simple weaving sites. Weave Description RMSE (mph) Simple and are positive and unbounded, 0.025 0.156 0.311 3.0 3.22 Complex is positive and unbounded 0.056 0.300 0.400 3.0 4.86 Table 22. Parameter and RMSE values for proposed weave model. Analysis Simple Merge Site Location Highway Acceleration Lane Length (ft) Sample Size Simple Merge_8 Salt Lake City, UT UT-201 550 901 Simple Merge_9 Daly City, CA I-280 775 6,140 Simple Merge_10 French Camp, CA I-5 780 7,575 Simple Merge_11a Centerville, UT UT-67 2,000 110 Simple Merge_12 Centerville, UT UT-67 950 75 Simple Merge_13 Salida, CA CA-99 785 5,513 Simple Merge_14a Salt Lake City, UT I-80 720 697 Simple Merge_15a Concord, CA CA-242 750 2,720 Simple Merge_16 Salt Lake City, UT I-215 530 1,607 Total 25,338 a Sites used only for speed estimation and not capacity estimation, as these sites were not the source of congestion, which affected their capacity but not speeds during the undersaturated flow regime. Table 23. Summary of analysis datasets for simple merge sites.

82 Update of Highway Capacity Manual : Merge, Diverge, and Weaving Methodologies HCM Model Results Figure 26 compares the HCM’s estimated speeds with the field-observed speeds. Unlike the simple weaving sites, the HCM merge model did a good job estimating field speeds with an overall RMSE of 3.81 mph. However, it is important to note that the Lane 1 and 2 volume V12, which is an input to the HCM model, was obtained directly from the sensor data. This approach avoided additional errors related to V12 estimation from using HCM Exhibit 14-8. NCHRP 07-26 Model Results Similar to the simple weave sites, the NCHRP 07-26 framework estimates merging segment speed SM by reducing the average speed of an equivalent basic segment Sb (from the HCM’s basic freeway segment methodology) using a speed impedance term SIM: = − (35)S S SIMM b Four model structures, shown below as Equation 36 through Equation 39, were tested to estimate SIM by considering the effects of on-ramp volume Vrf, volume on Lanes 1 and 2 V12, mainline volume per lane (V/Nl), and acceleration length La. The results were then compared to field-observed speeds to determine the proposed model for simple merge sites. Model 1 500 1 (36)12 1 ea b wg d ( ) ( )= − × × × × × −   ×    S S V V V N L M b rf l a Model 2 500 1 (37)12 1 a b w g d ( )= − × × + × × −   ×    S S V V V N L M b rf l a Model 3 500 1 (38)12 1 a b g d ( )= − × × × −   ×    S S V V N L M b R l a Figure 26. Comparison of HCM-estimated and field-observed speeds for simple merge sites.

Findings and Applications 83   Model 4 500 1 (39) 1 a b g d ( )= − × × × −   ×    S S V V N L M b rf l a where Vrf = on-ramp volume (pc/h/ln); V12 = volume in upstream Lane 1 (rightmost) and Lane 2 (pc/h/ln), based on sensor data; VR12 = Vrf + V12 (pc/h/ln); La = acceleration lane length (ft); and other variables are as previously defined. Based on the model fit, testing results, and considerations of model simplicity for application by practitioners, the research team proposes Model 4 (Equation 39) for estimate speeds for simple merge sites. Including additional variables or parameters (for example, V12) did not improve the model performance much, and therefore the research team selected a simpler model form to estimate merge speeds that are sensitive to ramp demand, mainline demand, and acceleration lane length. Note that the effects of FFS are captured in the basic segment speed Sb. The calibrated model parameters and the resulting RMSE for the simple merge sites are sum- marized in Table 24, while Figure 27 compares the model’s estimated speeds with the observed speeds. Compared to the HCM model, the RMSE of Model 4 is almost the same (3.81 mph for the HCM model versus 3.93 mph for Model 4); however, Model 4 substantially simplifies the Model RMSE (mph) Model 4 0.015 0.272 1 1 3.93 Table 24. NCHRP 07-26 model parameters for simple merge sites. Figure 27. Comparison of NCHRP 07-26 estimated and field-observed speeds for simple merge sites.

84 Update of Highway Capacity Manual : Merge, Diverge, and Weaving Methodologies calculation process and input data requirements by dropping V12. In addition, the distribution of the Model 4 scatter plots is more evenly spread around the 45-degree line and can provide a greater range of speeds, while the HCM model speed estimates are almost always in the range of 50 to 65 mph, with limited variability in speed. Simple Diverge Sites Eight simple diverge sites were used to calibrate the speed estimation model, as shown in Table 25. The mainline and off-ramp volume and speed data were collected for 15-minute inter- vals. The selection criteria for including a 15-minute-interval speed were the same as described above for the simple weaving sites. HCM Model Results Figure 28 compares the HCM’s estimated speeds with observed speeds. The overall RMSE for the HCM method is 6.12 mph. Note that the Lane 1 and 2 volumes V12 used in the calculation Analysis Simple Diverge Site Location Highway Deceleration Lane Length (ft) Sample Size Simple Diverge_5 Petaluma, CA US-101 210 5,706 Simple Diverge_6 Salt Lake City, UT I-215 215 431 Simple Diverge_7 French Camp, CA I-5 160 7,321 Simple Diverge_8 El Cajon, CA I-8 170 6,073 Simple Diverge_9 Wood Cross, UT UT-67 220 119 Simple Diverge_10 Vacaville, CA I-80 220 6,646 Simple Diverge_11 Tracy, CA I-205 1,250 3,034 Simple Diverge_12 Salt Lake City, UT I-215 285 1,368 Total 30,698 Table 25. Summary of analysis datasets for simple diverge sites. Figure 28. Comparison of HCM-estimated and field-observed speeds for simple diverge sites.

