Improved Analysis of Two-Lane Highway Capacity and Operational Performance (2018)

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NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 63 3. Analysis Methodology Development This chapter describes the development of the performance measure models recommended for use in the analysis methodology. The analysis methodology is outlined in Appendix G. 3.1. Segmentation In this analysis methodology, segment types are defined as follows: • Passing Zone: Length of two-lane highway for which passing in the oncoming lane is permitted, and the length and location of such passing zone provides reasonable accommodation of passing maneuvers under certain traffic conditions. • Passing Lane: This segment type consists of an added lane in the same direction as the analysis direction, with the intent to break up platoons that have formed upstream by allowing faster vehicles to pass slower vehicles. • Passing Constrained: Length of two-lane highway in which passing in the oncoming lane is either prohibited or effectively negligible due to lack of utilization of passing zone(s). The latter might be due to insufficient sight distance and indicates an area where passing should be formally prohibited. These segment types are discussed in further detail in the following subsections. 3.1.1. Passing Zone Passing opportunities are a major influence on two-lane highway performance. One way this is accomplished is through the provision of passing zones—locations where passing in the oncoming lane is allowed. However, to be effective in accommodating passing maneuvers, these zones must be of a minimum length and also not placed in locations that lead to underutilization of passing opportunities. The effectiveness of a passing zone in improving traffic operations is a function of: • Analysis direction flow rate • Opposing direction flow rate • % heavy vehicles • Horizontal alignment • Vertical alignment • Length Furthermore, the extent of the improvement in performance measures relative to the upstream segment is a function of the level of platooning entering the passing zone.

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 64 3.1.2. Passing Lane A passing lane segment, a relatively short length of roadway where an additional lane is provided in the same travel direction, is another mechanism for providing passing opportunities. The effectiveness of a passing lane in improving traffic operations is a function of: • Analysis direction flow rate • % heavy vehicles • Horizontal alignment • Vertical alignment • Length 3.1.3. Passing Constrained For this segment type, adjacent stretches of roadway with varying geometric conditions can be combined into a single analysis segment when the vehicle performance of passenger cars and heavy vehicles is relatively consistent from one sub-segment to another and the difference in vehicle performance between passenger cars and heavy vehicles is not large. Thus, truck performance is the critical factor for determining when a "general segment analysis" can be performed, as opposed to a "specific segment analysis". Additionally, stretches of roadway where passing in the oncoming lane is allowed but essentially does not take place (regardless of opposing traffic demand) can also be included in this extended length of analysis segment. The condition could occur due to insufficient sight distance (this location may need to be restriped to explicitly prohibit passing). For this condition, it may be preferable to consider this stretch of roadway as a passing zone to provide more flexibility in testing the sensitivity of performance measure values to various design parameters (e.g., length, grade). This type of segment may contain some heterogeneity in the geometric alignment; however, no specific length of roadway within this segment should have significantly different operating conditions than other stretches of roadway within this segment. In such cases, the length of roadway with significantly different operating conditions should be split out into a separate segment. The traffic operations along this type of segment are a function of: • Analysis direction flow rate • % heavy vehicles • Horizontal/vertical alignment • Length The discussion for Task 9 describes how horizontal and vertical alignment are considered in the segmentation process. In particular, see Table 3-5, Table 3-6 and Table 3-7.

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 65 3.2. Estimation of Free-Flow Speed FFS values for various roadway and traffic conditions were obtained from non-linear regression analysis of the general speed-flow model presented in Equation (3-1). This model assumed that the FFS equaled the ATS corresponding to a directional flow rate of 100 veh/h. Using these FFS values, a general model was developed to estimate the FFS for the various roadway and traffic conditions. FFS models were estimated separately for tangent segments and horizontal curves. This section describes the FFS model forms and dependent variables that provided the best fit to the data. 3.2.1. Tangent Segments The final model form is presented in Equations (3-1) and (3-2). This model applies to all segment types (i.e., passing constrained, passing zone, and passing lane). The differences between these segment types were captured through the opposing flow rate (vo) term in Equation (3-2). = − × % (3-1) = 0.0333, 0 + 1 × + 2 ×+ 0, 3 + 4 × + 5 × × (3-2) where FFS = free-flow speed in the analysis direction (mi/h) BFFS = base free-flow speed in the analysis direction (mi/h) a = slope coefficient for FFS-HV% relationship (decimal) HV% = percentage of heavy vehicles in the analysis direction (%) L = segment length (mi) vo = flow rate in the opposing direction (1000’s of veh/h) (equals 0 for passing lane segment and 1.5 for passing constrained segment) a0, a1, a2, a3, a4, a5 = FFS-HV% slope model coefficients (obtained from Table 3-1) Equation (3-2) shows that the FFS equals the BFFS when the heavy vehicle percentage is zero. As the heavy vehicle percentage increases, the FFS linearly decreases at a rate equal to a, the slope coefficient. Equation (3-3) shows that the slope coefficient is a function of the BFFS, segment length, and opposing flow rate. For passing lane and passing constrained segments, an opposing flow rate of 0 veh/h and 1500 veh/h should be used, respectively. An analysis of the FFS on passing lane and passing zone segments showed that passing lane segments had a similar FFS as passing zone segments with no opposing flow rate. Similarly, passing constrained segments had a similar FFS as passing zone segments with a 1500 veh/h opposing flow rate. Equation (3-3) also shows that the slope coefficient is a function the vertical alignment classification. This is because the slope model coefficients (a0, a1, a2, etc.) differ for each vertical alignment class. Table 3-1 presents these slope model coefficients as well as the adjusted R2 values for each coefficient model. The coefficients for vertical class 1 are listed as “N/A” because the

