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

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107   Overview This chapter presents the recommended speed and capacity models for merge, diverge, and weaving segments developed through this research along with the recommended value of density at capacity for these segment types and compares the recommended models to the HCM 6th Edition models. The recommended implementation of these models in the HCM, the project’s primary deliverable, is presented in four draft HCM chapters. The chapter concludes with recommendations for future research. Recommended Speed Model This research developed new speed estimation models for HCM merge, diverge, and weaving segments. The general speed model form for all three segment types shares the same consistent approach in which the average segment speed So is adjusted with an impedance factor SI as shown below. = − (46)S S SIo b The specific speed reduction term that is applied accounts for impedances due to the presence of weaving SIW, merging SIM, or diverge SID maneuvers. The model formulation is consistent with the fundamental speed–flow–capacity relationship while providing the necessary sensitivity to factors that influence the average speed of weaving, merge, and diverge segments. Weaving Segments Weaving segment speed is estimated by the following equations, obtained by substituting the NCHRP 07-26 model parameters from Table 22 into Equation 33 for complex weaves and Equa- tion 34 for simple weaves. The resulting equations for complex weaves and simple weaves are shown in Equations 47 and 48, respectively. Note that the weaving segment speed is constrained to be no greater than the speed of an equivalent basic freeway segment. 0.056 1 1 1 1 500 1 (47) 0.300 1 0.400 3.0 ( ) ( ) ( ) ( ) = − × + + + + +           × −   ×     ≤ − S S LC NW V LC NW V N V N L So b rf rf rf fr fr fr l GP l s b 0.025 500 1 (48) 0.156 1 0.311 3.0 = − × +    × −   ×     ≤ − S S V V N V N L So b rf fr l GP l s b C H A P T E R 4 Conclusions and Suggested Research

108 Update of Highway Capacity Manual : Merge, Diverge, and Weaving Methodologies where So = average speed of 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, 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 in 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). Merge Segments For merge segments, the segment speed is estimated by the following equation, obtained by substituting parameters from Table 24 into Equation 39. Merge segment speed is constrained to be no greater than the speed of an equivalent basic freeway segment. S S V V N L M b rf l a b( )= − × × × −   ×     ≤0.015 0.272 500 1 S (49)1 1 1 where La = acceleration lane length (ft) and other variables are as previously defined. Diverge Segments For diverge segments, the segment speed is estimated by the following equation, obtained by substituting parameters from Table 26 into Equation 44. Diverge segment speed is constrained to be no greater than the speed of an equivalent basic freeway segment. S S V V N L D b fr l d b( )= − × × × −   ×     ≤0.001 0.14 500 1 S (50)1 1 0.536 where Ld = deceleration lane length (ft) and other variables are as previously defined. Discussion The speed models in Equation 48 through Equation 50 follow the same general model form and generally use the same model parameters, notwithstanding those unique to the specific segment type. This approach introduces greatly improved consistency across all three segment types in the HCM. Furthermore, the model forms generally apply even to the more complex segment configurations, including complex weaves, two-lane merges and diverges, and closely spaced merges and diverges.

Conclusions and Suggested Research 109   Recommended Density at Capacity The field data collected by this project revealed that the capacity of freeway weaving, merge, and diverge segments occurs around 35 pc/mi/ln, a value considerably lower than the HCM’s current values of 43 pc/mi/ln for weaving segments and 45 pc/mi/ln for merge and diverge seg- ments. In accordance with the fundamental theory of traffic flow, a lower value of density at capacity results in a lower value of segment capacity. Recommended Capacity Models Weaving Segments Given that weaving capacity is based on reaching a density of 35 pc/mi/ln, Equation 46 can be rewritten as Equation 51, which evaluates the overall speed at the weaving segment capacity: ( )= − 35 (51)C S C SIWW b W where CW = weaving segment capacity (pc/h/ln), Sb(CW) = basic segment speed evaluated at the weaving segment capacity (mph), and SIW = speed impedance term due to weaving and segment configuration (mph). Equation 51 is a quadratic equation in CW since the basic segment speed uses the squared value of the flow rate in its calculation. Thus, it can be solved analytically to estimate capacity. Substituting the speed impedance term of Equation 47 into Equation 51 and solving for CW yields Equation 52 to estimate weaving segment capacity: = − + − 4 2 (52) 2 C b b ac a W with =1 (53)a = + −1 35 2 (54)b W B B BP = − − 500 (55)2c BP FFS B W B ( ) = − − (56)2B FFS S C BP c b 1 1 1 1 1 (57)a e g d = + + + + +              W LC NW v LC NW v N L RF RF RF FR FR FR S