Findings and Applications 85   were based on sensor data. This approach avoided additional errors related to V12 estimation using HCM Exhibit 14-9. The results highlight that the HCM model is limited in its ability to provide speed ranges, resulting in almost identical speeds for each site, while the observed speeds varied as the mainline and off-ramp demand changed. NCHRP 07-26 Model Results The NCHRP 07-26 framework estimates diverging segment speed SD by reducing the average speed of an equivalent basic segment Sb (from the HCM’s basic freeway segment methodology) using a speed impedance term SID: = −S (40)S SIDD b Five model structures, shown below as Equation 41 through Equation 45, were tested to esti- mate SID by considering the effects of off-ramp volume Vfr, volume on Lanes 1 and 2 V12, mainline volume per lane (V/Nl), distance to the upstream Lus and downstream Lds ramps, and deceleration length Ld. The results were then compared to field-observed speeds to determine the proposed model for simple diverge sites. Model 1 500 1 1 1 (41) 1 e a b g d w ( )= − × × × −   ×            S S V V N L L L D b fr l d us ds Model 2 500 1 (42)12 1 a b w g d ( )= − × × + × × −   ×    S S V V V N L D b fr l d Model 3 500 1 (43)12 1 a b g d ( )= − × × × −   ×    S S V V N L D b l d Model 4 500 1 (44) 1 a b g d ( )= − × × × −   ×    S S V V N L D b fr l d Model 5 500 1 (45)12 1 ea b wg d ( ) ( )= − × × × × × −   ×    S S V V V N L D b fr l d where Vfr = off-ramp volume (pc/h/ln), Ld = deceleration lane length (ft), Lus = distance to upstream ramp (ft), Lds = distance to downstream ramp (ft), and other variables are as previously defined. Based on the model fit, testing results, and considerations of model simplicity for application by practitioners, the research team proposes Model 4 to estimate speeds for simple diverge sites. The additional variables or parameters (for example, Lus, Lds, V12) did not improve the model per- formance. The calibrated model parameters and the resulting RMSE for the simple diverge sites are summarized in Table 26. Figure 29 compares the model’s estimated speeds with the observed Model RMSE (mph) Model 4 0.001 0.14 1 0.536 4.04 Table 26. NCHRP 07-26 model parameters for simple merge sites.

86 Update of Highway Capacity Manual : Merge, Diverge, and Weaving Methodologies speeds. Compared to the HCM model, the RMSE of the Model 4 is lower (6.12 mph for the HCM model versus 4.04 mph for Model 4), and it substantially simplifies the calculation process and input data requirements by dropping V12. In addition, the distribution of the model’s scatter plots is more evenly spread around the 45-degree line, while the HCM model provided very limited speed variability within each site. Speed Estimation Sensitivity Tests A key consideration for any new HCM model is an evaluation of the proposed model’s boundary conditions. One of the shortcomings of the existing HCM models is the lack of sen- sitivity to model parameters that would be expected to significantly impact the results (for example, weaving segment short length). Therefore, the research team conducted a series of sensitivity tests of the proposed models. Simple Weave Sites Sensitivity tests were conducted to ensure that the proposed model parameters are sensitive to varying operational and geometric conditions and that the estimated speeds are reasonable. Figure 30 displays speed–flow curves for the proposed NCHRP 07-26 model for two simple weav- ing sites: • FFS = 70 mph, weaving short length = 750 ft, VR = 0.2 • FFS = 70 mph, weaving short length = 750 ft, VR = 0.4 Curves for equivalent basic freeway segments are provided for comparison purposes. The black solid and dashed lines in the graphs correspond to the speed and density of a basic freeway segment, respectively. The green lines indicate the results for a weaving segment. Figure 29. Comparison of NCHRP 07-26 estimated and field-observed speeds for simple diverge sites.

Findings and Applications 87   Unsurprisingly, at low-flow rates (<500 pc/h/ln), the simple weave functions like a basic seg- ment, as there is minimal turbulence from the weaving volume. As the flow rate increases, the speed reduction becomes much more significant than in an equivalent basic segment because of the weaving friction. In addition, the reduction in speed is more pronounced with a VR of 0.4. This result is also expected as higher weave volumes cause additional turbulence and therefore lower speeds under the same flow rate, compared to a VR of 0.2. Another important finding is that if the HCM’s recommended weaving segment density of 43 pc/mi/ln is used at capacity, one obtains a weaving segment capacity in the range of 2,050 to 2,150 pc/h/ln, which is generally consistent with previous research findings. (Note, however, that this research found that weaving density at capacity is lower than 43 pc/mi/ln, resulting in lower capacity values, as discussed with the density findings below.) Simple Merge and Diverge Sites Figure 31 depicts speed–flow curves for simple merge and simple diverge sites, assuming an FFS of 65 mph, acceleration/deceleration lane lengths of 1,000 ft, and identical ramp-volumes. Speed and density for merge segments are shown in red, while curves for diverge segments are shown in blue. Curves for a basic segment (in black) are also included for comparison purposes. Weaving Basic Weaving Density Basic Density Flow Rate (pc/h/ln) Simple Weave: FFS=70 mph; Ls=750 ft; VR=0.2 Sp ee d (m ph ) 1,000 1,500500 0 10 20 30 40 50 60 70 80 2,000 2,500 Weaving Basic Weaving Density Basic Density Simple Weave: FFS=70 mph; Ls=750 ft; VR=0.4 Sp ee d (m ph ) 0 10 20 30 40 50 60 70 80 Flow Rate (pc/h/ln) 1,000 1,500500 2,000 2,500 Figure 30. Sensitivity of the proposed NCHRP 07-26 model for simple weave sites.

88 Update of Highway Capacity Manual : Merge, Diverge, and Weaving Methodologies The sensitivity results show that as the overall segment flow rate increases, speeds start to drop, and the reduction in speed is much greater compared to a basic segment. The speed impedance at merge sites is slightly higher than for equivalent simple diverge sites. Variable Ranges for Speed Estimation The datasets used for model development was limited in the ranges of values for the different variables. Table 27 shows the calibrated ranges for the speed estimation model based on the available datasets for simple geometries. Model Results for Density-at-Capacity Estimation Empirical Evidence for Revisiting Density-at-Capacity Assumptions The HCM uses 43 pc/mi/ln as the density at capacity of simple weaving sites; this assumption was also used in the STRIDE model (Rouphail et al. 2021). The HCM assumes that the density at capacity of merge and diverge segments is the same as that of basic segments, 45 pc/mi/ln. Variable Ranges Segment Type Sites Ls, La, Ld (ft) FFS (mph) Nl (lanes) Sample Size Simple ramp weave 13 630–4,650 57–81 3–5 152–8,617 Simple merge 9 530–2,000 60–70 2–4 75–7,575 Simple diverge 8 160–1,250 59–70 2–4 119–7,321 NOTES: Volume inputs to the HCM simple merge and diverge speed estimation models were obtained directly from sensor data. This approach avoided additional errors related to estimating V12 using the HCM method. Table 27. Variable ranges for speed estimation. (FFS=65 mph, La=Ld=1,000 ft) O VE R AL L SE G M EN T SP EE D (m ph ) - - 10.0 20.0 30.0 40.0 50.0 60.0 70.0 D EN SI TY (p c/ m i/l n) 10.0 20.0 30.0 40.0 50.0 60.0 70.0 OVERALL SEGMENT FLOW RATE PER LANE Merge Basic Diverge Density-Merge Density-Diverge Density-Basic 1,400 1,800 2,0001,000 1,200 1,600 2,200 Figure 31. Sensitivity of the proposed NCHRP 07-26 models for simple merge and diverge sites.