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 66 slope coefficient is constant for this vertical class. Models fit to the vertical class 1 data showed that the BFFS, segment length, and opposing flow rate exerted little to no influence on the slope coefficient. A constant slope coefficient model fit the vertical class 1 data just as well as a variable slope coefficient model (i.e., the non-constant portion of Equation (3-2). The constant value of 0.0333, shown in Equation (3-2), produced the best R2 value for the vertical class 1 data. Table 3-1. Coefficients for FFS-HV% Slope Model (Used in Equation (3-3) Vertical Class a0 a1 a2 a3 a4 a5 1 N/A N/A N/A N/A N/A N/A 2 −0.45036 0.008140 0.01543 0.01358 0 0 3 −0.29591 0.00743 0 0.01246 0 0 4 −0.40902 0.00975 0.00767 −0.18363 0.00423 0 5 −0.38360 0.01074 0.01945 −0.69848 0.01069 0.12700 3.2.2. Horizontal Curves As mentioned in the previous section on tangents, the HCM defines BFFS as “the speed that would be expected on the basis of the facility’s horizontal and vertical alignment, if standard lane and shoulder widths were present and there were no roadside access points” (Transportation Research Board, 2010, p. 15-15). Therefore, the BFFS on some horizontal curves will be lower than the BFFS on the preceding tangent segment. An equation for the BFFS on horizontal curves was developed to account for this difference. Equation (3-3) presents the model form. = , 44.32 + 0.3728 × − 6.868 × (3-3) where BFFSHCi = base free-flow speed of horizontal curve subsegment i (mi/h) BFFST = base free-flow speed of the preceding tangent sub/segment (mi/h) HorizClassi = horizontal alignment classification of curve subsegment i (integer) Equation (3-3) shows that BFFSHCi increases with an increase in BFFST and decreases with an increase in HorizClass. It also shows that BFFSHC cannot exceed BFFST. The relationships between these variables were as expected, since they reflected the relationships in the curve speed models of that were incorporated in the simulation tool (see Appendix D). All model coefficients were statistically significant at the 99.9 percent confidence level, and the adjusted R2 value of the model equaled 0.996. The relationship between BFFS and FFS for horizontal curves was the same as that for tangent segments. Therefore, Equation (3-2) was fit to the horizontal curve FFS data. The resulting FFS model is shown in Equation (3-4). = − 0.0255 × % (3-4)

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 67 where FFSHCi = free-flow speed of horizontal curve subsegment i (mi/h) BFFSHCi = base free-flow speed of horizontal curve subsegment i (mi/h) HV% = percentage of heavy vehicles in the analysis direction (%) Equation (3-4) shows that the FFS linearly decreases with an increase in the heavy vehicle percentage. This is because heavy vehicles generally have a lower desired curve speed as compared to passenger cars. This relationship was also as expected, since it is reflected within the curve speed models (Equation (3-5) and Equation (3-6)) in the simulation tool. The FFS-HV% slope coefficient in Equation (3-4) was statistically significant at the 99.9 percent confidence level, and the adjusted R2 value for the model equaled 0.996. 3.3. Models for Estimation of Average Speed This study developed a new, general speed-flow model that captured variations in the shape of the speed-flow relationship. This model is presented in Equation (3-5). = − × − 0.1 (3-5) where ATSd = average travel speed in the analysis direction (mi/h) FFSd = free-flow speed in the analysis direction (mi/h) vd = flow rate in the analysis direction (1000’s of veh/h) m = speed-flow slope coefficient p = speed-flow power coefficient The model assumes that ATS is equal to FFS when the directional flow rate (vd) is equal to 100 veh/h (i.e., 0.1 thousands of vehicles per hour). This assumption was based on observations from a sample of simulation data, which showed that ATS did not vary significantly for flow rates between 0 and 100 veh/h. For flow rates less than 100 veh/h, ATS should be set equal to FFS. The main advantage of Equation (3-5) is that the power coefficient (p) can vary by segment type, segment length, heavy vehicle percentage, etc. Therefore, different shapes of the speed-flow relationship can be modeled using this coefficient. 3.3.1. Estimation of Slope Coefficient The speed-flow slope coefficient controls how quickly average speed decreases with an increase in flow rate. As mentioned earlier in this chapter, this coefficient differed for each combination of roadway and traffic conditions. This section discusses the models developed to estimate this slope coefficient as well as the underlying relationships in these models. Separate models were developed for tangent segments and horizontal curves. These models are presented in their respective sections.

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 68 Tangent Segments Regression analysis was used to fit a model to the speed-flow slope coefficient data for tangent segments. Various linear and non-linear model forms were investigated and assessed based on accuracy and simplicity. Similar to the FFS models, slope coefficient models that incorporated vertical alignment classification as an independent variable produced lower R2 values as compared to fitting separate models for each vertical alignment classification. Fitting separate models also reduced the total number of independent variables, since the vertical alignment interacted with the majority of the independent variables. In order to achieve greater model accuracy, separate models were used for each vertical alignment classification. The accuracy of the models also increased when fitting separate models for passing lane segments and passing zone/passing constrained segments. The passing zone and passing constrained segments were grouped together, since the differences between the two could be accounted for through the opposing flow rate term. The general model form selected for each vertical class and segment type is shown below in Equation (3-6), Equation (3-7), and Equation (3-8). = 5, 0 + 1 × + 2 × + (0, 3) × √ + (0, 4)× √ % (3-6) 3 = 0 + 1 × √ + 2 × + 3 × × √ (3-7) 4 = 0 + 1 × √ % + 2 × + 3 × × √ % (3-8) where m = speed-flow slope coefficient (decimal) FFS = free-flow speed in the analysis direction (mi/h) L = segment length (mi) vo = flow rate in the opposing direction (1000’s of veh/h) (equals 0 for passing lane segment and 1.5 for passing constrained segment) HV% = percentage of heavy vehicles in the analysis direction (%) b0, b1, b2, b5 = coefficients for speed-flow slope model (obtained from Table 3-2 or Table 3-3) b3 = segment length coefficient for speed-flow slope model b4 = heavy vehicle percentage coefficient for speed-flow slope model c0, c1, c2, c3 = coefficients for b3 model (obtained from Table 3-4 or Table 3-5) d0, d1, d2, d3 = coefficients for b4 model (obtained from Table 3-6 or Table 3-7) Equations (3-6), (3-7), and (3-8) show that the speed-flow slope coefficient is a function of the FFS, opposing flow rate, segment length, and heavy vehicle percentage. The slope coefficient is also a function of the vertical alignment classification and segment type, since the coefficients in these equations differ by vertical class and segment type. Table 3-2, Table 3-4, and Table 3-6

