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

Below is the uncorrected machine-read text of this chapter, intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text of each book. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 11 2. Research Approach This chapter provides an overview of the following topics: • Review of alternative analysis methodologies • Field data analysis • Service measure evaluation • Simulation tools • Approach for accounting for large truck impacts • Approach for determining follower status 2.1. Review of Alternative Analysis Methodologies In this section, a review of alternative methodologies for the analysis of two-lane highways is presented. As the U.S. HCM is the most extensive reference document for conducting capacity analyses using the latest research in the field, it has found widespread use in many other countries all over the world. However, the significant limitations of the current HCM analysis methodologies for two-lane highways (discussed in detail in Task 1 of this project) were the main impetus for researchers in the U.S. and abroad to search for alternative analysis methods or to modify the current HCM analysis procedures to better fit local conditions. In general, the search for alternative two-lane highway analysis methodologies in this project confirmed the limited amount of research that has been done in this area, which explains the few applications in practice that substantially deviate from the current HCM methodologies. Many of the alternative methods encountered in the literature are concerned with translating field measurements into computed performance measures that could be used in assessing performance and/or establishing LOS, but not necessarily in predicting the effects of demand, grades, passing lanes, truck climbing lanes, or other variables on the performance of two-lane highways. In reporting alternative methodologies, this review includes examples of new methodologies, modified HCM-based methodologies (including calibrated HCM models), and proposed methods in the literature that may not have moved yet into practice. 2.1.1. Alternative Analysis Methodologies in Practice In this section, a summary of two-lane highway methodologies and procedures that have been used in practice in other countries outside the U.S. is presented. South Africa The most extensive method, which reflects a major deviation from the U.S. HCM procedures, is the two-lane highway analysis methodology that was developed by the South African National Roads Agency around ten years ago (Van As, 2003; Van As and Niekerk, 2004). The lack of adequate methodologies used in other countries that suit local conditions in South Africa caused the agency to look for other alternative methods and, ultimately develop a new analytical method. In regards to the U.S. HCM (TRB, 2000), limitations that were identified by the researchers involved in developing the new South African methodology included the inability to apply the

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 12 HCM method to more complex situations such as the interaction of climbing and passing lanes and the use of wide shoulders for overtaking purposes, which is a common practice in South Africa. Other important reported limitations involved the significant overestimation of PTSF (which could exceed 100%), the difficulty of measuring PTSF in the field, and the insensitivity of performance measures to traffic level, which is important for assessing the roadway improvement needs on two- lane highways. In the development process, the researchers used field data collected from 25 two-lane highway facilities and microscopic traffic simulation to: 1) examine alternative performance measures on two-lane highways and select the most appropriate, 2) develop analytical models for performance measures that are calibrated for local conditions, and 3) develop quality of service scheme and threshold criteria for LOS. In selecting the most appropriate performance measure, the researchers investigated several alternative measures including percent followers, follower flow, follower density, average travel speed, percent speed reduction due to traffic, traffic density and total queuing delay. Upon careful assessment and evaluation, follower density, defined as the number of followers per kilometer per lane, was eventually selected as the most appropriate performance measure that best satisfied selection criteria. Specifically, experience with the above measure of effectiveness indicates that it provides a relatively good indication of when capacity upgrading is warranted. It will only indicate a need for such upgrading when both a poor level of service is experienced and traffic volumes are high (Van As and Niekerk, 2006). Further, this measure combines three other measures in one, namely: percentage followers, traffic flow and travel speed (Van As, 2003). Follower density is estimated as the product of percent followers and density using the following Equation (2-1): = (2-1) where KF = Follower density (followers/km/ln) PF = Percent followers Q = Traffic flow rate in direction of flow (veh/h) N = Number of lanes in direction of travel U = Average speed (km/h) Percent followers represent the percentage of vehicles traveling in the same lane with headways less than a pre-specified threshold value. If the headway is smaller than the pre-specified value, the vehicle is considered to be in a following mode. Using empirical data from various two-lane sites in South Africa, the researchers found 3.5 seconds to be the most appropriate value for headway threshold. It is important to mention that the PTSF estimation method in the HCM assumes a headway threshold of 3 seconds (TRB, 2000, 2010). According to the procedure developed in South Africa, a vehicular platoon would consist of one or more vehicles traveling on the same lane. A single vehicle is a platoon with length of one vehicle. The speed of vehicles in a platoon is approximately the same as that of the leading vehicle. The relationship between percent follower and length of platoon is shown in Equation (2-2).

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 13 = ( ) (2-2) Where PF is the percent followers and N is the average length of platoon (in number of vehicles). The research team also established an LOS scheme for levels A to D using the new measure of effectiveness, i.e., follower density, as shown in Table 2-1. Table 2-1. Follower density ranges for measuring LOS LOS “Typical” Follower Density (followers/km/lane) Range of Follower Densities (followers/km/lane) A 1 0.3-1.4 B 2 1.3-3.3 C 4 3.0-6.7 D 8 6.3-9.5 Source: Van As, 2003 For road improvement and upgrade projects, it was determined that LOS D is the worst operating condition beyond which the two-lane highway should be considered for improvement. Table 2-2 shows the minimum acceptable level of service using the new methodology for class I and class II two-lane highways, which are defined in the HCM 2000 (TRB, 2000). It is a customary practice in South Africa to base rural highway design on the 30th highest hour volume of the year and to base the design of urban highways on the peak hour of a normal day of the week. Table 2-2. Acceptable LOS on two-lane highways Two-Lane Highway Type Acceptable Level of Service Normal Day Peak Hour 30th Highest Hour Class I C D Class II D D Germany In Germany, efficiency is given preference over user experience in LOS analysis. Therefore, PTSF, which is a measure of driver inconvenience, has not been used as a measure of effectiveness (MOE) for two-lane highways (Brilon and Weiser, 2006). Instead, the current German highway capacity handbook (HBS, 2001) utilizes density as the primary service measure for two-lane highways. Density is calculated as the ratio of traffic volume and the ATS of passenger cars. The density threshold values that are used to establish service levels are shown in Table 2-3.

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 14 Table 2-3. Density thresholds for measuring level of service LOS Density (veh/km) A 5 B 12 C 20 D 30 E 40 F > 40 Further, the same study reported that, in the past, the ATS of passenger cars, over a longer stretch of the highway (i.e., 5 to 20 km), had been used in Germany as the preferred MOE (Brilon and Weiser, 2006). The speed-flow curves, which were developed using empirical data from two-lane highways in Germany, are concave up in shape, and not linear, as suggested by the U.S. HCM. Further, PCE factors are not used in the current handbook. Instead, different speed-flow curves are provided for different geometries and HV percentages, since PCE factors are sensitive to roadway and traffic conditions, including the HV percentage (Brilon and Weiser, 2006). In the 2015 German capacity handbook, density per lane is used as the service measure, and the analysis is directional, not two-way as in the previous handbook. Denmark The Danish capacity manual (Vejdirektoratet, 2010) defines ATS and volume-to-capacity (v/c) ratio as the service measures for two-lane highways. The v/c ratio is seen as a measure of pressure, representing the impact of other vehicles on the driver. Average travel speed, on the other hand, focuses on travel time and speed which many drivers see as measures of the fluency of traffic flow. The ATS and v/c ratio are, however, used only as quality measures, with no threshold values for service levels since the LOS concept is not in use in Denmark. Finland The two-lane highway analysis methodology in the HCM 2000 (TRB, 2000) has been adapted (calibrated) to meet Finnish conditions (Luttinen, 2001). A directional analysis method is retained in the Finnish methodology, but platoon percentage (with a 3-second follower headway threshold value) replaces PTSF because the latter is difficult to measure in the field. Also, ATS is measured for passenger cars only, since the differential speed limit of heavy vehicles on Finnish roads resulted in too low LOS under low volumes when the percentage of heavy vehicles was high. The PCE concept in the HCM 2000 (TRB, 2000) is not retained as it was deemed too simplistic, but it was retained in a modified form. Also, since the LOS analysis has no official status and simply provides additional information, decisions on transport projects are based on economic assessment, rather than LOS. Consequently, travel time savings have a central role in the analysis. Sweden In Sweden, transportation investment decisions are based on the economic assessment of alternatives. Since travel time savings have a central role in this assessment, the most important quality measure is ATS. PCEs are not used, but correction factors are used to account for the