Findings and Applications 89   However, this project’s analysis found that density at capacity is considerably lower than 43 or 45 pc/mi/ln, and it varies substantially based on a site’s geometric and operational site charac- teristics. Figure 32 shows average density at capacity for the NCHRP 07-26 sites (represented by the bars), organized by geometry type. The orange line indicates the number of sites used for the analysis. These results show that the average density at capacity of simple ramp weave sites is 33.5 pc/mi/ln, a value that is much lower than the HCM’s 43 pc/mi/ln. Similar results were obtained for other segment types, with the average density at capacity typically falling in the range of 30 to 40 pc/mi/ln. These results suggest the need to revisit the HCM’s density-at-capacity assumption. This evaluation is possible with the project’s proposed model formulations; the results are discussed in the following subsections. Simple Weave Sites To gain additional insights into the density at capacity and select a recommended density value for the capacity estimation, the research team conducted additional analysis to explore the relationship between density at capacity and site geometric and operational characteristics. This analysis sought to identify whether clear trends exist between density at capacity and certain site attributes, rather than assuming a single density-at-capacity value for all simple weave sites. The attributes used for this analysis were • Area type (rural, suburban, urban), • Terrain type (level, rolling), • Short length (Ls), • Number of mainline lanes, and • Annual average daily traffic (AADT). Figure 33 shows the relationship between key site attributes and density at capacity for the simple weave analysis sites. Some patterns are visible; for example, density at capacity increases slightly as weaving short length increases, and sites with higher AADT tend to have higher densities. C-D Weave Close Diverge Close Merge Complex Weave Lane- Drop Diverge Simple Diverge Simple Merge Simple Ramp Weave Two-Lane Off-Ramp Two-Lane On-Ramp pc /m i/l an e 0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0 N um be r o f S ite s An al yz ed 0 5 10 15 20 25 36.3 30.4 38.4 32.6 35.2 34.8 35.6 33.5 35.1 28.0 Figure 32. Density at capacity for analysis sites.

90 Update of Highway Capacity Manual : Merge, Diverge, and Weaving Methodologies 225,000200,000175,000150,000 Mainline AADT 125,000100,00075,000 PC - D en si ty a t C ap ac ity 20 25 30 35 40 PC - D en si ty a t C ap ac ity 20 25 30 35 40 PC - D en si ty a t C ap ac ity 20 25 30 35 40 45 PC - D en si ty a t C ap ac ity 20 25 15 30 35 40 45 5 Number of Mainline Lane (Weaving section) 4 Urban Area Type AADTArea Type Suburban 6,0005,0004,000 Short Length (Ls) (ft.) Number of Mainline Lane (Weaving section)Short Length (Ls) (ft.) 3,0002,0001,000 PC = passenger cars. Figure 33. Relationship between density at capacity and key site attributes for simple weave sites. In addition, while average density at capacity is similar for suburban and urban sites, urban sites exhibit more variability. Importantly, in all but one case, the observed density at capacity was considerably less than the HCM’s recommended value of 43 pc/mi/ln. Based on these findings, the research team proposes using a density at capacity of 35 pc/mi/ln for simple weave sites. Simple Merge Sites As discussed in “Modeling Framework” in Chapter 2, the HCM procedure for merge and diverge segments is unclear on the relationship between capacity and density at capacity. HCM Exhibit 14-3 indicates that LOS E conditions are observed when density is above 35 pc/mi/ln, while LOS F is defined simply as “demand exceeds capacity.” Given that the HCM defines the capacity of merge and diverge segments to be the same as that of an equivalent basic freeway segment, a density at capacity of 45 pc/mi/ln is implied. As shown in Figure 32, the average density at capacity for the simple merge sites was 36.3 pc/mi/ln. Further investigation of density trends for the simple merge sites found variations in density at capacity depending on a site’s geometric and operational characteristics (Figure 34). However, no clear trends were found and, most sites on average had a density at capacity around

Findings and Applications 91   200,000175,000150,000 Mainline AADT 125,000100,00050,000 75,000 PC - D en si ty a t C ap ac ity 27.5 30.0 32.5 35.0 37.5 40.0 42.5 PC - D en si ty a t C ap ac ity 27.5 30.0 32.5 35.0 37.5 40.0 42.5 PC - D en si ty a t C ap ac ity 30 32 34 36 38 44 42 40 PC - D en si ty a t C ap ac ity 27.5 30.0 32.5 35.0 37.5 40.0 42.5 Rolling Terrain Type Level Urban Area Type AADTArea Type SuburbanRural 900800 Length of acceleration lane Terrain Type Length of acceleration lane 700600500 PC = passenger cars. Figure 34. Relationship between density at capacity and key site attributes for simple merge sites. 35 pc/mi/ln. Therefore, consistent with the simple weave sites, the project team proposes a den- sity at capacity of 35 pc/mi/ln for capacity estimation. Simple Diverge Sites The average density at capacity of the simple diverge sites was 35.6 pc/mi/ln, a value consistent with the simple weave and merge sites. Figure 35 shows the relationship between density at capacity and key site attributes for the simple diverge sites. The results show that certain attributes, such as area type or the length of deceleration lane, can lead to higher density values. However, because of the large variability observed and to provide consistency with the other segment types, the research team proposes using 35 pc/mi/ln as the density at capacity for simple diverge sites. Model Results for Capacity Estimation Simple Weave Sites Nine study sites with good data quality for capacity estimation (for example, sites that were not influenced by a downstream spillback) were analyzed using the HCM and original and proposed NCHRP 07-26 models. Table 28 summarizes the capacity estimates. The speed and

92 Update of Highway Capacity Manual : Merge, Diverge, and Weaving Methodologies volume inputs for capacity estimation were the average speed and volume during the hour with the most observed prebreakdown intervals. The field-observed capacities were estimated based on the methodology described in Chapter 2. Based on the density-at-capacity findings described in the previous section, the research team used a density of 35 pc/mi/ln as the density at capacity. The averages shown in the bottom row of Table 28 indicate that the HCM model resulted in closer estimates of the observed capacity than the NCHRP 07-26 models for some sites. This result is because the HCM method controls a weaving segment’s capacity by the lower of (a) the capacity at a density of 43 pc/mi/ln, or (b) the weaving demand flow rate exceeding a value dependent on the number of weaving lanes. In contrast, the NCHRP 07-26 method removed the weaving demand flow rate condition to prevent inconsistencies for the boundary conditions. For sites with a high VR, the removal of this criterion resulted in the original and proposed NCHRP 07-26 models overestimating capacity, compared to the HCM 6 model (for example, Simple Ramp Weave_2). Simple Merge Sites Six study sites with good data quality to estimate observed capacities were analyzed using the HCM and proposed NCHRP 07-26 models. Table 29 summarizes the capacity estimates. The 200,000180,000160,000 Mainline AADT 140,000120,00080,000 100,000 280260240 Length of deceleration lane PC - D en si ty a t C ap ac ity 220200160 25.0 27.5 30.0 32.5 35.0 37.5 40.0 42.5 45.0 PC - D en si ty a t C ap ac ity 25.0 27.5 30.0 32.5 35.0 37.5 40.0 42.5 45.0 PC - D en si ty a t C ap ac ity 25.0 27.5 30.0 32.5 35.0 37.5 40.0 42.5 45.0 PC - D en si ty a t C ap ac ity 25.0 27.5 30.0 32.5 35.0 37.5 40.0 42.5 45.0 180 Urban Area Type AADTArea Type SuburbanRural 4 Number of Mainline Lane (Upstream) Length of deceleration lane Number of Mainline Lane (Upstream) 32 PC = passenger cars. Figure 35. Relationship between density at capacity and key site attributes for simple diverge sites.