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 69 these equations differ by vertical class and segment type. Table 3-2, Table 3-4, and Table 3-6 present the coefficients for the passing zone/passing constrained segment models. Table 3-3, Table 3-5, and Table 3-7 report the coefficients for the passing lane segment models. Generally, the coefficients in these tables show that an increase in FFS, opposing flow rate, segment length, heavy vehicle percentage, or vertical alignment classification increased the slope coefficient. Table 3-2. Coefficients Used in Speed-Flow Slope Model (Equation (3-6)) for Passing Zone and Passing Constrained Segments Vertical Class b0 b1 b2 b3 b4 b5 1 0.0558 0.0542 0.3278 0.1029 N/A N/A 2 5.7280 −0.0809 0.7404 Varies Varies 3.1155 3 9.3079 −0.1706 1.1292 Varies Varies 3.1155 4 9.0115 −0.1994 1.8252 Varies Varies 3.2685 5 23.9144 −0.6925 1.9473 Varies Varies 3.5115 Table 3-3. Coefficients Used in Speed-Flow Slope Model (Equation (3-6)) for Passing Lane Segments Vertical Class b0 b1 b2 b3 b4 b5 1 −1.1379 0.0941 N/A Varies Varies N/A 2 −2.0688 0.1053 N/A Varies Varies N/A 3 −0.5074 0.0935 N/A N/A Varies N/A 4 8.0354 −0.0860 N/A Varies Varies 4.1900 5 7.2991 −0.3535 N/A Varies Varies 4.8700

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 70 Table 3-4. Coefficients Used to Calculate b3 (Equation (3-7)) for Passing Zone and Passing Constrained Segments Vertical Class c0 c1 c2 c3 1 0.1029 N/A N/A N/A 2 −13.8036 N/A 0.2446 N/A 3 −11.9703 N/A 0.2542 N/A 4 −12.5113 N/A 0.2656 N/A 5 −14.8961 N/A 0.4370 N/A Table 3-5. Coefficients Used to Calculate b3 (Equation (3-7)) for Passing Lane Segments Vertical Class c0 c1 c2 c3 1 N/A 0.2667 N/A N/A 2 N/A 0.4479 N/A N/A 3 N/A N/A N/A N/A 4 −27.1244 11.5196 0.4681 −0.1873 5 −45.3391 17.3749 1.0587 −0.3729 Table 3-6. Coefficients Used to Calculate b4 (Equation (3-8)) for Passing Zone and Passing Constrained Segments Vertical Class d0 d1 d2 d3 1 N/A N/A N/A N/A 2 −1.7765 N/A 0.0392 N/A 3 −3.5550 N/A 0.0826 N/A 4 −5.7775 N/A 0.1373 N/A 5 −18.2910 2.3875 0.4494 −0.0520 Table 3-7. Coefficients Used to Calculate b4 (Equation (3-8)) for Passing Lane Segments Vertical Class d0 d1 d2 d3 1 N/A 0.1252 N/A N/A 2 N/A 0.1631 N/A N/A 3 N/A −0.2201 N/A 0.0072 4 N/A −0.7506 N/A 0.0193 5 3.8457 −0.9112 N/A 0.0170

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 71 Horizontal Curves For horizontal curves, the slope coefficient is estimated with Equation (3-9). 0.277, 25.8993 0.7756 10.6294 Max 2.4766 9.8238 HCi HCi i i FFS FFS HorizClass HorizClas m s × + × + − −  =   × × − (3-9) Where all terms are as defined previously. 3.3.2. Estimation of Power Coefficient Like the slope coefficient, the power coefficient differs for each combination of roadway and traffic conditions. This section discusses the models developed to estimate this power coefficient. Tangent Segments Regression analysis was used to fit a model to the speed-flow power coefficient data for tangent segments. Various linear and non-linear model forms were investigated and assessed based on accuracy and simplicity. Similar to the FFS models, power coefficient models that incorporated vertical alignment classification as an independent variable produced lower R2 values as compared to fitting separate models for each vertical alignment classification. Fitting separate models also reduced the total number of independent variables, since the vertical alignment interacted with the majority of the independent variables. In order to achieve greater model accuracy, separate models were used for each vertical alignment classification. The accuracy of the models also increased when fitting separate models for passing lane segments and passing zone/passing constrained segments. The passing zone and passing constrained segments were grouped together, since the differences between the two could be accounted for through the opposing flow rate term. The general model form selected for each vertical class and segment type is shown in Equation (3-10). = Max 8, 0 + 1 × + 2 × + 3 × + 4 × + 5 × %+ 6 × √ % + 7 × × % (3-10) where p = speed-flow power coefficient (decimal) f0–f8 = coefficient values (obtained from Table 3-6, Table 3-8 or Table 3-9), and Other terms as defined previously. Equation (3-10) shows that the speed-flow power coefficient is a function of the FFS, segment length, heavy vehicle percentage, and opposing flow rate (except in the case of a passing lane segment, in which case the f3 and f4 coefficient values are zero). The power coefficient is also a function of the vertical alignment classification and segment type, since the coefficients in these