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 15 presence of heavy vehicles. The v/c ratio is used as an additional service quality measure. The LOS concept is also not used (Trafikverket, 2014). Britain In Britain, the design-standard approach is used in road design (O'Flaherty, 1997). Different road designs have different design flows, which are expressed in vehicles. The concept of PCE is not used because PCE values vary under different road and traffic conditions. Design alternatives are prioritized and selected based on economic capacity (lowest traffic volume needed for the project to be economically feasible) and environmental capacity (highest volume allowed to maintain environmental standards). The final decision is based on economic (cost-benefit analysis) and environmental appraisal. The LOS concept is not used. China The v/c ratio is used as the primary service measure for Chinese two-lane highways (Rong et al., 2011). A survey indicated that drivers could perceive significant differences in traffic flow at four different levels of service. Based on these surveys and studies on overtaking ratio and acceleration noise, v/c thresholds have been set for levels of service A, B, C, and D. Japan In Japan, highway planning and design is based on a preset v/c ratio for the "planning level" of the highway section (Nakamura & Oguchi, 2006) on the so called two-lane expressways. It is important to note that, given the not-so-ordinary nature of two-lane expressways, its classification may fall somewhere between multilane expressways and ordinary two-lane highways, with full access control and relatively high speed limits of around 70 km/h, but having only one lane per direction of travel. Traffic patterns could be significantly different from either category due mainly to passing restrictions caused by the presence of median barriers (Catbagan and Nakamura, 2006). 2.1.2. Analysis Methods Proposed in Recent Literature This section presents a few alternative analytical methods for two-lane highway analysis that have been reported in the literature, but have not been moved yet into practice. Method Proposed by Polus and Cohen In their proposed methodology, Polus and Cohen (2009) used the M/M/1 queuing to model vehicular platoons on two-lane highways. In their approach, a platoon is considered as a queue system with random arrivals (vehicles joining the back of queue), random departures (vehicles passing platoon leader), and a single processing channel. For this investigation, data were collected from 15 two-lane highway sites in northern Israel. Field data included vehicle speeds, volumes, and headways both inside and outside of platoons. To identify platooned vehicles, the researchers used a 3-second follower headway threshold, which is consistent with the HCM headway threshold for PTSF field estimation. In their research, two proposed traffic parameters were introduced: traffic intensity and freedom of flow. Similar to queuing analysis, traffic intensity in the context of platoon analysis refers to the ratio between the average time spent in the first position when waiting for an appropriate gap and the average inter-arrival times at the back

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 16 of the queue. On the other hand, freedom of flow refers to the ratio between the time of undisturbed driving (between platoons) and the time interval in which the driver is in first position behind a slower moving vehicle while waiting to pass. Freedom of flow can be estimated using Equation (2-3) below. = (2-3) where η = Freedom of flow = Traffic intensity = Average number of headways between platoons The study then used empirical data collected from various two-lane highway sites to estimate the LOS using some conventional and proposed MOEs. Specifically, the study investigated traffic flow, PTSF, average length of platoon, traffic intensity, and freedom of flow, and consequently established LOS threshold values using PTSF, combined flow in the two directions, and freedom of flow as shown in Table 2-4. Table 2-4. Level of service thresholds based on freedom of flow Level of Service PTSF Flow in Two Directions (pc/h) Freedom of Flow A 0-15 0-300 ≥ 16.5 B 15-30 300-700 7.1-16.5 C 30-45 700-1200 4.1-7.1 D 45-60 1200-1800 2.8-4.1 E 60-75 1800-2700 1.8-2.8 F 75-100 ≥ 2700 ≤ 1.8 Methods Proposed by Al-Kaisy and Durbin In their study of Montana two-lane highways, Al-Kaisy and Durbin (2008) proposed two new methods for estimating PTSF using field data. The difficulty in measuring PTSF in the field and the reported discrepancies between the PTSF estimation using HCM models and field data were the motivation behind the proposed new methods. The researchers used the HCM concept of PTSF as the underlying principle of the proposed methodologies. Regression models were developed that could be used for PTSF prediction using flow rate in the direction of travel, flow rate in the opposing direction, percent no-passing zone and percentage of heavy vehicles. However, the models were developed using limited field data from only a few sites in the state of Montana. Probabilistic Method The first method classifies vehicles into slow-moving and faster vehicles regardless of vehicle class, performance, etc. In this method, the term “slow-moving vehicles” is used to refer specifically to those vehicles that are, or potentially, leading platoons in the traffic stream. In other words, those are the vehicles that impede the flow of other faster vehicles in the traffic stream.

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 17 The term “faster vehicles” refers to those vehicles that are impeded by slow-moving vehicles and become part of vehicular platoons upon encountering slower vehicles in the traffic stream. The term “desired speed” is used to refer to vehicle speed that is not influenced by the speed of the vehicle traveling ahead. This method is based on establishing two probabilities that are used in estimating the new measure, percent impeded (PI) as was referred to in later research efforts (Al- Kaisy and Freedman 2011). Those probabilities are: (1) Pp: Probability of a vehicle being part of a vehicular platoon using the time headway definition of a platoon, and (2) Pi: Probability of a vehicle being impeded, and thus forced to travel at a speed less than the desired speed. Using the above two probabilities, the PI can be estimated using Equation (2-4) below: ip PPPI ×= (2-4) Time headway data can be used to estimate Pp using the headway platoon definition, i.e., platoon to consist of successive vehicles on the same travel lane with time headways less than a pre- specified threshold value. To estimate Pi, the proportion of vehicles with desired speeds higher than the average speed of “slow-moving” vehicles should be determined. This can be achieved by: 1) measuring the average speed of “slow-moving” vehicles, and 2) establishing the distribution of desired speeds for all vehicles in the traffic stream. Platoon leaders can be used as a representative sample of slow-moving vehicles, while the distribution of desired speeds can be established using speed measurements of vehicles traveling outside of platoons. Figure 2-1 shows the probability Pi assuming a normal distribution for desired speeds. Figure 2-1. Theoretical speed distribution with probability Pi represented Weighted-Average Method This method is aggregate in nature and utilizes a weighted average speed formula in estimating the percentage of vehicles impeded/affected by the platooning phenomenon. The method is based on the premise that vehicle mix on two-lane highways consists mainly of two groups of vehicles: (1) heavy vehicles (i.e. trucks, buses, and recreational vehicles) with relatively inferior