Site Observed HCM an PB Average Volume (pc/h/ln) VR* FFS (mph) Capacity (pc/h/ln) Capacity (pc/h/ln) Capacity (pc/h/ln) v/c Ratio Space Mean Speed (mph) Density (pc/mi/ln) Capacity (pc/h/ln) v/c Ratio Space Mean Speed (mph) Density (pc/mi/ln) Simple Ramp Weave_1 58.9 2,249 0.24 73.3 2,408 2,033 2,055 1.09 53.6 42.0 2,018 1.11 51.98 43.26 Simple Ramp Weave_2 67.3 1,887 0.43 73.3 1,624 1,402 2,047 0.92 62.1 30.4 2,005 0.94 59.85 31.52 Simple Ramp Weave_7 50.2 1,809 0.27 59.3 1,845 1,764 1,878 0.96 54.4 33.2 1,833 0.99 52.72 34.28 Simple Ramp Weave_8 54.2 1,940 0.29 60.3 2,143 1,992 1,866 1.04 52.2 37.1 1,826 1.06 50.45 38.43 Simple Ramp Weave_9 54.9 1,492 0.06 62.3 1,533 2,130 1,884 0.79 57.7 25.9 1,862 0.80 57.64 25.89 Simple Ramp Weave_10 70.4 1,238 0.30 81.4 1,417 1,979 1,991 0.62 74.4 16.6 1,989 0.62 75.37 16.42 Simple Ramp Weave_12 50.9 1,505 0.46 58.4 1,654 1,312 1,849 0.81 54.6 27.6 1,805 0.83 54.15 27.78 Simple Ramp Weave_14 51.9 2,000 0.22 56.6 1,991 1,987 1,784 1.12 48.4 41.3 1,750 1.14 46.81 42.69 Simple Ramp Weave_15 49.8 1,603 0.31 57.9 1,658 1,927 1,866 0.86 54.8 29.2 1,823 0.88 53.99 29.67 Average 56.5 1,747 0.29 64.7 1,808 1,836 1,913 0.91 56.9 31.5 1,879 0.93 55.88 32.22 NOTE: PB = prebreakdown, VR = volume ratio, v/c = volume-to-capacity. Density at capacity = 35 pc/mi/ln, peak-hour factor = 1.0. Sites 3, 4, and 6 not included due to insufficient data quality for capacity estimation. Site 5 not included because its weaving short length is greater than 6,000 ft. Site 11 not included because its off-ramp goes to a weigh station (that is, not a typical weaving segment). *Site 9’s VR is estimated from ramp detector data assuming Vrr = 2% of Von-ramp. VR for other sites was estimated from StreetLight data. Original NCHRP 07-26 Model Revised NCHRP 07-26 Model Table 28. Capacity results for simple weave sites.

94 Update of Highway Capacity Manual : Merge, Diverge, and Weaving Methodologies speed and volume inputs for capacity estimation were the average speed and volume during the hour with the most observed prebreakdown intervals. The field-observed capacities were estimated based on the methodology described in Chapter 2. Based on the density-at-capacity findings described in the previous section, the research team used a density of 35 pc/mi/ln as the density at capacity. Table 29 shows that the proposed NCHRP 07-26 model outperformed the HCM model, resulting in capacity estimates much closer to the observed capacities. Another important find- ing is that the HCM model considerably overestimated field capacity for simple merge sites. This finding is consistent with several other studies of the capacity of simple merges as summarized in the literature review. Simple Diverge Sites Five study sites with good data quality and the presence of ramp sensors (to obtain off-ramp volumes) were analyzed to estimate capacity using the HCM and proposed NCHRP 07-26 methods. Table 30 summarizes the capacity estimates. The speed and volume inputs for capacity estimation were the average speed and volume during the hour with most observed prebreakdown intervals. The field-observed capacities were estimated based on the methodology described in Chapter 2. Like the simple weave and merge sites, a density of 35 pc/mi/ln at capacity was used for the capacity calculations. Table 30 indicates that the proposed NCHRP 07-26 model resulted in substantially closer estimates of the observed capacity, compared to the HCM model. The HCM model consistently overestimated capacity; the model does not incorporate the effects of geometric (for example, deceleration lane length) and operations characteristics (for example, off-ramp demand) that result in lower capacities. Model Validation To validate the effectiveness of the proposed NCHRP 07-26 models, the speed and capacity models were applied to Bundle 3 (complex) sites. This validation process analyzed four complex weave sites, two close diverge sites, two close merge sites, two 2-lane on-ramp sites, two 2-lane Site Observed HCM NCHRP 07-26 Model PB Avg. Speed (mph) PB Average Volume (pc/h/ln) Von / V FFS (mph) Capacity (pc/h/ln) Capacity (pc/h/ln) Capacity (pc/h/ln) v/c Ratio Space Mean Speed (mph) Density (pc/mi/ln) Simple Merge_8 63.5 1,800 0.12 70.0 1,962 2,400 1,978 0.91 60.2 29.9 Simple Merge_9 59.1 1,825 0.09 66.7 2,021 2,370 1,978 0.92 59.3 30.8 Simple Merge_10 57.0 1,816 0.12 65.7 1,929 2,360 1,973 0.92 59.1 30.7 Simple Merge_12 57.0 1,971 0.13 60.4 2,184 2,300 1,931 1.02 54.6 36.1 Simple Merge_13 55.9 2,040 0.14 65.6 2,152 2,360 1,946 1.05 53.6 38.0 Simple Merge_16 58.8 1,520 0.17 65.7 1,901 2,360 1,913 0.80 60.5 25.2 Average 58.6 1,829 0.13 65.7 2,025 2,358 1,953 0.94 57.9 31.8 NOTE: Von / V = (on-ramp volume) / (total volume entering the merge segment), v/c = volume-to-capacity. Density at capacity = 35 pc/mi/ln, peak-hour factor = 1.0. Table 29. Capacity results for simple merge sites.