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 72 equations differ by vertical class and segment type. Table 3-8 and Table 3-9 present the coefficients for the passing zone/passing constrained segment models. All coefficients in these tables were statistically significant at the 95 percent confidence level, except b0 in three of the models. Despite its insignificance, b0 was retained in these models because it was an intercept coefficient. Generally, the coefficients in these tables show that an increase in FFS, opposing flow rate, segment length, heavy vehicle percentage, or vertical alignment classification increased the slope coefficient. These relationships were as expected and are discussed later in more detail. Table 3-8. Coefficients Used in Speed-Flow Slope Model (Equation (3-10)) for Passing Zone and Passing Constrained Segments Vertical Class f0 f1 f2 f3 f4 f5 f6 f7 f8 1 0.67576 0 0 0.12060 -0.35919 0 0 0 0 2 0.34524 0.00591 0.02031 0.14911 -0.43784 -0.00296 0.02956 0 0.41622 3 0.17291 0.00917 0.05698 0.27734 -0.61893 -0.00918 0.09184 0 0.41622 4 0.67689 0.00534 -0.13037 0.25699 -0.68465 -0.00709 0.07087 0 0.33950 5 1.13262 0 -0.26367 0.18811 -0.64304 -0.00867 0.08675 0 0.30590 Table 3-9. Coefficients Used in Speed-Flow Slope Model (Equation (3-10)) for Passing Lane Segments Vertical Class f0 f1 f2 f3 f4 f5 f6 f7 f8 1 0.91793 -0.00557 0.36862 0 0 0.00611 0 -0.00419 0 2 0.65105 0 0.34931 0 0 0.00722 0 -0.00391 0 3 0.40117 0 0.68633 0 0 0.02350 0 -0.02088 0 4 1.13282 -0.00798 0.35425 0 0 0.01521 0 -0.00987 0 5 1.12077 -0.00550 0.25431 0 0 0.01269 0 -0.01053 0 Horizontal Curves For horizontal curves, the ‘p’ coefficient is set to a constant value of 0.5. For the estimation of the horizontal curve subsegment speed, it is constrained to not exceed the preceding tangent average speed.

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 73 3.4. Models for Estimation of Percent Followers The model development process for the estimation of percent followers largely followed that for the average speed models. The general functional form that was found to provide a good fit to both the field and simulation data is as follows. = 100 × 1 − × (3-11) where PF = percent followers in the analysis direction, vd = the analysis direction flow rate (1000’s of veh/h), m = slope coefficent, and p = power coefficient. The ‘m’ and ‘p’ coefficients are calculated according to the following equations. Calculate PF at Capacity Passing Constrained/Passing Zone: = + ( ) + √ + ( ) + √ S + ( %) + ( × ) + (3-12) where PFcap = percent followers at capacity flow rate, b1–b7 = coefficient values, given in Table 3-10, FFS = free-flow speed in the analysis direction (mi/h), HV% = percentage of heavy vehicles. L = segment length (mi), and vo = demand flow rate in opposing direction flow rate in the opposing direction (1000’s of veh/h) (equals 0 for passing lane segment and 1.5 for passing constrained segment). Table 3-10. Coefficient Values for Equation (3-12) Vertical Class b0 b1 b2 b3 b4 b5 b6 b7 1 37.68080 3.05089 –7.90866 –0.94321 13.64266 –0.00050 –0.05500 7.1376 2 58.21104 5.73387 –13.66293 –0.66126 9.08575 –0.00950 –0.03602 7.1462 3 113.20439 10.01778 –18.90000 0.46542 –6.75338 –0.03000 –0.05800 10.0324 4 58.29978 –0.53611 7.35076 –0.27046 4.49850 –0.01100 –0.02968 8.8968 5 3.32968 –0.84377 7.08952 –1.32089 19.98477 –0.01250 –0.02960 9.9945 Passing Lane: = + ( ) + √ + ( ) + √ + ( %) + √ % + ( × %) (3-13)

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 74 where b1–b7 = coefficient values, given in Table 3-11, and Other terms as defined previously. Table 3-11. Coefficient Values for Equation (3-13) Vertical Class b0 b1 b2 b3 b4 b5 b6 b7 1 61.73075 6.73922 –23.68853 –0.84126 11.44533 –1.05124 1.50390 0.00491 2 12.30096 9.57465 –30.79427 –1.79448 25.76436 –0.66350 1.26039 –0.00323 3 206.07369 –4.29885 0 1.96483 –30.32556 –0.75812 1.06453 –0.00839 4 263.13428 5.38749 –19.04859 2.73018 –42.76919 –1.31277 –0.32242 0.01412 5 126.95629 5.95754 –19.22229 0.43238 –7.35636 –1.03017 –2.66026 0.01389 Calculate PF at 25% of Capacity Passing Constrained/Passing Zone: = + ( ) + √ + ( ) + √ + ( %) + ( × ) + (3-14) where PF25cap = percent followers at 25% of capacity flow rate, c0–c7 = coefficient values, given in Table 3-12, and Other terms as defined previously. Table 3-12. Coefficient Values for Equation (3-14) Vertical Class c0 c1 c2 c3 c4 c5 c6 c7 1 18.01780 10.00000 –21.60000 –0.97853 12.05214 –0.00750 –0.06700 11.6041 2 47.83887 12.80000 –28.20000 –0.61758 5.80000 –0.04550 –0.03344 11.3557 3 125.40000 19.50000 –34.90000 0.90672 –16.10000 –0.11000 –0.06200 14.7114 4 103.13534 14.68459 –23.72704 0.664436 –11.95763 –0.10000 0.00172 14.7007 5 89.00000 19.02642 –34.54240 0.29792 –6.62528 –0.16000 0.00480 17.5661 Passing Lane: = + ( ) + √ + ( ) + √ + ( %) + √ % +( × %) (3-15) where c0–c7 = coefficient values, given in Table 3-13, and Other terms as defined previously.