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 18 performance and lower average speed, and (2) passenger vehicles (autos, SUVs, minivans, and other smaller vehicles) with relatively higher performance and higher average speed. The proposed method utilizes two aggregate speed measures for each group of vehicles; mean actual travel speed and mean desired travel speed. The weighted average speed formula is used to derive the proportion of faster vehicles impeded by slower vehicles based on the following assumptions: i. Heavy vehicles are not impeded by passenger vehicles, but passenger vehicles may be impeded by heavy vehicles. The assumption is largely consistent with the findings of a study by Polus et al. (2000) that investigated 1500 passing maneuvers from six sites on tangent two-lane highways using video recording and aerial photography. ii. Based on the assumption in (i) above, the method assumes that the mean actual travel speed and mean desired travel speed of heavy vehicles are approximately the same. iii. The mean speed of passenger vehicles in platoons that are impeded by slower vehicles is roughly the same as the mean speed of platoon leaders. The proposed method classifies passenger vehicles into two groups, i.e., those that are free to travel at their desired speeds and those that are impeded by slower vehicles. Equation (2-5) was proposed for estimating the percentage of passenger cars that are impeded by slower heavy vehicles. Satot ≈ Sdpv × (Ppv − Ppv2) + Sahv × (Ppv2 + Phv) (2-5) where Satot = Mean actual travel speed of all vehicles (mi/h) Sdpv = Mean desired travel speed of passenger vehicles (mi/h) Ppv = Proportion of passenger vehicles in the traffic mix Ppv2 = Proportion of passenger vehicles impeded by slower vehicles Sahv = Mean actual travel speed of heavy vehicles (mi/h) Phv = Proportion of heavy vehicles in the traffic mix Equation (2-5) involves variables that can readily be measured in the field except for the proportion of passenger vehicles impeded by slower vehicles, which can be used to estimate PI or PTSF on two-lane highways at a point location. Desired speeds of passenger vehicles can be measured in the field using time headway and speed data. For more details on this proposed methodology, please refer to Al-Kaisy & Durbin (2008). Method Proposed by Bessa and Setti Bessa and Setti (2011) studied two-lane highways in Brazil with the objective of adapting the HCM 2000 (TRB, 2000) ATS and PTSF functions to local conditions in Brazil. The researchers collected traffic data, including travel speed, flow rate and traffic mix, from 11 two-lane highway sites. These data were used along with genetic algorithms (GA) to calibrate and validate TWOPAS. This program was then used to generate a synthetic traffic data set for a wide range of conditions. The ATS and PTSF functions were calibrated for two-lane highways in Brazil using the synthetic data set. The calibrated models included those in the HCM 2000 (TRB, 2000) and the 2001 German highway capacity handbook (HBS, 2001). The research confirmed that the speed-flow

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 19 model is concave in shape, which is consistent with the shape of the relationship in the German highway capacity handbook (HBS, 2001). This model had a better fit to field data compared to the linear models provided in the HCM 2000 (TRB, 2000). Moreover, a new form of the PTSF function was developed, which provided better estimations than those from the HCM 2000 (TRB, 2000) PTSF function. The new equations for ATS and PTSF are as follows. = − − (2-6) = 100 1 − exp (− ) (2-7) where ATSd = average travel speed in one direction (km/h) FFSd = free flow speed in one direction (km/h) PTSFd = percent time spent following in one direction (%) qd = traffic flow rate in the direction of analysis (veh/h) q0 = traffic flow rate in the opposite direction of analysis (veh/h) b1, b2, a, b, c, d = calibration parameters Method Proposed by Romana and Perez Romana and Perez (2006) proposed an alternative way of using ATS and PTSF to evaluate LOS on class I highways using field data from two-lane highways in Spain. The researchers used a critical headway of 4 seconds to identify vehicles that are part of vehicular platoons. The study introduced “threshold speed” as “the minimum speed users consider acceptable in traveling on a uniform road section under heavy flows and platooning traffic” (Romana and Perez, 2006). Once established, threshold speed can be used to select the performance measure that best represents the service level under certain operating conditions. The premise behind the proposed approach is that travelers have different expectations on different roads, and in the case of two-lane highways, the desire to pass and the frustration of being delayed are not simply a function of the difference between a driver’s actual and desired speed. In their proposed approach, when ATS is greater than the threshold speed, only PTSF should be used to assess the LOS; otherwise, ATS should be used. The threshold speed should be selected to reflect users’ perception while exercising engineering judgment. In their research, 80 km/h was suggested as the threshold speed. Table 2-5 shows a comparison of the proposed method with reference to the HCM 2000 procedures (TRB, 2000). Table 2-5. Comparison of LOS boundaries in HCM 2000 and the proposed approach LOS HCM 2000 Procedures Proposed Method Class I, ATS (km/h) PTSF (%) Speeds > 80 km/h Speeds < 80 km/h A > 90 PTSF ≤ 35 % DVb ≤ 30 - B 80 < sa ≤ 90 35 < PTSF ≤ 50 30 < % DV ≤ 55 - C 70 < s ≤ 80 50 < PTSF ≤ 65 55 < % DV ≤ 75 - D 60 < s ≤ 70 65 < PTSF ≤ 80 75 < % DV 60 < s ≤ 80 E 50 < s ≤ 60 80 < PTSF - 40 < s ≤ 60 F 40 < s ≤ 50 - - s ≤ 40 a Average travel speed b Percentage of delayed vehicles Source: Romana and Perez, 2006

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 20 Probability-Based Follower Identification Catbagan and Nakamura (2010), building upon previous similar efforts, developed a method that can better estimate whether or not a driver is following or freely moving (Hammontree, 2010). Current procedures identify followers by a chosen headway, but those procedures do not account for driver variability or changes in roadway conditions. Some drivers may feel unrestricted while driving with a headway of three seconds or less, which is what the 2010 HCM uses as a standard for determining follower status, while others may have a headway larger than three seconds and feel like they are following. Also, a certain driver may have a different desired headway based on weather conditions, pavement conditions, the time of day, and other factors that affect drivers’ comfort levels (Catbagan and Nakamura, 2010). Probability-based follower identification takes a stochastic approach that incorporates both speed and headway into determining when a driver is following. This procedure uses a mixed distribution model of headways, known as the Semi-Poisson Model in order to separate following and free vehicles based only on the headway portion of this method. As headways increase, the probability that a vehicle is following decreases until a critical headway is reached, at which point no vehicles should be considered as followers. Equation (2-8) shows the proportion of vehicles that are following and free. )()1()()( thtgtf ⋅−+⋅= φφ (2-8) where f(t) = total observed headway distribution φ = proportion of constrained vehicles g(t) = constrained headway distribution function h(t) = unconstrained headway distribution function Equation (2-9) can be manipulated to give the probability that a vehicle is following, as follows. )( )()( tf tgFollP headway ⋅= φ (2-9) where P (Follheadway) = probability that a vehicle is following given its headway The speed-based portion of this method is hindered by the difficulty in collecting data on the ever- changing desired speeds of different drivers. This procedure assigns different desired speeds to certain conditions, and if a vehicle’s speed drops below the assumed desired speed, then it is considered to be in the following state. The unified speed distribution method was used to approximate the desired speeds. Equation (2-10) gives the probability that a vehicle is following based only on desired speeds.  ∞ = iv di dvvfvFollP )()|( (2-10)

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 21 where vi = travel speed of vehicle i (km/h) P(Foll | vi) = probability that vehicle i traveling at speed vi is following fd(v) = desired speed distribution function Equation (2-11) combines the headway and desired speed models into one formula for finding the probability that a vehicle is following. )()(),|( vStvtFollP iii ⋅= θ (2-11) where i = driving condition Pi(Foll | t,v) = probability that a vehicle is following at condition i θi(t) = following probability at condition i based on headway Si(v) = following probability at condition i based on speed This study was conducted in Japan, the results of which may not necessarily transfer directly to conditions in the U.S. or other countries, particularly since Japan does not allow passing on any two-lane highways. 2.2. Field Data Analysis Summary Two-lane highway field data were an important aspect of the research approach. Field data were used to: • identify performance measure relationships (e.g., speed vs. flow), • calibrate and validate traffic simulation models, • validate heavy vehicle effects on specific grades (however, sites with a significant grade were very limited), and • verify passing lane behavior As the budget for field data collection in this project was limited, the research team sought the assistance of transportation agencies for providing field data. Individuals with the departments of transportation of Oregon, North Carolina, Idaho, Montana, and California assisted the research team with collecting and providing field data. The field data were collected with ATR-type detectors. The provided data was vehicle event- level data and each vehicle record generally consisted of following data items: • Direction/lane of travel • Time of detector passage • Headway • Spacing • Speed • Vehicle classification This chapter provides a brief summary of the key findings from the field data analysis. More detail on the field data collection and analysis can be found in Appendix H of this report.