Findings and Applications 95   off-ramp sites, and one lane drop diverge site. No C-D weave site was included due to data limi- tations, as sensors were only available on the mainline and not on the C-D system. Speed Model Complex Weaves Table 31 summarizes the basic information for each complex weave site, the sample size used for the RMSE calculation, and the resulting RMSEs. The proposed NCHRP 07-26 model’s RMSEs are lower than those of the HCM model for two of the validation sites and higher for Complex Weave_5 and Complex Weave_7. As shown in Figure 36, even with a slightly higher RMSE, the distribution of the NCHRP 07-26 model scatter plots is more evenly spread around the 45-degree line, and the model provides a better fit overall. Complex Merges and Diverges Table 32 and Table 33 summarize the basic information for the complex merge and diverge sites, respectively. The tables also provide the sample size used for RMSE calculation and the resulting RMSEs. The RMSE was only calculated for the NCHRP 07-26 model because the vali- dation sites lacked the lane-by-lane volume data needed to determine the volume in the right two lanes V12, which is an input used by the HCM model. Figure 37 and Figure 38 compare the proposed NCHRP 07-26 speed model’s estimated speeds to observed speeds at complex merge and diverge sites, respectively. In comparison to simple merges (Figure 26) and simple diverges (Figure 29), where the NCHRP 07-26’s speed estimates Site Observed HCM NCHRP 07-26 Model PB Avg. Speed (mph) PB Average Volume (pc/h/ln) Voff / V FFS (mph) Capacity (pc/h/ln) Capacity (pc/h/ln) Capacity (pc/h/ln) v/c Ratio Space Mean Speed (mph) Density (pc/mi/ln) Simple Diverge_5 63.5 1,771 0.02 66.0 1,890 2,360 2,051 0.86 62.9 28.2 Simple Diverge_6 62.3 1,912 0.06 70.0 2,080 2,400 2,021 0.95 60.0 31.9 Simple Diverge_7 56.8 1,865 0.05 66.0 1,992 2,360 1,996 0.93 59.4 31.4 Simple Diverge_10 57.4 1,802 0.01 67.0 2,031 2,370 2,059 0.88 63.1 28.6 Simple Diverge_11 57.2 1,368 0.31 70.0 2,055 2,400 1,992 0.68 66.3 20.6 Average 59.4 1,744 0.09 67.8 2,010 2,378 2,024 0.86 62.3 28.1 NOTES: Voff / V = (on-ramp volume) / (total volume entering the merge segment), v/c = volume-to-capacity. Density at capacity = 35 pc/mi/ln, peak-hour factor = 1.0. Table 30. Capacity results for simple diverge sites. Site Location Highway Weave Short Length (ft) Sample Size HCM RMSE (mph) Original NCHRP 07- 26 RMSE (mph) Revised NCHRP 07- 26 RMSE (mph) Complex Weave_5 West Valley City, UT UT-201 1,633 1,798 2.43 2.38 5.74 Complex Weave_6 San Jose, CA I-680 1,000 4,667 12.8 2.73 2.62 Complex Weave_7 Salt Lake City, UT UT-201 1,230 4,372 4.04 5.87 6.02 Complex Weave_8 Oakland, CA I-880 2,730 2,967 8.74 4.20 4.07 Overall 7.43 4.24 4.86 Table 31. Summary of analysis datasets and results for complex weave validation sites.

96 Update of Highway Capacity Manual : Merge, Diverge, and Weaving Methodologies Site Location Highway Acceleration Lane Length (ft) Sample Size NCHRP 07-26 RMSE (mph) Close Merge_1 Sacramento, CA I-5 3,790 1,393 5.40 Close Merge_3 Federal Way, WA I-5 795 7,974 4.14 Two Lane On Ramp_1 Fremont, CA CA-262 6,975 17,804 4.95 Two Lane On Ramp_2 Tampa, FL I-275 3,519 16,496 5.74 Overall 5.15 Table 32. Summary of analysis datasets and results for complex merge validation sites. Site Location Highway Deceleration Lane Length (ft) Sample Size NCHRP 07-26 RMSE (mph) Close Diverge_1 Federal Way, WA I-5 555 7,347 3.70 Close Diverge_4 Shoreline, WA I-5 150 7,260 2.47 Lane Drop Diverge_6 Bothell, WA I-405 2,530 7,791 4.20 Two Lane Off Ramp_6 Lynwood, WA I-405 4,435 1,082 4.36 Two Lane Off Ramp_9 Manassas, VA I-66 1,010 6,730 4.28 Overall 3.76 Table 33. Summary of analysis datasets and results for complex diverge validation sites. NOTE: The number 69 through 72 indicated the site numbers assigned to the location by the research team. Figure 36. Comparison of HCM and proposed NCHRP 07-26 speeds for complex weave validation sites.

Findings and Applications 97   Close Merge_3 Close Merge_1 Two Lane on Ramp_1 Two Lane on Ramp_2 Figure 37. NCHRP 07-26 speed compared to observed speed for complex merge validation sites. Close Diverge_1 Close Diverge_4 Lane Drop Diverge_6 Two Lane Off Ramp_6 Two Lane Off Ramp_9 Figure 38. NCHRP 07-26 speed compared to observed speed for complex diverge validation sites.

98 Update of Highway Capacity Manual : Merge, Diverge, and Weaving Methodologies were evenly spread around the 45-degree line, the model consistently overestimated speed for the complex merges and generally overestimated speed for the complex diverges. Capacity Model Complex Weaves Table 34 summarizes the capacity estimates from the HCM and proposed NCHRP 07-26 models for the complex weave sites and compares the estimates to the field-observed capacities. At three out of the four sites, the NCHRP 07-26 model outperformed the HCM model, producing capacities close to the observed capacity, while the HCM model considerably overestimated capacity. At the fourth site, which had a higher volume ratio, the observed capacity was greater than the HCM’s estimated capacity for an equivalent basic segment, let alone the capacity of a weaving segment. Complex Merges and Diverges Table 35 and Table 36 summarize the capacity estimates from the HCM and proposed NCHRP 07-26 model for the complex merge and complex diverge sites, respectively, and compare the estimates to the field-observed capacities. The proposed NCHRP 07-26 model outperformed the HCM 6th Edition, producing capacity estimates that were closer to the observed capacities, while the HCM 6th Edition model consistently and considerably overestimated the capacities of the complex merge and diverge sites. Ramp Metering The team gathered before-and-after data for three sites where a ramp meter was installed. The team applied the same speed and capacity field estimation procedures described in Chapter 2 to these sites. The results are presented in Table 37. The ramp metering results were inconclusive regarding the effect of ramp metering on capacity. One site saw a 6% increase in capacity, one site an 8.8% decrease, and the third site a marginal increase of only 1.3%. These results indicate that the capacity impacts of ramp meters may be more nuanced than can be captured in a planning-level HCM analysis, as system-wide effects and relative volume patterns between the ramp and the freeway, as well as with adjacent ramps, have a significant impact on the capacity. Site Observed HCM Original NCHRP 07-26 Model Proposed NCHRP 07-26 Model PB Avg. Speed (mph) PB Average Volume (pc/h/ln) VR* FFS (mph) Capacity (pc/h/ln) Capacity (pc/h/ln) Capacity (pc/h/ln) v/c Ratio Space Mean Speed (mph) Density (pc/mi/ln) Capacity (pc/h/ln) v/c Ratio Space Mean Speed (mph) Density (pc/mi/ln) Complex Weave_5 50.8 1,712 0.12 55.7 1,807 2,222 1,785 0.96 51.3 33.4 1,850 0.93 55.24 30.99 Complex Weave_6 56.5 1,786 0.14 65.6 1,902 2,135 1,940 0.92 58.2 30.7 1,800 0.99 51.68 34.56 Complex Weave_7 60.1 2,345 0.20 67.7 2,524 2,249 1,952 1.20 45.5 51.6 1,782 1.32 35.60 65.87 Complex Weave_8 51.5 1,632 0.13 64.8 1,935 2,270 1,981 0.82 61.5 26.6 1,857 0.88 58.63 27.85 Average 54.8 1,869 0.15 63.4 2,042 2,219 1,915 0.98 54.1 35.6 1,822 1.03 50.29 39.82 NOTE: Density at capacity = 35 pc/mi/ln, peak-hour factor = 1.0. *VR is estimated from ramp detector data assuming Vrr = 2% of Von-ramp. Table 34. Capacity validation results for complex weave sites.