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 75 Table 3-13. Coefficient Values for Equation (3-15) Vertical Class c0 c1 c2 c3 c4 c5 c6 c7 1 80.37105 14.44997 –46.41831 –0.23367 0.84914 –0.56747 0.89427 0.00119 2 18.37886 14.71856 –47.78892 –1.43373 18.32040 –0.13226 0.77217 –0.00778 3 239.98930 15.90683 –46.87525 2.73582 –42.88130 –0.53746 0.76271 –0.00428 4 223.68435 10.26908 –35.60830 2.31877 –38.30034 –0.60275 –0.67758 0.00117 5 137.37633 11.00106 –38.89043 0.78501 –14.88672 –0.72576 –2.49546 0.00872 Calculate the Slope Coefficient = . + (3-16) where d1–d2 = coefficient values, given in Table 3-14, and Other terms as defined previously. Table 3-14. Coefficient Values for Equation (3-16) Segment Type d1 d2 Passing Zone and Constrained -0.29764 -0.71917 Passing Lane -0.15808 -0.83732 Calculate the Power Coefficient = + . + + . + (3-17) where e0–e4 = coefficient values, given in Table 3-15, and Other terms as defined previously. Table 3-15. Coefficient Values for Equation (3-17) Segment Type e0 e1 e2 e3 e4 Passing Zone and Constrained 0.81165 0.37920 -0.49524 -2.11289 2.41146 Passing Lane -1.63246 1.64960 -4.45823 -4.89119 10.33057 Calculate Percent Followers for the Segment = 100 × 1 − × (3-18) where all terms are as previously defined. It should be noted that horizontal curvature is not considered for follower percentage, as it has a much less significant impact on follower percentage than on travel speed.

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 76 3.5. Passing Lanes Passing is an important operational phenomenon on two-lane, two-way, highways. On these highways, platoons will form as a result of infrequent passing opportunities. The speeds of vehicles in platoons are restricted by the speed of slow-moving platoon leaders. As the amount of platooning increases, the level of service on these highways deteriorates. Providing a passing lane on a two-lane highway can improve the operational performance and level of service, as it helps in providing passing opportunities and breaking up vehicular platoons. Passing lanes on steep upgrades are also referred to as climbing lanes, which are also discussed in this section. 3.5.1. Effective Length of Passing Lanes The operational improvement of a passing lane typically extends for some distance downstream of the passing lane, and is referred to as the “Effective Length”. Specifically, effective length is the distance from the start of passing lane to a point downstream where the performance returns to its original value; that is, the performance immediately upstream of the start of the passing lane. Figure 3-1 shows the follower density as it changes along a 1.5-mile passing lane. The general trend exhibited in this figure is that follower density decreases significantly just downstream of the start of the passing lane before it starts to increase again as traffic progresses along farther downstream of the start of the passing lane. The latter increase in FD is most significant beyond just a mile from the end of the passing lane) and then FD increases slightly the farther traffic moves away from the passing lane until it eventually becomes more or less constant. The point at which follower density becomes essentially constant designates the end of passing lane effective length. Figure 3-1. Follower density along the highway (%NP = 50) The following equation can be used to approximate the effective length for a passing lane length of 1.5 miles. EffectiveLength = 25.7 – 0.04 × FlowRate + 0.000027 × FlowRate2 – 0.031 × %NP (3-19) 0 1 2 3 4 5 6 7 8 9 10 0 5 10 15 20 25 30 Fo llo w er D en si ty (fo llo w er s/ m i) Distance from Upstream Station (mi) Flow Level 200 veh/hr Flow Level 300 veh/hr Flow Level 400 veh/hr Flow Level 500 veh/hr Flow Level 600 veh/hr Flow Level 700 veh/hr Flow Level 800 veh/hr

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 77 Where the effective length of passing lane is measured in miles, flow rate is measured in veh/h in the direction of analysis, and %NP represents the percent-no passing on the two-lane highway for several miles upstream of the passing lane segment in the direction of analysis. 3.5.2. Optimum Length of Passing Lanes The guidelines on optimum length of passing lane provided in this section were derived from an approach that considered the rate of change in performance for different lengths of passing lane. It is hypothesized that the rate of performance improvement would be highest as passing lane length increases from some minimum value (0.5 mile in this investigation), and as the length increases further, this rate would decrease until it diminishes or reaches some constant value. To verify the hypothesis, the percent change in PF at passing lane lengths between 0.5 mi and 3 mi using 0.1-mi increments up to 2.0 mi length and 0.25-mi increment thereafter was calculated using simulation. Only passing lanes on level terrain are considered here. The results are shown in Figure 3-2. The general pattern exhibited in this figure is that increasing passing lane length beyond the 0.5 mile results in performance improvement that would decrease steadily with the increase in passing lane length. The reduction in PF is greater at shorter passing lane lengths resulting in an upward convex curvilinear shape (decreasing slope) which gradually becomes linear (constant slope) with the increase in passing lane length. This general pattern is common to all traffic levels. The length at which this change in shape takes place is largely a function of traffic level; that is, this length is soon reached at low traffic levels, while it happens at longer lengths for higher traffic levels. Table 3-16 shows the optimum passing lane lengths derived using the proposed approach for different traffic levels, which fall in the range of 0.9 to 2.0 miles. As shown in this table, the passing lane lengths derived using the proposed approach correspond closely to the lengths provided by 22.5% and 25% reductions in PF.