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 22 2.2.1. Key Traffic Flow Parameter Values/Relationships Base/Free-Flow Speed Despite obtaining data from more than a dozen field sites, the geometric variability and posted speed limits across these sites was quite limited. Nearly all sites were level, or mostly level, terrain, with little to no horizontal curvature. Only the sites in Oregon exhibited some vertical and horizontal curvature. These were also the only sites with passing lanes. The posted speed limit for all but just a few sites was 55 mi/h. Thus, the variability in the data was insufficient to develop any guidelines for adjusting free- flow speed as a function of geometry. Therefore, we recommend leaving the current guidelines for the effect of lane width and shoulder width (as well as access density) on free-flow speed per the current HCM. Although there was little variability in the posted speed limit (PSL) for our field sites, the analysis of the data showed that free-flow speeds were, on average, 14% higher than the posted speed limit. Since posted limit is certainly considered by drivers in selecting a desired speed, we recommend that base free-flow speed can be estimated as the PSL + 14%. Speed versus Flow Rate Very few sites had hourly flow rates in excess of 400 veh/h; thus, it was not possible to obtain a “full” (i.e., up to capacity) speed-flow curve except in a couple of cases. Based on the small sample of sites with moderate to high flow rates, as well as more recent studies of speed-flow relationships from other countries, a non-linear functional form was decided upon, for both non-passing lane segments and passing lane segments. Figure 2-2 illustrates speed-flow plots from one of the higher flow sites, as well as a regression fit line for the plotted points. This regression line is based on the function given in Equation (2-11). Figure 2-2. Non-linear regression analysis 15-, 30- and 60-min aggregation intervals at NC Site 2 For passing lane segments, it is even more difficult to obtain a full speed-flow plot, as volumes are split across two lanes. Figure 2-3 is a plot of speed-flow data from a passing lane (i.e., the lane used by faster vehicles within a passing lane segment).

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 23 Figure 2-3. Speed-flow data in passing lane of passing lane segment (Oregon site) This plot is fairly representative of all the plots for passing lane segments, both for the passing lane and non-passing lane. Consequently, fitting any particular functional form to this type of plot is going to yield a poor goodness-of-fit. Based on other studies in the literature, as well as simulation data, a non-linear functional form was also decided upon for the speed-flow relationship in passing lane segments, such as that shown in Figure 2-4. Figure 2-4. Example functional form for speed-flow data in passing lane segment For non-passing lane segments the shape of the speed-flow curve is concave, whereas for passing lane segments the shape of the speed-flow curve is convex. Not that the descriptions of concave/convex refer to the shape of the curve, not the mathematical property of a function that yields such shape. As a passing lane segment essentially functions as a multilane highway, it is reasonable that the shape of its speed-flow relationship is more similar to that for a multilane

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 24 highway. The specific mathematical forms used for both passing lane segments and non-passing lane segments are described in Appendix F. Percent Followers An example percent followers-flow plot is shown in Figure 2-5. Figure 2-5. Percent followers-flow data The shape of this relationship can generally be described well with an exponential relationship, such as illustrated in Figure 2-6. Figure 2-6. Example functional form for percent followers-flow data

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 25 Again, the specific mathematical form used for this relationship is described in Appendix F. Follower Density Follower density is the product of percent followers and density. This measure was ultimately chosen as the service measure for this analysis methodology, which is described further in Appendix B. An example follower density-flow plot is shown in Figure 2-7. Figure 2-7. Follower density-flow data The shape of this relationship, as generated from multiplying percent followers by density (with the percent followers and average speed values generated from the aforementioned relationships) is illustrated in Figure 2-8.

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 26 Figure 2-8. Example functional form for follower density-flow data Capacity Of all the field sites, only two experienced flow rates on the order of expected capacity. One site is in North Carolina. As shown in Figure 2-9, maximum flow rates observed at this site are on the order of 1600 veh/h. This value is based on an aggregation level of 5 minutes. Larger aggregation levels would result in lower values. Figure 2-9. High flow site in North Carolina (Site 2) Another site is in California. As shown in Figure 2-10, maximum flow rates observed at this site are on the order of 1400 veh/h. This value is based on an aggregation level of 60 minutes.

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 27 Figure 2-10. High flow site in California (SR-37/Sears Point Rd) With this limited amount of data for high flow rates, it is not justifiable to recommend changing the values currently used in the HCM (1700 pc/h one direction). However, it should be noted that the values from these two field sites, which are in units of vehicles as opposed to passenger cars, are similar to the current HCM values. Vehicle Classifications Overall, heavy vehicle percentages ranged from about 5-15%. Within the heavy vehicle classifications, single-unit trucks (which also included recreational vehicles) comprised about half of the truck percentage, with the other half fairly evenly split between intermediate and interstate tractor+semi-trailer trucks. Double-trailer trucks represented less than 1% of the traffic stream. Likewise, motorcycles represented only about 1% of the traffic stream. These percentages were used for specifying the traffic stream composition in the simulation experiments. 0 10 20 30 40 50 60 70 80 0 200 400 600 800 1000 1200 1400 1600 Sp ee d (m i/ h) Flow (veh/h) SR 37 Westbound

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 28 2.3. Service Measure Evaluation 2.3.1. Introduction Performance measures are essential for assessing the quality of service, which describes how well a transportation facility or service operates from a traveler’s perspective (TRB, 2010). From a highway agency’s perspective, performance measures are essential in determining the need for operational improvements on two lane highways (e.g., passing lanes) or the need to upgrade to a multi-lane highway. Ideally, performance measures used for traffic operations and capacity analysis should (Luttinen et al., 2005): 1. Reflect the perception of road users on the quality of traffic flow. 2. Be easy to measure, estimate, and interpret. 3. Correlate to traffic and roadway conditions in a meaningful way. 4. Be compatible with the performance measures of other facilities. 5. Describe both uncongested and congested conditions. 6. Be useful in analyses concerning traffic safety, reliability, transport economics, and environmental impacts. The six criteria above consider the common operational objectives of most highway agencies, namely: mobility (criterion 1), productivity (criteria 2, 3 and 5), safety (criterion 6), reliability (criterion 6) and low environmental impacts (criterion 6). This chapter discusses findings from an agency survey, current performance measures in the Highway Capacity Manual (HCM), other performance measures proposed in the literature, an empirical evaluation of potential performance measures, and finally the selection of performance/service measures for the new two-lane highway analysis methodology. 2.3.2. Summary of Agency Survey Findings In an attempt to better understand the transportation agency’s perspective with regard to what constitutes a good performance measure for two-lane highways, a questionnaire survey was sent to all state DOTs in the U.S. and the provincial ministries of transport in Canada. The survey also included a few questions about the agency experience with the use of the HCM and proposed changes and revisions to the current analytical procedures. A total of 35 usable responses were received, representing transportation agencies at 25 states and 4 Canadian provinces. The most important findings of the survey on the use of two-lane highway performance measures are summarized below: • Almost all highway agencies reported the use of the current HCM performance measures on two-lane highways, i.e., average travel speed, percent-time-spent-following, and percent of free flow speed. Among other non-HCM measures used by some agencies were follower density, percent follower for vehicles traveling at headways of less than 2 seconds, traffic flow, delay, v/c ratio and AADT/c ratio.