110 Update of Highway Capacity Manual : Merge, Diverge, and Weaving Methodologies where CW = weaving segment capacity (pc/h/ln); a, b, c = intermediate calculation parameters; W = weaving segment intensity; B = basic segment term; BP = basic segment breakpoint, from HCM Exhibit 12-6 (pc/h/ln); FFS = free-flow speed of the weaving segment (mph); Sc = speed at capacity of an equivalent basic segment = Cb/45 (mph); Cb = equivalent per-lane basic segment capacity, from HCM Exhibit 12-6 (pc/h/ln); α, γ, δ, ε = regression coefficients from Table 38; and all other variables are as defined previously. Merge Segments The capacity of a merge segment is derived similarly to that of a weave segment. First, Equa- tion 46 is rewritten as Equation 58: ( )= − 35 (58)C S C SIMM b M where CM = merge segment capacity (pc/h/ln), Sb(CM) = basic segment speed evaluated at the merge segment capacity (mph), and SIM = speed impedance term due to merging and segment configuration (mph). Equation 58 is a quadratic equation in CM and thus can be solved analytically to estimate capacity. Substituting the speed impedance term of Equation 49 into Equation 58 and solving for CM yields Equation 59 to estimate merge segment capacity: = − + − 4 2 (59) 2 C B B AC A M with ( ) = × − − 35 45 (60)2A FFS C C BP B B B v L A BPR a ( )= +    − ×1 0.143 2 (61) C A BP FFS v L R a ( ) ( )= × − × −   35 71.4 (62) 2 Segment Type α δ ε Simple 0.025 0.156 0.311 3 Two-sided 0.025 0.156 0.311 3 Complex 0.056 0.300 0.400 3 Table 38. Regression coefficients for use with Equation 57.

Conclusions and Suggested Research 111   where CM = merge segment capacity (pc/h/ln), A, B, C = intermediate calculation parameters, vR = demand flow rate for ramp movement (pc/h), La = acceleration lane length (ft), and all other variables are as defined previously. Diverge Segments The capacity of a diverge segment is derived similarly to that of a merge segment. First, Equa- tion 46 is rewritten as Equation 63: ( )= − 35 (63)C S C SIDD b D where CD = diverge segment capacity (pc/h/ln), Sb(CD) = basic segment speed evaluated at the diverge segment capacity (mph), and SID = speed impedance term due to diverging and segment configuration (mph). Equation 63 is a quadratic equation in CD and thus can be solved analytically to estimate capacity. Substituting the speed impedance term of Equation 50 into Equation 63 and solving for CD yields Equation 64 to estimate diverge segment capacity: = − + − 4 2 (64) 2 C B B AC A D with ( ) = × − − 35 45 (65)2A FFS C C BP B B B v L A BPR d ( )= +     − ×1 0.0049 2 (66) 0.536 C A BP FFS v L R d ( ) ( )= × − × −     35 2.45 (67)2 0.536 where CD = diverge segment capacity (pc/h/ln), Ld = deceleration lane length (ft), and all other variables are as defined previously. Comparison of the Recommended Models to the HCM 6th Edition Models With few exceptions, the speed and capacity models developed by this project outperformed their counterpart HCM 6th Edition models. The following compares the project’s models to

112 Update of Highway Capacity Manual : Merge, Diverge, and Weaving Methodologies the HCM 6th Edition models and provides support for why they are recommended to replace the HCM 6th Edition models. • General advantages of the recommended models: – The recommended models are consistent with the fundamental speed–flow–capacity relation- ship, unlike the HCM 6th Edition models. The recommended models’ speeds converge to basic freeway segment speeds at low demand volumes, and the models avoid discontinuities at boundary locations. – The recommended models are based on larger datasets than those used to develop the HCM 6th Edition models or used in prior research efforts. – The recommended models follow the same general model form and generally use the same model parameters, notwithstanding those unique to the specific segment type, provid- ing greatly improved consistency across all three segment types. Furthermore, the model forms generally apply even to the more complex segment configurations, including com- plex weaves, two-lane merges and diverges, and closely spaced merges and diverges. – The recommended models require fewer inputs than the HCM 6th Edition models, use inputs that are more likely to be available to practitioners, and are sensitive to the inputs included in the model. – The recommended value of density at capacity (35 pc/mi/ln) is consistent with the project’s field measurements; this value is considerably lower than the HCM 6th Edition’s values of 43 pc/mi/ln for weaving segments and 45 pc/mi/ln for merge and diverge segments, imply- ing that the recommended models will produce lower capacities than the HCM 6th Edition models. • Weaving – The recommended speed model has a much lower RMSE for both simple weaves (the most common type of weave) and complex weaves (3.22 mph and 4.86 mph, respectively), compared to the HCM 6th Edition model (12.92 mph). The HCM 6th Edition model con- sistently underestimates simple weave speeds, while the recommended model’s speed esti- mates are more evenly distributed above and below the field-measured speed. – The recommended capacity model produced considerably better estimates of capacity than the HCM 6th Edition for three out of four complex weaves. At the fourth site, the field- measured capacity exceeded that of a basic freeway segment. – The HCM 6th Edition model produced somewhat better estimates of capacity for simple weaves, but results are generally comparable. The recommended model removed the HCM 6th Edition’s maximum weaving demand flow rate criterion to prevent inconsistencies under boundary conditions; for sites with a high weaving volume ratio, the removal of this criterion resulted in the recommended model overestimating capacity. • Merges – The recommended speed model has a similar RMSE as the HCM 6th Edition for simple merges (3.93 mph versus 3.81 mph), with the caveat that the HCM 6th Edition estimation error would be higher if the volume in the right two lanes was estimated using the HCM 6th Edition method rather than being field measured. – The recommended speed model overestimates speeds for complex merges. No comparison to the HCM 6th Edition was possible due to a lack of field data for the volume in the right two lanes at these sites. – The HCM 6th Edition considerably overestimates the capacity of simple merge sites, while the recommended model produces capacity estimates much closer to the field-measured values. – The HCM 6th Edition consistently and considerably overestimates the capacity of complex merge sites. The recommended model does a better job, but also tends to slightly over- estimate capacity.