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 78 Figure 3-2. Percent reduction in PF vs length of passing lane. Table 3-16. Optimum Length of Passing Lane (Proposed Approach) Traffic Flow (veh/h) 200 300 400 500 600 700 800 Length of Passing Lane (mi) 0.9 1.0 1.2 1.2 1.6 1.9 2.0 3.5.3. Climbing Lanes Climbing lane sections are similar to passing lane sections in that they consist of an added lane so that faster vehicles can pass slower vehicles without using the oncoming lane. They both also serve to break up platoons. However, the considerations for when to implement a climbing lane are distinctly different from the considerations for adding a passing lane. As the name implies, climbing lanes are implemented on upgrade sections of roadway. They are intended to allow large trucks to move out of the way of faster vehicles on the upgrade, as the speed differential between passenger vehicles and large trucks can be large when the grade exceeds 3%. AASHTO [2011], in A Policy on Geometric Design of Highways and Streets, provides the following criteria for when a climbing lane should be considered: • Upgrade traffic flow rate in excess of 200 veh/h.

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 79 • Upgrade truck flow rate in excess of 20 veh/h. • One of the following conditions exists: o A 10 mi/h or greater speed reduction is expected for a typical heavy truck. o Level of service E or F exists on the grade. o A reduction of two or more levels of service is experienced when moving from the approach segment to the grade. Refer to the truck speed-distance curves in Figure 3-3, Figure 3-4, and Figure 3-5, to determine speed reduction on the grade. Alternatively, Equation 3-20 can be used as an approximation. The double semi-trailer trucks were excluded, since field data showed this heavy vehicle type was not prevalent on two-lane highways. As indicated by AASHTO [2011], a climbing lane should be extended beyond the crest of the curve for a distance that allows a truck to accelerate to a speed that is within 10 mi/h of the passenger vehicle speed, and at an absolute speed of at least 40 mi/h. More detail about the geometric design aspects of climbing lane implementation can be found in AASHTO [2011]. The readers need to refer to the most recent edition of the AASHTO policy for climbing lane design guidelines. Figure 3-3. Upgrade speed versus distance curves for a single-unit truck 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000 Ve hi cl e Sp ee d (m i/h ) Distance Traveled Along Segment (ft) 1% 2% 3% 4% 5% 6% 7% 8% 9% 10%

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 80 Figure 3-4. Upgrade speed versus distance curves for an intermediate semi-trailer truck Figure 3-5. Upgrade speed versus distance curves for an interstate semi-trailer truck 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 Ve hi cl e Sp ee d (m i/h ) Distance Traveled Along Segment (ft) 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 Ve hi cl e Sp ee d (m i/h ) Distance Traveled Along Segment (ft) 1% 2% 3% 4% 5% 6% 7% 8% 9% 10%

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 81 = 75 + × + × + × (3-20) where V = speed of heavy vehicle at the end of the upgrade segment (mi/h) L = length of the upgrade segment (mi) a, b, c = model coefficients (decimal), obtained from the following tables. Table 3-17. Upgrade Speed Model Coefficients for a Single-Unit Truck. Grade Slope (%) Model Coefficient a Model Coefficient b Model Coefficient c 1 −7.99117 3.34943 −0.80873 2 −16.79550 1.90540 1.36780 3 −32.09620 21.98800 −5.51770 4 −39.03610 21.53390 −5.45420 5 −52.54130 37.09590 −17.43770 6 −61.54480 38.29370 −22.79690 7 −80.51610 54.45520 −12.78160 8 −88.40130 47.70330 −5.71440 9 −97.19730 41.85210 0.00000 10 −93.95550 −33.73320 93.20230 Table 3-18. Upgrade Speed Model Coefficients for an Intermediate Semi-Trailer Truck. Grade Slope (%) Model Coefficient a Model Coefficient b Model Coefficient c 1 0.00000 0.00000 0.00000 2 −9.11990 6.63672 −2.51232 3 −17.52110 5.44550 0.00000 4 −29.10240 11.41810 0.00000 5 −42.79200 24.99010 −4.85490 6 −52.06060 26.76310 −3.74860 7 −63.70110 30.18420 0.00000 8 −77.24510 40.32630 0.00000 9 −89.75260 48.34020 0.00000 10 −90.21160 1.41830 56.44760

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 82 Table 3-19. Upgrade Speed Model Coefficients for an Interstate Semi-Trailer Truck. Grade Slope (%) Model Coefficient a Model Coefficient b Model Coefficient c 1 −7.92121 4.78662 −1.63570 2 −16.71740 3.63040 0.37130 3 −29.79650 11.81370 −1.39070 4 −39.51320 13.24520 −0.52500 5 −49.57050 11.49140 4.32190 6 −60.94040 12.96240 7.63790 7 −66.62850 −9.65440 32.62600 8 −75.89060 −24.93370 57.74360 9 −82.36480 −55.27030 101.05490 10 −85.01500 −114.73900 188.34900 3.5.4. “2+1” Configuration The 2+1 configuration is a continuous three-lane cross section, with the middle lane being a passing lane that alternates direction. An example illustration of this configuration is shown in Figure 3-6. Modern designs also include a transition area between the reversing of the passing lane direction. An illustration of example transition area is shown in Figure 3-7. This design has become quite popular in Europe. While there are some similarities in this design to the typical three-lane cross section with a passing lane in the U.S., there are some significant differences. The 2+1 design typically extends for many miles, with several changes of direction for the passing lane accommodated within this distance. Additionally, passing vehicles always use the center lane. This design is intended to be an intermediate option between a two-lane highway with or without occasional passing lanes and a four-lane highway. The 2+1 configuration is currently quite rare in the U.S., but there are a handful of installations, mostly in the southwest. In the U.S., these highway sections are more commonly referred to as “Super 2” sections. However, it should be noted that in some instances the “Super 2” label is also applied to two-lane highways with frequent passing lanes, not necessarily continuously alternative passing lanes. Some guidelines on the geometric design of 2+1 sections can be found in AASHTO [2011].