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 29 • While almost all highway agencies in the U.S. and Canada use binned vehicle counts as part of their regular data collection programs on two-lane highways, per vehicle data, which is critical in estimating some performance measures on two-lane highways, is only collected by 17% of the responding agencies. This restricts the ability of those agencies in using many performance measures included in this survey, which require the more detailed per vehicle data. • The top three criteria that were ranked as being most important characteristics for two- lane highway performance measures are: sensitivity to traffic conditions, sensitivity to road conditions, and relevance to road user perception, respectively. • Among traffic flow aspects that are most relevant to two-lane highway operations, speed followed by flow were ranked as the most important aspects for all two-lane highway classes. • With regard to the merit of using individual performance measures within each traffic flow aspect category, the best measures were found to be v/c ratio, average travel speed, PTSF, and overtaking ratio for all two-lane highway classes in the flow, speed, headways and passing maneuvers categories respectively. For the density flow aspect, follower density was found superior on class I and class III while density was found superior on class II two-lane highways. Percent followers, used by the current HCM as a surrogate measure for PTSF, was associated with much lower average ranking compared with PTSF for all highway classes. The responses to the practice survey included some of the limitations of the current HCM performance measures from the agencies’ perspective, as well as some valuable suggestions and feedback on two-lane highway performance measures that were discussed in the paper. The results from the agency survey revealed that a wide range of performance measures are used by agencies. The results suggest that the top three criteria for good performance measures on two-lane highways are: sensitivity to traffic conditions, sensitivity to road conditions, and relevance to road user perception. Further, agencies identified average travel speed as the most relevant traffic flow aspect to two-lane highway operations. Other performance measures that were found meritorious were volume-to-capacity ratio and flow rate, for class I and class II highways, respectively, versus average travel speed, volume-to-capacity ratio, and percent-time- spent-following for class III highways. More information about the agency survey is contained in Appendix A. 2.3.3. Highway Capacity Manual Performance Measures The current HCM (TRB, 2016) classifies two-lane highways into three different classes based on the degree to which they serve mobility and the adjacent land use character (e.g., rural versus developed areas). These classes are: a. Class I two-lane highways: Highways where motorists expect to travel at relatively high speeds and they include major intercity routes, daily commuter routes, and major links in state or national highway network.

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 30 b. Class II two-lane highways: Highways where motorists do not necessarily expect to travel at high speeds and they include access routes to class I facilities, some scenic and recreational routes, and routes passing through rugged terrain. c. Class III two-lane highways: These primarily include highways serving moderately developed areas. They may be portions of class I and class II highways that pass through small towns or developed recreational areas. Traffic stream characteristics on each of these highway classes are different and as such different performance measures are proposed. A total of three performance measures are used in the current HCM analysis methodology for the assessment of level of service (hereafter referred to as service measures), namely: percent time spent following (PTSF), average travel speed (ATS), and percent of free flow speed (PFFS). PTSF is defined as the average percent of total travel time that vehicles must travel in platoons behind slower vehicles due to the inability to pass (TRB, 2010). PTSF represents the freedom to maneuver and the comfort and convenience of travel and is used on class I and class II two-lane highways (TRB, 2010). While this performance indicator may relate well to the quality of service on two-lane highways, it is impractical to measure in the field. Therefore, the HCM recommends the use of a surrogate measure, referred to in this study as percent followers (PF), for field estimation of PTSF. PF is defined as the percentage of vehicles in the traffic stream with time headways smaller than 3 seconds. ATS on the other hand reflects mobility and is defined as the highway segment length divided by the average travel time taken by vehicles to traverse it during a designated time interval (TRB, 2010). ATS is considered for estimating performance on class I two-lane highways only. Finally, PFFS represents the ability of vehicles to travel at or near the posted speed limit and is measured as the ratio of ATS to free flow speed (FFS) multiplied by 100 (TRB, 2010). PFFS is used as the service measure only for class III two-lane highways. Limitations in the HCM methodology for measuring performance on two-lane highways have been reported in several studies and some of those limitations are concerned with the appropriateness of the service measures used (Al-Kaisy and Freedman, 2011; Al-Kaisy and Freedman, 2010; Al-Kaisy and Karjala, 2008; Brilon and Weiser, 2006; Luttinen, 2001). Specifically, the PTSF is difficult to measure in the field and does not readily describe the extent of congestion on the facility, which is important for operational analysis and highway improvement decisions. Average travel speed, on the other hand, is easy to measure in the field; however, it is not very sensitive to traffic level on the highway. Since the analysis section of a two- lane highway facility is usually several miles long, there could be many changing conditions, such as posted speed limit and roadway alignment that affect ATS, yet it is not related to varying traffic conditions. This can make ATS somewhat meaningless for determining how the highway is operating (Al-Kaisy and Freedman, 2011). The PFFS is meant to account for the limitations of ATS as it measures the speed reduction due to increased traffic volume and/or platooning, which makes it possible to compare the current conditions to the ideal conditions (Al-Kaisy and Freedman, 2011). One of the limitations of PFFS is that it is largely unaffected by the addition of a passing lane, which indicates that it is not particularly helpful in capturing the delay caused by platooning (Al-Kaisy and Freedman, 2010).

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 31 2.3.4. Alternative Performance Measures A number of alternative performance and/or service measures for two-lane highways have been suggested in the literature. Most of the studies that proposed new performance measures were driven by the obvious limitations of the HCM procedures, including those of the performance measures used. As discussed previously, PTSF is difficult to measure in the field, is not compatible with the service measures of other facilities, does not describe the extent of congestion, and is not very useful in other analyses. PTSF is also a poor performance measure for indicating if improvements should be made to a highway that has low volumes with a high percentage of heavy vehicles and few passing opportunities. ATS, on the other hand, is not very informative about the efficiency of the highway. Since the analysis section of a two-lane highway facility is usually several miles long, there could be many changing conditions, such as posted speed limit and roadway alignment that affect ATS, yet it is not related to varying traffic conditions. In this section, a review of alternative performance measures that have been proposed in the literature or reported as part of current practice is presented. The review does not include the two measures currently used by the HCM procedures, PTSF and ATS, as these two measures were discussed previously. In this document, the use of the term “performance measure” is intended to refer to the performance measure, or measures, that would be used to base the classification of LOS upon; that is, the “service measure”. In this section, performance measures are classified and presented in the following common categories: 1. Speed-related measures 2. Flow-related measures 3. Density-related measures 4. Measures related to passing maneuvers 5. Combination measures Speed-Related Measures The vast majority of two-lane highways can be thought of as “uninterrupted flow facilities”, thus enjoying relatively higher travel speeds. This is particularly true for class I highways, which represent important arterials and major collectors in rural areas. On these highways, ATS has long been used by the HCM as a performance measure with the premise that average speed is affected by traffic level and, thus, the amount of platooning due to limited passing opportunities. However, two-lane highways involve most of highway classifications, have a wide range of geometric standards, and consequently, a wide range of operating speeds. Therefore, using average speed alone may not provide enough information about the level of traffic performance (in the absence of a reference point) to make performance comparison across sites practical. In their investigation of proposed performance measures, Al-Kaisy and Karjala (2008) examined three speed-related measures: • Average travel speed of passenger cars (ATSPC) • ATS as a percent of free-flow speed (ATS/FFS) • ATSPC as a percent of free-flow speed of passenger cars (ATSPC/FFSPC)