Findings and Applications 99   Table 37. Ramp metering before-and-after data. Site Ramp Metering Start Date End Date FFS (mph) Estimated Capacity % Change SR-4/Port Chicago Hwy-EB on-ramp Before 1/1/2012 12/31/2012 66 1,829 After 1/1/2014 12/31/2014 63 1,939 6.0% I-80/SR-12 (east) WB on-ramp Before 3/1/2014 2/28/2015 69 1,595 After 1/1/2016 12/21/2016 70 1,455 −8.8% I-80/Travis Blvd WB loop on-ramp Before 3/1/2015 9/30/2015 70 1,559 After 1/1/2016 12/21/2016 70 1,579 1.3% NOTE: EB = eastbound; WB = westbound Site Observed HCM NCHRP 07-26 Model PB Avg. Speed (mph) PB Average Volume (pc/h/ln) Von / V FFS (mph) Capacity (pc/h/ln) Capacity (pc/h/ln) Capacity (pc/h/ln) v/c Ratio Space Mean Speed (mph) Density (pc/mi/ln) Close Merge_1 54.7 1,664 0.19 62.9 1,588 2,330 1,999 0.83 61.1 27.2 Close Merge_3 49.1 1,770 0.07 56.2 1,949 2,260 1,848 0.96 53.1 33.3 Two Lane On Ramp_1 56.0 1,630 0.03 70.5 1,763 2,400 2,108 0.77 67.7 24.1 Two Lane On Ramp_2 51.5 1,660 0.15 64.4 1,844 2,340 2,032 0.82 62.7 26.5 Average 52.8 1,681 0.11 63.5 1,786 2,333 1,997 0.84 61.2 27.8 NOTE: Von / V = (on-ramp volume) / (total volume entering the merge segment), v/c = volume-to-capacity. Density at capacity = 35 pc/mi/ln, peak-hour factor = 1.0. Table 35. Capacity validation results for complex merge sites. Site Observed HCM NCHRP 07-26 Model PB Avg. Speed (mph) PB Average Volume (pc/h/ln) Voff / V FFS (mph) Capacity (pc/h/ln) Capacity (pc/h/ln) Capacity (pc/h/ln) v/c Ratio Space Mean Speed (mph) Density (pc/mi/ln) Close Diverge_1 48.6 1,632 0.05 55.4 1,746 2,250 1,847 0.88 53.2 30.7 Close Diverge_4 52.1 1,851 0.06 58.9 1,853 2,290 1,843 1.00 52.6 35.2 Lane Drop Diverge_3 51.4 1,552 0.12 59.6 1,527 2,300 1,958 0.79 58.7 26.4 Two Lane Off Ramp_6 54.9 1,469 0.08 60.0 1,595 2,300 1,979 0.74 59.5 24.7 Two Lane Off Ramp_9 52.6 1,108 0.06 63.8 1,745 2,340 2,017 0.55 63.4 17.5 Average 51.9 1,522 0.08 59.5 1,693 2,296 1,929 0.79 57.5 26.9 NOTE: Voff / V = (on-ramp volume) / (total volume entering the merge segment), v/c = volume-to-capacity. Density at capacity = 35 pc/mi/ln, peak-hour factor = 1.0. Table 36. Capacity validation results for complex diverge sites.

100 Update of Highway Capacity Manual : Merge, Diverge, and Weaving Methodologies Pilot Implementation Testing The project included a pilot implementation testing phase of the recommended freeway merge, diverge, and weaving methods with two state DOTs. The objective of the testing was to obtain practitioner feedback on the recommended methods, using case study examples of actual facilities familiar to the participants. The project initially envisioned that pilot testing would take place during a 1-day, in-person workshop at each participating state DOT. Due to the ongoing effects of the COVID-19 pandemic, it was not feasible to conduct in-person training during the time allocated for Task 10 (conduct the pilots and revise the HCM updates). Therefore, the research team instead conducted the testing in a virtual format, in the form of four 90-minute sessions with each DOT. The research team screened state DOTs for participation in the pilot testing based on the fol- lowing criteria: • None of (or only a limited number of) the sites from the state were used to develop the models. • The state offers a variety of merge, diverge, and weaving configurations to test. • Data required to apply the models are readily available for potential test locations, with the possible exception of weaving volumes. • The research team has contacts at the state DOT to facilitate getting DOT approval to partici- pate and recruit staff to participate. • The selected states are in different parts of the United States. Based on these criteria, the research team proceeded with partnering with Wisconsin DOT and Pennsylvania DOT for the pilot testing. Workshop Preparations The research team coordinated with each state DOT’s contact person to (1) establish dates and times for the workshop, (2) identify case study locations, (3) test technology well in advance of the workshop to identify any potential DOT firewall or other issues that could interfere with the workshop and, if necessary, (4) coordinate with DOT information technology staff to address those issues. The DOT contact person was also responsible for recruiting participants (8 to twelve people per state). The research team developed presentation slides consistent with the workshop outline given below, assembled required data for each case study location, and developed a spreadsheet-based computational engine that implemented each method. These open-source spreadsheet tools were made available to workshop participants to test the methods. Workshop Outline The pilot implementation training was held online via Microsoft Teams in four 90-minute sessions. Each workshop was recorded to allow those unable to participate on the day of the training to view it soon afterward and provide feedback. The sessions were divided up as follows: • Session 1: Introduction, freeway analysis basics, current HCM merge/diverge methods, devel- opment and application of proposed merge/diverge methods. • Session 2: Computational engine training, work case study examples, and discussion of the results. • Session 3: Current HCM weaving method, development and application of proposed weaving method, computational engine training. • Session 4: Work case study examples and discussion of the results, general group discussion, training evaluation. A detailed outline of the sessions is provided below.