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 83 Figure 3-6. Schematic of example 2+1 configuration (passing vehicles use center lane) Figure 3-7. Schematic of typical transition area design for European 2+1 configurations

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 84 The following models were obtained to estimate the change in performance between a 2+1 configuration and a comparable two-lane highway with no passing lanes, approximately 50% passing zones, and 16-18 miles in length. ( ) ( ) % ,2 1 147.5 15.8 LN 0.05 0.11 % 3.1 LN 0.3, Followers%Improve FlowRate FFS HV PassLaneLength + = − × + × + × − × (3-21) ( ) ( ) ( ) ( ) ,2 1 0, Max 21.8 1.86 LN 0.1 Max 0,Min ,70 30 0.05 Max 0,30 % 1.1 LN Max 0.3, AvgSpeed%Improve FlowRate FFS HV PassLaneLength +       = − × − × −     − × − + ×    (3-22) % ,2 1 ,2 1 ,2 1 % 1 100 100 1 100 Followers adj AvgSpeed %ImproveFollowersFollowerDensity FlowRate %Improve S + + +   = × −    ×   × +    (3-23) where %Improve%Followers,2+1 = % improvement to percent followers, %ImproveAvgSpeed,2+1 = % improvement to the average speed, FollowerDensityadj,2+1 = adjusted follower density, FlowRate = flow rate entering the 2+1 configuration (veh/h), FFS = free-flow speed (mi/h), %HV = percent heavy vehicles (%), PassLaneLength = Passing lane length (mi), %Followers = percent followers entering the 2+1 configuration (i.e., percent followers estimated at the end of the segment just upstream of the first passing lane), and S = average speed in the analysis direction (mi/h).

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 85 3.6. Level of Service The service measures, and corresponding level of service (LOS) threshold values for the HCM 2010 two-lane highway analysis methodology are shown in Table 3-20. Table 3-20. HCM 2010 Analysis Methodology LOS Threshold Values LOS Class I Class II Class III Percent time spent following (PTSF) Average travel speed (ATS) mi/h Percent time spent following (PTSF) Percent free-flow speed (PFFS) A ≤ 35 > 55 ≤ 40 > 91.7 B ≤ 50 > 50 ≤ 55 > 83.3−91.7 C ≤ 65 > 45 ≤ 70 > 75.0−83.3 D ≤ 80 > 40 ≤ 85 > 66.7−75.0 E > 80 ≤ 40 > 85 ≤ 66.7 Note: LOS F applies whenever the flow rate exceeds the segment capacity. Source, Highway Capacity Manual, 6th Edition, Copyright, National Academy of Sciences, Washington, D.C. 2016. Exhibit 15-3, p. 15-8. The service measure proposed for the new methodology is follower density. As with any service measure, appropriate LOS threshold values must be defined. The challenge, of course, is determining what is “appropriate”. Generally, it is preferable to set the threshold values such that the resulting levels of service are not consistently significantly different from those produced by the previous methodology. However, with a new analysis methodology and new service measure, it may be very difficult to avoid different LOS values relative to the previous methodology for certain combinations of input conditions. Nonetheless, it is desirable to be sensitive to this issue when defining the threshold values. Wholesale changes in LOS results between the two methodologies, especially if the LOS results from the new methodology are consistently worse, can be problematic for transportation agencies. A large number of highway facilities that previously were shown to be operating at acceptable levels of service now showing unacceptable levels of service, for the same input conditions, can cause unintended consequences for transportation agency project programming priorities. With this issue in mind, follower density LOS threshold values were identified that would generally, but not necessarily always, yield the same LOS as from the HCM 2010 methodology (Table 3-20). This was accomplished through the following process: • Develop an experimental design for applicable input values. Variables considered were directional and opposing flow rates, % heavy vehicles, terrain, passing conditions, and so on. • Segment length is a factor for the new methodology, but only for passing lane segments in the previous methodology • % no-passing zones values were set to either 0 or 100, as the new methodology does not use that input—passing zones are treated as a separate segment type

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 86 • Run the experimental design with the batch processing utility in HCM-CALC (Figure 3-8) for the HCM 2010 methodology. • The batch processing utility created an output file that contained a row with each combination of input values and the corresponding results (service measure and LOS values). For the HCM 2010 methodology, separate experimental designs were run for each of the three highway classifications. Additionally, separate experimental designs were run for each target LOS. • The resulting output file with hundreds of output values were filtered to identify the input scenarios (each scenario is a unique combination of inputs) that yielded service measure values within close range of the threshold value (e.g., 34-36% for Class I PTSF LOS A). Typically, anywhere from several dozen to a couple hundred input scenarios yielded service measure results within the specified range. • The input scenarios identified from the previous step were run through the new analysis methodology. This resulted in a range of follower density values, for which the minimum, maximum, and average were identified. • For a rough comparison, follower density values were also identified for the HCM 2010 results at each LOS threshold level, using PTSF as a surrogate for percent follower (i.e., follower density = (PTSF/100)×(directional flow/average speed)). Figure 3-8. Batch Processing Utility for HCM-CALC A summary of the experimental design results are shown in Table 3-21 and Table 3-22. Not surprisingly, the range of follower density values for each LOS value was not very narrow. Thus, a significant amount of judgement was needed to arrive at appropriate values. Additionally, it was decided to create two sets of threshold values—one for higher speed highways (≥ 50 mi/h) and one for lower speed highways (< 50 mi/h). The issue with lower-speed highways is that there is not a proportional decrease in percent followers with the decrease in speed. Thus, it is necessary to have higher LOS thresholds for lower-speed highways to offset the disproportionate increase in

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 87 follower density due to the lower speed. The LOS threshold values derived from this process are shown in Table 3-23. Table 3-21. HCM 2010 Methodology Experimental Design Results Table 3-22. NCHRP 17-65 Methodology Experimental Design Results Table 3-23. Follower Density Thresholds LOS Follower Density (followers/mi/ln) High-Speed Highways Low-Speed Highways Posted Speed Limit ≥ 50 mi/h Posted Speed Limit < 50 mi/h A ≤ 2.0 ≤ 2.5 B > 2.0 – 4.0 > 2.5– 5.0 C > 4.0 – 8.0 > 5.0– 10.0 D > 8.0 – 12.0 > 10.0 – 15.0 E > 12.0 > 15.0 Follower density, for use with Table 3-23 is calculated as follows.