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 32 The researchers argued that average travel speed of passenger cars may more accurately describe speed reduction due to traffic, since passenger car speeds are more affected by high traffic volumes than heavy vehicle speeds. Further, using ATS as a percentage of free-flow speed was viewed as a good indicator of the amount of speed reduction due to traffic and the amount of vehicular interaction in the traffic stream. However, evaluations using field data showed that the speed measures did not exhibit good correlations with platooning variables as compared to other performance measures investigated in the study. Luttinen (2001a) reported on a study by Kiljunen and Summala in 1996 which proposed the use of ATS/FFS as a performance measure on Finnish two-lane highways. In their article on the German experience, Brilon and Weiser (2006) reported the use of average speed of passenger cars over a longer stretch of highway, averaged over both directions, as a major performance measure on two-lane highways. Truck speeds are not very sensitive to increases in traffic volume, but traffic volume is the main factor affecting the ATS of passenger cars (Brilon and Weiser, 2006). In his study on PTSF in Finland, Luttinen (2001) reported on an old study by O.K. Normann, who suggested the use of speed differences between successive vehicles on two-lane highways among other proposed performance measures. A study by Washburn et al. (2002) proposed a third class for two-lane highways and the service measure of ATS/FFS for this class. This proposed third class and corresponding service measure is intended to apply to two-lane highways that are considered scenic in nature (e.g., along a coastline) and/or serve well-developed areas. For these situations, it was determined that drivers do not have much expectation for being able to pass other vehicles and that their main desire is to be able travel at a speed close to the free-flow speed. A study by Yu and Washburn (2009) and Li and Washburn (2014) proposed the percent delay service measure for two-lane highway facilities (i.e., a combination of two-lane highway segments and intersections). This service measure is based on the difference between free-flow travel time and actual travel time. The use of a speed-based measure allows the service measure to be applied to both two-lane highway segments and intersections, which individually use delay as the service measure. Flow-Related Measures Several flow-related measures have been used in practice or proposed in the literature for measuring performance on two-lane highways. This is somewhat expected, given that traffic flow level is largely associated with platooning and delay and, consequently, with users’ perception of the quality of service. The v/c ratio, or degree of capacity utilization, has been used as the main performance measure on two-lane highways in Denmark, China and Japan (Vejdirektoratet, 2010; Rong et al., 2011; Nakamura & Oguchi, 2006). It is important to note that the two-lane expressways in Japan are different from the conventional two-lane highways in the U.S. and most other countries in that they have limited access (no at-grade intersections) and a median barrier present in all sections (Catbagan and Nakamura, 2006). Further, the v/c ratio has been used as an additional performance measure in Sweden (Trafikverket, 2014).

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 33 Another measure that has been used extensively both in practical applications as well as in published research is time headway, a major traffic flow microscopic characteristic. For various practical reasons, time headway has been used solely for identifying platoons using empirical traffic data and field measurements. One important reason for using time headway is that this measure can readily be extracted from the output of conventional traffic recorders, which have the ability to provide raw data (i.e., timestamp records for individual vehicle arrivals). The second equally important reason is the fact that time headway is a good indicator of the interaction between successive vehicles in the traffic stream and, thus, in determining the status of a vehicle being in a following mode (i.e., being part of a vehicular platoon). The most commonly used headway-based service measure is percent followers (PF). PF is used by the HCM to estimate PTSF with field data. It is defined as the percentage of vehicles in the traffic stream with headways of less than three seconds (TRB, 2000, 2010). A few recent studies have examined PF along with other proposed performance measures to evaluate their suitability for use on two-lane highways (Al-Kaisy and Karjala, 2008; Catbagan and Nakamura, 2006; Hashim and Abdel-Wahed, 2011; Van As, 2003; ODOT, 2014). Another headway-based measure that was reported in the literature is follower flow, which was investigated by the South African National Roads Agency (Van As, 2003). It is defined as the hourly rate of vehicles in following mode that pass a point along a two-lane highway. This measure can easily be estimated as the product of PF and the flow rate. Follower flow was investigated among several other performance measures in the development of the current South African two-lane highway methodology. While this performance measure was found superior to most other performance measures investigated by this study, it was outperformed by follower density that was eventually adopted for use as a service measure in the current South African two- lane highway methodology. Density-Related Measures In their study, Brilon and Weiser (2006) reported that the then current German Capacity Handbook (HBS, 2001) utilized density as the primary service measure for two-lane highways. Density is calculated as the ratio of traffic volume and the ATS of just passenger cars (i.e., ATSpc). The rationale for using density as a performance measure on two-lane highways in Germany is that efficiency is given preference over user experience (perception) of the quality of service (Brilon and Weiser, 2006). Further, this performance measure is compatible with other facility types, mainly freeways and multi-lane highways, when those highway types are analyzed as part of a larger system. Measures Related to Passing Maneuvers The platooning phenomenon on two-lane highways and the associated delay are directly related to passing opportunities and the ability of platoon vehicles to pass slower vehicles and improve their speeds. As such, a few performance measures were proposed for assessing performance on two- lane highways that are related to passing maneuvers. A study by Morrall and Werner (1990) proposed the use of overtaking ratio as a supplementary indicator of the level of service on two-lane highways. This measure is obtained by dividing the number of passes achieved by the number of passes desired. According to the study, the number

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 34 of passes achieved is the total number of observed passes for a given two-lane highway, while the number of passes desired is the total number of passes for a two-lane highway with continuous passing lanes with similar vertical and horizontal geometry. Overtaking ratio, along with the average number of passes per vehicle, were also proposed by O.K. Norman, as reported by McLean (1989), and Luttinen (2001). Combination Measures A couple of measures proposed in the literature are associated with more than one traffic stream parameter, and as such, they are discussed independently from the previous measures. The merit of using compound measures is the fact that those measures usually combine the advantages of more than one indicator of traffic performance on two-lane highways (e.g., amount of platooning and traffic level). One important combination measure is follower density, which was originally adopted by the South African National Roads Agency about ten years ago (Van As, 2003; Van As and Niekerk, 2004) and was later investigated in other studies (Catbagan and Nakamura, 2006; Al-Kaisy and Karjala, 2008; Hashim and Abdel-Wahed, 2011; Moreno et al., 2014). Follower density is defined as the product of PF and traffic density; therefore, this measure is derived using two important flow characteristics: traffic flow and density. Again, PF is estimated using time headway, which is a microscopic flow characteristic. Another combination measure that was proposed in the literature is percent impeded. This measure was originally proposed by Al-Kaisy and Freedman (2011) and was later investigated by Hashim and Abdel-Wahed (2011), Ghosh et al. (2013), and Moreno et al. (2014). PI is defined as the product of PF and the probability of desired speeds being greater than the average speed of platoon leaders. Therefore, this measure is derived using flow and speed characteristics. 2.3.5. Preliminary Assessment of Proposed Performance Measures In this section, an initial qualitative assessment of the proposed alternative performance measures is presented. The HCM performance measures will also be included in this assessment to help in understanding the merits of the proposed alternative measures. As discussed earlier in this report, it is desired for prospective performance measures on two-lane highways to meet the following criteria. 1. Performance measure should reflect the perception of road users on the quality of traffic flow. • It is a common understanding that platooning and lack of passing opportunities (and its associated delay) primarily affect the motorists’ perception of the quality of service on two-lane highways. 2. Performance measure should be easy to measure and estimate using field data. • Specifically, it is expected that the performance indicator of choice can be measured in the field using conventional data collection methods used by highway agencies and the professional community. 3. Measure should correlate to traffic and roadway conditions in a meaningful way.

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 35 • On two-lane highways, the prospective performance measure should closely correlate to the platooning phenomenon (and passing opportunities) as well as to traffic level in a logical and meaningful way. 4. It is recommended that the prospective measure be compatible with performance measures used on other facilities. • This criterion may be hard to satisfy as it is expected that different aspects of traffic operations are perceived as most important by drivers on different highway facilities. For example, while platooning on two-lane highways is a major determinant of the quality of operation, it is not a major factor in determining the quality of operations on other facilities. 5. Performance measure should be able to describe both uncongested and congested conditions. • While this requirement is applicable to all highway facilities per the definition of the LOS scheme, it has been perceived to have less significance on two-lane highways, since these facilities are rarely congested and are usually upgraded to four lanes when they do become congested. 6. Measure should be useful in analyses concerning traffic safety, transport economics, and environmental impacts. • Increasingly, the capacity analysis procedures have been used in supporting the aforementioned analyses. To be of use in safety analyses, the prospective measure should correlate well to traffic exposure. On the other hand, for economic and environmental impact analyses, the prospective measure should be useful in estimating delay and its associated fuel consumption and tailpipe emissions. Table 2-6 summarizes all of the performance measures discussed in this report and the degree to which each measure satisfies the six criteria discussed above. In this subjective assessment, each performance measure is evaluated against the six criteria independently (i.e., assessed assuming it’s used solely for measuring performance on two-lane highways). At a glance, it can be clearly seen that no single measure largely satisfied all evaluation criteria and that each measure satisfied some criteria to a higher degree but scored low on other criteria. Therefore, identifying a single performance measure that satisfactorily meets all of the above criteria may not be realistic.