Findings and Applications 101   Session 1 • Welcome (15 minutes). – Introduction, housekeeping, sign in. – How to use Microsoft Teams features. – How to participate in discussion (for example, use hand raise feature). – Poll to understand audience familiarity with current HCM methods. – Purpose and objectives of workshop. ◾ Provide advance look at proposed HCM freeway merge, diverge, weaving methods. ◾ Obtain feedback on reasonableness and ease of use of proposed methods by applying spreadsheet tools to analyze sites familiar to workshop participants. – Agenda. • Freeway Analysis Basics (30 minutes). – Definition of capacity. ◾ HCM word definition. ◾ HCM field measurement definition. – Definition of demand volume. ◾ HCM methods use pc/h, field measurements use vph. ◾ Passenger car equivalent concept for heavy vehicles. ◾ Peak-hour factor concept for traffic peaking. – Speed−flow curve example (using actual sensor data, vph). ◾ Types of flow (undersaturated, oversaturated, queue discharge). ◾ Example of determining FFS from sensor data. ◾ Example of determining capacity from sensor data. – HCM basic segment speed−flow curves (ideal conditions, pc/h). ◾ Relationship of capacity and density. ◾ Breakpoint. ◾ HCM basic segment capacity and speed estimation equations. – Factors influencing basic segment capacity. ◾ Roadway geometric factors. ◾ Nonrecurring events (severe weather, incidents, work zones). ◾ Driver population (future: CAVs). ◾ Use of CAFs. – Freeway segment types. ◾ Definitions (basic, merge, diverge, weaving). ◾ Influence areas. • Current HCM Merge/Diverge Segment Method (15 minutes). – Developed by NCHRP 03-37 (1993). – 68 sites in 10 states with varying characteristics. ◾ Video camera observations. ◾ Breakdowns observed at only 16 sites. ◾ Maximum stable flows at other sites compared to HCM basic segment capacities. ◾ No evidence that turbulence effects reduced merge/diverge capacity below basic seg- ment values. – Overview of methodological steps. – Merge/diverge segment capacity same as basic segment capacity. ◾ Values of “maximum desirable flow entering the merge (diverge) influence area” (flow in the right two mainline lanes and flow in the right two mainline lanes plus the ramp) also provided; exceeding these values alone does not indicate LOS F (breakdown) but does indicate that operations may be worse than predicted by the HCM method. – Density and speeds estimated from regression equations.

102 Update of Highway Capacity Manual : Merge, Diverge, and Weaving Methodologies – Special cases. ◾ Lane add/drop. ◾ Two-lane ramps. ◾ 10-lane freeways. ◾ Major merges and diverges. – Issues identified with current method. ◾ Inconsistent with traffic flow theory (speed−flow−density curves). ◾ Speeds/densities not consistent with basic segments at boundary conditions. ◾ Numerous studies have found ♦ Lower capacities generally in merge segments. ♦ Additional factors influence merge capacity, particularly ○ Ramp volume and ○ Evenness of ramp volume. • NCHRP 07-26 Data Collection (10 minutes). – Number of merge/diverge sites and states. – Geometric variability in sites. – Types of data collected for merge/diverge. – Findings for merge/diverge. • Proposed Merge/Diverge Segment Analysis Method (20 minutes). Session 2 • Software Tool Use (20 minutes). – The trainers will do a worked example using the spreadsheet tool, while the participants duplicate the trainer’s steps using their own copy of the tool, which they will need to have downloaded in advance. • Example Applications with Local Data (70 minutes). – This module gives participants hands-on practice applying the method and tool to local sites and includes time for group feedback following each example. The team will have requested and preprocessed the data prior to the course, so the focus is on working with the data, not downloading/processing sensor data. – For each example, participants enter data into the tool and obtain capacity, speed, LOS results. Participants can share their screen and work with the trainers if they experience difficulty. – Following each example, group discussion of reasonableness of results, based on their local knowledge and comparison to field data. Session 3 • Current HCM Weaving Segment Method (20 minutes). – Developed by NCHRP 03-75 (2008). • Fourteen usable sites in six states with varying characteristics. – Observations mostly from fixed-winged aircraft (10 sites) plus two NGSIM sites (computer- ized vehicle tracking) and two sites from camera-recorded video; tethered blimp also tested but was not stable enough for good-quality video. – Only three sites were ramp weaves. • Key definitions. – Weaving length. – One-sided versus two-sided. – Ramp weave versus major weave. – Conditions when capacity is reached. ◾ Density > 43 pc/mi/ln, or ◾ Weaving demand flow rate exceeds threshold value.

Findings and Applications 103   – Overview of methodological steps. – Regression equations used to estimate lane-changing rate and speed. – Issues identified with current method. ◾ Inconsistent with traffic flow theory (speed−flow−density curves). ◾ Speeds/densities not consistent with basic, merge, or diverge segments at boundary conditions. ◾ Studies have found ♦ Method underestimated capacity with high weaving ratios, ♦ Method underestimated speed in the 50 to 65 mph range, ♦ Method overestimated density by an average of 22%, ♦ Method can indicate that volumes are less than capacity but produce densities greater than the density at capacity, and ♦ Method sometimes estimates weaving speeds > nonweaving speeds. • NCHRP 07-26 Data Collection (10 minutes). – Number of weaving sites and states. – Geometric variability in sites. – Types of data collected for weaving. – Findings for weaving sites. • Proposed Weaving Segment Analysis Method (30 minutes). – This module presents the calculation steps involved in applying the proposed method. • Software Tool Use (20 minutes). – The tool will be the same as used in Session 1 but will require some different inputs. The trainers will do a worked example using the tool, while the participants duplicate the trainer’s steps using their own copy of the tool. Session 4 • Example Applications with Local Data (70 minutes). – This module gives participants hands-on practice applying the method and tool to local sites and includes time for group feedback following each example. – For each example, participants enter data into the tool and obtain capacity, speed, LOS results. Participants can share their screen and work with the trainers if they experience difficulty. – Following each example, group discussion of reasonableness of results, based on their local knowledge and comparison to field data. • General Group Discussion (10 minutes). – Solicit additional comments on ease of use and understanding of the method and tool. • Training Evaluation (10 minutes). – Poll-based evaluation form to obtain feedback about the training content and presentation as well as to obtain written comments about the methods and tool that participants did not share in the group discussions. The Wisconsin DOT workshop was held August 19, 2021, with a total of 10 agency partici- pants. The Pennsylvania DOT workshop was held September 10, 2021, with a total of nine agency participants. In addition, NCHRP 07-26 panel members were invited to attend either session; several took advantage of the opportunity. Workshop Summary Feedback received at both workshops was generally positive. Participants welcomed the oppor- tunity to see the newly proposed HCM methods for merge, diverge, and weaving segments and commended the large number of samples used to develop the new methods. Several participants noted having had concerns with the existing HCM methods and having seen unreasonable results