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 88 = × (3-24) where FD = follower density in the analysis direction (followers/mi), PF = percent follower in the analysis direction, vd = flow rate in the analysis direction (veh/h), and S = average speed in the analysis direction (mi/h). While this methodology provides estimation equations for all of the key performance measures, it is also possible to assess level of service through direct field measurement of speed, flow rate, and percent followers at a specific point. In that case, the analyst can just use Equation (3-24) with the directly-measured values and then use the calculated FD value to obtain LOS from Table 3-23. 3.7. Facility Level Analysis Framework Individual segments can be analyzed with this methodology. Additionally, multiple contiguous two-lane highway segments (in the same direction) may be combined to analyze a longer section (with varying characteristics) as a facility. The operational performance of a segment, either individually or within a facility, is reported for the end of the segment, as opposed to corresponding to an aggregated value across the full length of the segment. Thus, these are point estimates of performance, and not necessarily representative of the average conditions across an extended length of segment. This was done to make it easier for practitioners to use point measurements for direct use with method and/or validation of method outputs. However, when considering multiple contiguous segments, the point measures of performance will be used an estimate of segment performance for calculating facility performance. From a traveler’s perspective, the conditions at the end of the segment (particularly passing zones and passing lanes) probably factor more heavily into their assessment of the quality of service. While guidance on segment types (passing constrained, passing zone, passing lane) was provided earlier, some discussion about the role of intersections is warranted. An intersection (with control on the cross street only) that has a significant amount of traffic entering and/or exiting the main highway is a logical location to end one segment and start another. Of course, this is almost always going to apply to a stretch of ‘passing constrained’ two-lane highway. This methodology does not explicitly consider the effect of control on the main two-lane highway. However, the analyst is referred to studies by Yu and Washburn (2009) and Li and Washburn (2014) that can be used to supplement the methodology described here consider the effects of intersection within an extended length of two-lane highway. The methodology for intersections can be extended as additional future research is done in this area. To assess level of service across multiple contiguous segments (i.e., a facility), a weighted follower density value can be calculated, per Equation (3-25). = ∑ ×∑ (3-25)

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 89 where FDF = average follower density for the facility in the analysis direction (followers/mi), FDi = follower density for segment i in the analysis direction (followers/mi), and Li = segment length density for segment i (miles) This value can be used with Table 3-23 to arrive at the facility LOS. Passing Lane Segments This methodology does not explicitly adjust performance measure results for segments downstream of non-passing lane segments based on the range of speed and platooning conditions of the traffic stream that enter a given segment, for a given flow rate, heavy vehicle percentage, and free-flow speed. As mentioned previously, performance measure results for a segment are estimated at the end of the segment. Those results are not very sensitive to the specific flow profile entering the segment for a given set of input conditions, except in the cases of very short segments or a very significant change in the vertical geometry from one segment to the next. For passing- constrained or passing-zone segments, it is not recommended that segment lengths less than 0.25 miles be used for vertical grade classes 1-3 or 0.5 miles for vertical grade classes 4-5. For passing lane segments, it is not recommended that segment lengths less than 0.5 miles be used for all vertical grade classes. For segments downstream of a passing-lane segment, improvements to performance measures can persist well downstream of the end of the passing lane segment, particularly for percent followers, and consequently follower density. Improvements to average speed also result; however, those improvements are relatively minor and persist for a much shorter distance downstream. Additional discussion on this issue is contained in Section 3.5.1 and Appendix F. For a facility analysis, to account for the downstream improvements to performance measures for an upstream passing lane segment, the following equations are applied to estimate the percentage improvement to the performance measures, at a given distance downstream of the passing lane. ( )( ) ( ) ( ) % 0, 27 8.75 LN Max 0.1, Max 0.1 Max 0,% 30 3.5 LN 0.3, 0.01 Followers DistanceDownstream %Improve Followers PassLaneLength FlowRate     − ×  =  + × −   + × − ×  Eq. 26 ( ) 0, 3 0.8 Max 0.1 Max 0,% 30 0.75 0.005 AvgSpeed DistanceDownstream %Improve Followers PassLaneLength FlowRate    − × =  + × −   + × − ×  Eq. 27

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 90 %% 1 100 100 1 100 Followers adj AvgSpeed %ImproveFollowersFollowerDensity FlowRate %Improve S  = × −    ×   × +    Eq. 28 where %Improve%Followers = % improvement to the % followers on a segment downstream of a passing lane segment, %ImproveAvgSpeed = % improvement to the average speed on a segment downstream of a passing lane segment, FollowerDensityadj = adjusted follower density on a segment downstream of a passing lane segment (followers/mi), DownstreamDistance = distance downstream from the start of the passing lane segment (mi), %Followers = For the effective length calculation and downstream segment %Improve%Followers and %ImproveAvgSpeed calculations: % followers entering the passing lane segment (i.e., % followers estimated at the end of the segment just upstream of the passing lane segment, For the calculation of adjusted follower density downstream of the passing lane:% followers for the analysis segment, PassLaneLength = length of passing lane segment (mi), FlowRate = For the effective length calculation:flow rate entering the passing lane segment (veh/h), For the downstream segment %Improve%Followers, %ImproveAvgSpeed, and adjusted follower density calculations: flow rate for the analysis segment (veh/h), and S = average speed in the analysis direction for the analysis segment (mi/h). These improvements are applied across all segments downstream of the passing lane segment that are within the effective length of the passing lane (see Section 3.5.1 or Appendix F).