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 36 Table 2-6. Preliminary assessment matrix of performance measures on two-lane highways Performance Measure Type a (1) Road User Perception (2) Easy to Measure (3) Sensitive to Road Conditions (4) Compatible with Other Facilities (5) Describes All Flow Regimes (6) Support Other Analyses Safety Economic Environmental Reliability HCM – PTSFb FR XXXc X X X Xd X X X X HCM – ATS SR X XXX X XX Xd XX XX XX X HCM – (ATS/FFS) SR XX XXX XX X XXd X XXX XXX X Average travel speed of passenger cars (ATSPC) SR X XXX X XX XXX X XX XX X ATSPC as a percent of free-flow speed of passenger cars (ATSPC/FFSPC) SR XX XXX XX X XXX X XXX XXX X Speed Variance SR X XXX X X X XX X X X Demand-to-capacity (d/c) ratio FR XX XXX X X XXX XX XX XX XX Percent followers (PF) FR XX XX XX X X X X X X Follower flow FR X XX XX X X XX X X X Traffic density DR XX XXX XX XXX XXX XXX X X XX Overtaking ratio PASS X X XX X X X X X X Average number of passes per vehicle PASS X X XX X X XX X X X Follower density (FD) COMB XX XX XX XX X XX X X X Percent impeded (PI) COMB XX XX XXX X X XX X X X a – SR = speed-related, FR = flow-related, DR = density-related, PASS = passing maneuvers, COMB = combination b – PTSF is estimated using flow rates in the analytical methodology and using percent followers (PF) as a surrogate measure for field estimation. c – X = hardly meeting criterion, XX = fairly meeting criterion, XXX = largely meeting criterion d – Level of service F is not defined for any of the three HCM 2010 performance measures

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 37 2.3.6. Empirical Analysis of Field Data An empirical analysis based on field data was performed. The details for this effort are described in Appendix B. 2.3.7. Summary The results from the empirical analysis demonstrated that across all highway classes, follower density and follower flow had the highest correlation among several traffic variables. These measures are compatible with the desirable traits of performance measures identified in the agency survey. Likewise, follower density has gained appeal as a preferred service measure in other countries, such as South Africa, Brazil, and Spain. Follower flow is a function of percent follower and flow rate, whereas follower density is a function of percent followers, flow rate, and speed. Given the above considerations, and that follower density is sensitive to flow rate, speed, and platooning conditions, it is selected as the service measure for segment level of service. The calculation of follower density is as follows: 100 dvPFFD S = × (2-12) where FD = follower density (followers/mi/ln), PF = percent followers (%), vd = flow rate (veh/h/ln), and S = average speed (mi/h). As percent followers is part of the calculation for follower density, a significant issue is how following vehicles are defined. This issue is discussed in Appendix E. 2.4. Identification of Viable Simulation Tools for the Analysis of Two-Lane Highways The purpose of this task was to identify candidate simulation tools that are suitable for achieving the objectives of this project and are viable for use in simulation-based two-lane highway analyses for many years to come. The identified candidate simulation tools were evaluated based on considerations such as accessibility to the underlying modeling algorithms, opportunities and effort required for modifications to the algorithms as necessary for the purposes of this project, cost of the tool, future sustainability of the program, etc. 2.4.1. Identification of Candidate Simulation Tools While many simulation tools are commercially available, only a few have the ability to model passing in an oncoming lane of traffic, a key feature of two-lane highway operations. Two simulation tools that do include this ability are TWOPAS and TRARR, which were used extensively in two-lane highway research from the mid-1980s through the late 1990s. These programs, however, are not considered as candidate simulation tools for this project. This is

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 38 primarily because these programs are based on an outdated software architecture (which limits potential program modifications as well as its ability to run on modern computer operating systems) and/or there is no current developer support for these programs. The research team preliminarily identified several simulation tools as potential candidates for this project. Since the research team was not certain of the two-lane highway modeling capabilities of all of the tools, a survey was sent out to the vendors/developers of the software programs in question. Based on the survey responses and gathered information, the candidate simulation tools for this project were identified. Details on the preliminary identification of simulation tools, survey, survey responses, and final candidate simulation tools are provided in Appendix C. 2.4.2. Simulation Tool Recommendation Survey responses were received on behalf of TransModeler, Aimsun, and RuTSim. For Vissim and Paramics, the research team consulted available documentation for those tools to assess the previously listed criteria as best as possible. Based on the survey responses and other information gathered about the candidate simulation tools, the respective simulation tools were evaluated based on issues such as: ability to model passing in the oncoming lane and different configurations for passing/climbing lanes, ability to output user-defined performance measures, accessibility to the underlying modeling algorithms, adjustability of vehicle performance parameters, opportunities and effort required for modifications to the algorithms as necessary for the purposes of this project, public availability of the tool, cost of the tool, future sustainability of the program, and developer support. Based on the evaluation of the candidate simulation tools, the research team chose to use SwashSim as the primary simulation tool and TransModeler SE (a simpler version of TransModeler for small projects) as a secondary simulation tool. SwashSim and TransModeler met all of the desired criteria. SwashSim was used in all of the simulation tasks for this project. TransModeler was used to “spot check” the reasonableness of some of the SwashSim results. This is discussed further in Appendix I. 2.5. Approach for Estimating Impacts of Large Trucks on Two-Lane Highway Operations A key feature of the analysis methods for two-lane highways is estimating the impact of heavy vehicles on traffic operations. Heavy vehicles influence traffic operations for a number of reasons. First and foremost, the performance capabilities of these vehicles are much more limited than those of passenger cars. This affects the speeds at which heavy vehicles can ascend and descend moderate to steep grades. On upgrades, the speed of a heavy vehicle is largely affected by the difference between the engine-generated tractive effort, which propels the vehicle up the grade, and the vehicle resistances (grade, aerodynamic, and rolling), which inhibit the vehicle’s movement up the grade. As the vehicle traverses the length of the grade, the vehicle’s speed continually decreases until it reaches its “equilibrium” speed, at which point the vehicle will no longer decelerate. This “equilibrium” speed is referred to as the crawl speed. On downgrades, heavy vehicle speeds are limited by the braking abilities of the vehicle. Drivers must apply pressure to the brakes to prevent their vehicle from accelerating to an unsafe

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 39 speed. For moderate to steep downgrades, constant brake pressure increases the temperature of the brakes, which can lead to brake fading. This is a dangerous situation, which typically results in a runaway truck. In order to reduce the amount of pressure applied to the brakes on the downgrade, heavy vehicles must decelerate to a safe speed prior to reaching the top of the grade. They maintain this safe speed on the downgrade, applying the brakes intermittently as needed. Depending on the length and slope of the upgrade or downgrade, heavy vehicle speeds can be reduced considerably as compared to passenger car speeds. If a passing lane is not provided on these grades, passenger cars will catch up with the heavy vehicles, forcing them to reduce their speeds. This, in turn, reduces the overall speed of the traffic stream on the grade. The presence of heavy vehicles on a two-lane highway also impacts the passing opportunities for passenger cars. Heavy vehicles obstruct the view of passenger car drivers, making it more difficult for these drivers to observe acceptable gaps in the opposing traffic stream. Conversely, if a large percentage of heavy vehicles exists in the opposing flow, platooning in the opposing direction can increase, leading to larger gaps in the opposing traffic stream and increased passing opportunities. The analysis methods used to estimate performance measures on two-lane highways should account for these types of heavy vehicle impacts. The current version of the HCM (Transportation Research Board, 2010) does capture some of these effects, but only for a limited range of heavy vehicle types and heavy vehicle percentages. It also suffers from a lack of guidance on the typical downgrade speeds of heavy vehicles. In order to adequately capture the impact of heavy vehicles on two-lane highway traffic operations, a wider range of conditions should be considered. The level of accuracy of the two-lane highway methodology in the current HCM has also been questioned. Issues related to the speed-flow relationships, appropriate service measures, treatment of heavy vehicles, guidance on base free-flow speed estimation, accuracy of passing lane adjustments, and limitations of analysis scope have all been raised by researchers. While this study is mainly focused on the treatment of heavy vehicles issue, the remaining issues will be given consideration, as needed. The focus of this task was to develop a more accurate method for estimating the impact of heavy vehicles on two-lane highway operations. This method should adequately model the impact of various horizontal and vertical alignment on heavy vehicle speeds and the interaction between passenger cars and heavy vehicles on these alignments. The method should cover a wide range of traffic conditions and include multiple types of heavy vehicles. Due to the wide range of conditions needed for such a method, it was not possible to develop the method from field data alone. Simulation data was heavily relied on for this study. Therefore, data generated from the simulation tool should be representative of two-lane highway field conditions. This study investigates current microscopic simulation tools capable of modeling two- lane highway operations. These tools will be assessed, and one tool will be selected to carry out the experiments in this study. The following sub-sections present current research and methodologies for modeling the longitudinal movement (speed, acceleration) of heavy vehicles on two-lane highways and its impact on overall traffic stream operations. The first part discusses how the current HCM analysis methodology accounts for the impact of heavy vehicles on two-lane highway operations. This part