104 Update of Highway Capacity Manual : Merge, Diverge, and Weaving Methodologies when applying the methods. The list below summarizes feedback on the new NCHRP 07-26 methods, as well as some constructive feedback for the team’s consideration in refining the NCHRP 07-26 methods. The team’s action items are summarized at the end. Summary of Participant Feedback General Comments • Participants were generally supportive of the data collection and analysis approach taken by the research team, including the capacity definition used for field estimation. • Participants noted that while the equation form proposed in the NCHRP 07-26 models looked complicated at first, their application was straightforward and intuitive. • Participants appreciated the consistency in approaches between merge, diverge, and weaving segments and using the same computational approach for all freeway bottlenecks as opposed to very different models in the current HCM. • Participants appreciated having access to the computational engines developed by the project and found their use intuitive and generally helpful for understanding the methods and test- ing sensitivity. Several minor suggestions were made for the engines, including rounding capacities to nearest 10 or 50 vph and providing additional warning messages when entering unreasonable values. • Participants were interested in seeing direct side-by-side comparison of the example problem results for the current HCM and NCHRP 07-26 methods in a table. • Participants noted that bottleneck capacity was impacted by very high truck percentages (for example, greater than 20%) and that a disclaimer should be added to the method that sites used in NCHRP 07-26 generally did not have truck percentages that high. • Participants were generally supportive of capacity and LOS F being defined at a density of 35 pc/mi/ln, noting that breakdown at these lower densities generally matches their experi- ence and field observations at bottlenecks. Merge and Diverge Methods • Participants noted frustration related to existing HCM merge and diverge methods, with capacity values generally below what they had seen in field observations. Positive feedback was received for the new NCHRP 07-26 methods resulting in lower and more reasonable capacity values for merge and diverge segments, including the calibration sites. • Participants had previously questioned the HCM methods where the increase in length of an acceleration or deceleration lane did not change the resulting capacity and noted that the NCHRP 07-26 models are more sensitive to these geometric changes. • Participants were interested in design guidance for optimum length of acceleration and decel- eration lanes. It was noted that the NCHRP 07-26 models show a stabilization of capacity for acceleration and deceleration lane lengths in excess of 500 ft. • Participants noted that current HCM methods are not sensitive to ramp speeds or volumes and that field experience suggests both are important. It was noted that the proposed NCHRP 07-26 method explicitly considers ramp volumes in the speed and capacity estimation. It was sug- gested that future research look at impacts of ramp speed on capacity. • Participants appreciated having a single equation for analysis rather than having to use several different look-up tables to complete an analysis. • Participants noted that they felt the presence of upstream and downstream ramps should intuitively impact freeway operations but generally did not like the complex look-up tables in the current HCM. Participants were surprised by the low sample size used to develop the original HCM tables and were supportive of NCHRP 07-26 dropping this complexity without the data to support it. • Participants noted that current HCM methods sometimes produce counterintuitive results when adding an auxiliary lane to relieve congestion at a merge and diverge combination

Findings and Applications 105   segment, which would turn the location to a weaving segment. Participants appreciated that the new NCHRP 07-26 methods use the same computational approach for both segment types, providing greater consistency and more intuitive results when moving between seg- ment types. • Participants noted that they felt capacity of right-hand versus left-hand ramps should be dif- ferent and were hoping to see explicit consideration for this in the NCHRP 07-26 methods. Unfortunately, the project dataset did not include any left-hand ramps, leaving this question for future research. • Participants generally appreciated that the definition of the RIA (two rightmost lanes in the merge or diverge segment) was dropped from the method, noting that the use of the RIA was inconsistent with field observations and simulation results. Some participants suggested that future research explicitly look at very wide freeways (eight or more lanes per direction) and assess the lane-by-lane nature of congestion. It was noted that NCHRP 15-57 already inves- tigated some of these concerns in a lane-by-lane framework. Weaving Methods • Participants were supportive of an approach to weaving segments that is consistent with the approach for merge and diverge segments and generally supported the model form for simple ramp weaves. • Participants expressed concerns with the discontinuity in the speed and capacity estimate for weaving segments. In the version of the NCHRP 07-26 models shown to pilot participants, the team had retained the current HCM secondary capacity check based on volume ratios (VR) in the weaving segment. When combined with the NCHRP 07-26 model, this dual capacity definition resulted in some discontinuities and ‘jumps’ in capacity when switching from one model to the next. Participants expressed a strong preference for a single capacity definition for weaving segments to avoid this issue. • Participants expressed concerns that the weaving model was generally calibrated from simple weaving segments only (one-lane on-ramp and one-lane off-ramp, both on the right side and connected by an auxiliary lane), and used only complex weaves for validation of the model. Participants felt that operations for complex weave are quite a bit different from simple weaves, justifying a stand-alone model. • Participants expressed concerns that the weaving model was not as sensitive to different weav- ing configurations as the current HCM model. The version of the NCHRP 07-26 model used in the pilot tests explicitly distinguished entering and exiting weaving flow rates with different parameters but was not sensitive to the lane configuration for these movements (for example, required number of lane changes to complete the weave) or the number of lanes available for completing the weaving maneuver. Both geometric attributes are an explicit part of the existing HCM methods, and participants felt that their consideration was important for NCHRP 07-26. It was suggested that a combination term of weaving volumes and number of lane changes (for example, LCRF times VRF and LCFR times VFR) should be considered in the model. Actions Resulting from the Implementation Testing The feedback from the pilot implementation workshops in Wisconsin and Pennsylvania generally supported the team’s approach to data collection, analysis, and model development. Participants valued the fact that the NCHRP 07-26 methods appeared to overcome many of the limitations of the existing HCM methods, which participants had also encountered over the years. The biggest theme for constructive criticism was related to the weaving segment methodology and the desire to consider complex weaving geometry more explicitly in the NCHRP 07-26 method. While participants in both workshops generally agreed that simple weaves are the most common geometry, it was also noted that complex weaves are frequently evaluated using HCM methods.

106 Update of Highway Capacity Manual : Merge, Diverge, and Weaving Methodologies As a result, the team focused additional efforts following the workshop on the weaving pro- cedure. The team evaluated several additional model forms that are described in more detail in Chapter 3. Ultimately, the team completely revised and reran the model calibration process for weaving segments, including complex weaving data in the model development process. The team also reran all validation tests using this new model and generally found it to outperform the original NCHRP 07-26 models for complex weaves while producing comparable results for simple weaves. Recommended Changes to HCM Chapters Based on the results presented in this section, NCHRP 07-26 developed comprehensive changes to HCM Chapters 13 and 14. The research team prepared draft chapters that imple- ment these changes; these are provided in four proposed revised chapters: • Revised HCM, Volume 2, Chapter 13 – “Freeway Weaving Segments.” • Revised HCM, Volume 2, Chapter 14 – “Freeway Merge and Diverge Segments.” • Revised HCM, Volume 4 (online), Chapter 27 – “Freeway Weaving: Supplemental.” • Revised HCM, Volume 4 (online), Chapter 28 – “Freeway Merges and Diverges: Supplemental.”