Conclusions and Suggested Research 113   • Diverges – The recommended speed model has a better RMSE than the HCM 6th Edition for simple diverges (4.04 mph versus 6.12 mph). In addition, the HCM 6th Edition estimation error would be higher if the volume in the right two lanes was estimated using the HCM 6th Edition method rather than being field measured. – The recommended speed model overestimates speeds for complex diverges but to a lesser degree than for complex merges. No comparison to the HCM 6th Edition was possible due to a lack of field data for the volume in the right two lanes at these sites. – The HCM 6th Edition considerably overestimates the capacity of simple diverge sites, while the recommended model produces capacity estimates much closer to the field-measured values. – The HCM 6th Edition consistently and considerably overestimates the capacity of complex diverge sites. The recommended model does a better job but also tends to slightly over- estimate capacity. Suggested Future Research Although NCHRP 07-26 was able to develop improved HCM models for forecasting the operation of a variety of merge, diverge, and weaving segment types, additional research is sug- gested to address the lower-priority segment configurations that were not able to be studied by this project. In addition, to be able to fully implement the new models in the HCM, additional work will be required to update HCM Chapter 10 to incorporate the new methods into a freeway facility analysis and to update the freeway facilities computational engine, FREEVAL. The following list suggests research topics that would further improve the merge, diverge, and weaving models developed by this project: • Video data collection to develop a model to predict density at capacity as a function of geo- metric and traffic characteristics. Figure 32 showed that the observed density at capacity varied between different categories of sites and, in some cases, was considerably lower than the recom- mended value of 35 pc/mi/ln (which itself is considerably lower than the 43 or 45 pc/mi/ln used in HCM 6th Edition). • Data collection at managed lane sites to estimate capacities at managed lane access and egress points. This effort could use a similar data collection approach to the one used in this project to obtain data from a relatively large number of sites. Managed lane merging, diverging, and weaving were outside this project’s scope. • Additional data collection at bottleneck locations where active traffic management strategies are in use, including ramp metering and part-time shoulder use, to estimate the effects of these strategies on freeway operations. As described in Chapter 3, this project’s data collection effort only included three ramp metering sites, with inconclusive results. • Data collection for two-sided weaves using a similar approach to that used by NCHRP 07-26 to establish capacity and LOS models for this weaving type. A study of two-sided weaves was a lower-priority effort that was not able to be included in the project’s data collection effort. • Develop a model to estimate FFS near interchange influence areas. The current and proposed HCM models rely on the HCM Chapter 12 models for basic freeway segment FFSs to deter- mine the FFSs of a merge, diverge, or weaving segment. The Chapter 12 FFS model includes a generalized “total ramp density” term that incorporates the average number of ramps per mile within a section extending 3 miles upstream and 3 miles downstream of the subject segment. The FFSs of a weaving, merge, or diverge segment may be affected by more localized condi- tions or by other conditions not included in the basic freeway segment model. • Validate the current and proposed extension of the HCM weaving method to multiple weav- ing segments (that is, weaving segments containing overlapping weaving movements between

114 Update of Highway Capacity Manual : Merge, Diverge, and Weaving Methodologies different sets of ramps). The extension to the method suggests that the analyst divide a multiple weaving segment into a series of merge, diverge, and simple weaving segments, but it is not known how well this approach matches field conditions. Multiple weaving segments were not studied by this project. If necessary, as a follow-up effort, develop a new model to forecast the operation of multiple weaving segments. The following suggested research projects would help integrate the new analysis methods into the HCM’s freeway facility analysis procedures, along with improving freeway facility analysis generally: • Update HCM Chapter 10, “Freeway Facilities Analysis,” to integrate the new merge, diverge, and weaving methods into the overall freeway facilities analysis procedure. As part of this effort, update the freeway facilities computational engine, FREEVAL, to incorporate the new methods. • Perform additional work on freeway-flow modeling under oversaturated conditions and expanding the HCM’s point-based look at capacity to queuing models (that is, the scope of former NCHRP Project 03-96A, “Analysis of Oversaturated Traffic Flow Conditions on Freeway Facilities”). • Perform additional work on models for stochastic capacity estimation of freeways.