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 40 includes a discussion of the criticisms and limitations of the HCM methodology. The following sub-section presents alternative methodologies that can help address some of the limitations of the HCM methodology. Finally, the modeling of heavy vehicle speeds for microscopic simulation is discussed. 2.5.1. Current HCM Methodology The 2010 HCM accounts for the effect of heavy vehicles on traffic operations on two-lane highways through the use of passenger car equivalent (PCE) values. These values denote the number of passenger cars that cause the same impact on a given performance measure as a single heavy vehicle. For the two-lane highway methodology, the values used in the analysis depend on the highway terrain (general terrain type, specific upgrade, or specific downgrade), directional demand flow rate, and service measure being calculated (average travel speed (ATS) or percent time-spent-following (PTSF)). These values are provided in various tables, which differ for trucks and recreational vehicles (RVs). The PCE values are used along with the percentage of trucks and RVs to calculate the heavy vehicle adjustment factor as shown in Equation (2-12). = 11 + ( − 1) + ( − 1) (2-12) where fHV = heavy vehicle adjustment factor (decimal) PT = proportion of trucks in the traffic stream (decimal) PR = proportion of RVs in the traffic stream (decimal) ET = passenger car equivalent for trucks (decimal) ER = passenger car equivalent for RVs (decimal) This adjustment factor is used to convert the directional demand flow rate from units of vehicles per hour to passenger cars per hour. The adjusted flow rate is then used to estimate the ATS, PTSF, or percent of free-flow speed (PFFS) service measure, depending on the two-lane highway class being analyzed. For the case where ATS is estimated for a specific downgrade, the heavy vehicle adjustment factor calculation is slightly different. The HCM defines a specific downgrade as “any downgrade of 3% or more and 0.6 mi or longer” (Transportation Research Board, 2010, p. 15-19). For these downgrades, some proportion of truck drivers are assumed to operate their crawl speed, in order to prevent the vehicle from gaining too much momentum. Since trucks operating at crawl speeds have a larger impact on roadway capacity than trucks not operating at crawl speeds, a different table of PCE values are used for this proportion of truck drivers. These values are a function of the difference between the free-flow speed (FFS) and truck crawl speed as well as the directional demand flow rate. Equation (2-13) is used to calculate the heavy vehicle adjustment factor for this case.

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 41 = 11 + × ( − 1) + (1 − ) × ( − 1) + ( − 1) (2-13) where PTC = proportion of trucks operating at crawl speed (decimal) ETC = passenger car equivalent for trucks operating at crawl speed (decimal) Other variables as previously defined This adjustment factor is used in the same way as the value obtained from Equation (2-13). The heavy vehicle adjustment factor is also used to estimate the directional capacity of a two- lane highway. For this case, the adjustment factor needs to be reflective of capacity conditions (i.e., high flow rates), so the PCE values used in Equations (2-12) or (2-13) need to correspond to a directional demand flow rate greater than 900 veh/h (the highest flow rate category in the HCM PCE tables). The adjustment factor is used to adjust the base directional capacity of 1700 pc/h to a value that approximately reflects of the prevailing heavy vehicle composition of the highway. The PCE values also have a secondary effect on the service measure estimations. The adjusted flow rate, which is obtained using PCEs, is used to look up an adjustment factor for the percentage of no-passing zones and estimate the base PTSF. These variables are used to estimate ATS and/or PTSF. The heavy vehicle adjustment factor, which is also obtained using PCEs, can be used to estimate the FFS of highways with a total flow rate greater than 200 veh/h. The FFS is used to estimate ATS and PFFS. Similar secondary effects on service measures occur when analyzing segments with a passing or climbing lane. In both cases, the adjusted flow rate is used to look up an adjustment factor for the impact of a passing/climbing lane (fpl). For the passing lane case, the downstream length of roadway affected by the passing lane (Lde) is also obtained with this flow rate. These variables are used to calculate ATS and/or PTSF. 2.5.2. Limitations of HCM Methodology The two major criticisms of the two-lane highway HCM methodology are that the truck and RV PCE values do not vary for heavy vehicle percentage, and the truck PCE values do not vary by truck type. Both the truck and RV PCEs were developed for a “typical” heavy vehicle mix (trucks and RVs), which contained a “typical” truck mix (single-unit trucks (SUTs) and tractor trailer trucks (TTs)). Research has shown that both heavy vehicle percentage and the type of heavy vehicle (i.e., RV, SUT, or TT) significantly affect the impact of heavy vehicles on traffic operations. Other criticisms relate to the simplicity of the PCE approach, use of PCE tables, and specific downgrades. Each of these limitations is discussed in its respective section. PCE versus Heavy Vehicle Percentage St. John (1976) and St. John and Kobett (1978) found a nonlinear relationship between heavy vehicle percentage and passenger car speeds on two-lane highway upgrades. Each additional increase in the percentage of heavy vehicles caused a smaller reduction in the average passenger car speed. Therefore, the impact of the first few heavy vehicles added to a two-lane highway was greater than subsequent additions of heavy vehicles. Jacobs (1974) and Rakha et al. (2007) found

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 42 a similar relationship between heavy vehicle percentage and PCE values for two-lane highways and freeways. PCE values decreased with an increase in heavy vehicle percentage. Taylor et al. (1972) did not develop PCE values, but found that the impact of heavy vehicles on platoon lengths exponentially decreased as the percentage of heavy vehicles increased. PCE versus Heavy Vehicle Type Elefteriadou et al. (1997) and Webster and Elefteriadou (1999) found that a heavy vehicle’s weight-to-power ratio and length significantly affected its PCE value. This was especially true for heavy vehicles on long and steep grades (Webster and Elefteriadou, 1999). Studies in Brazil also confirmed that the impact of a heavy vehicle varies by heavy vehicle type (Setti and Neto, 1998; Cunha and Setti, 2011). These studies showed that the underpowered heavy vehicles in Brazil had larger PCE values than the more powerful heavy vehicles in the United States. Simplicity of PCE Approach Some researchers have argued that the PCE approach in the HCM is too simplistic. The use of a single PCE value to represent the impact of a heavy vehicle can overgeneralize the interdependent and sometimes complex relationships between heavy vehicles, speeds, flows, and other traffic measures. Research by Dowling et al. (2014) showed that PCE values may not be suitable for capturing the impact of heavy vehicles on freeway operations for long upgrade segments. In these cases, the ATS of the mixed flow of traffic (i.e., passenger cars and heavy vehicles) was lower than the lowest travel speed on the HCM’s passenger car speed-flow curve. This was because the ATS approached the heavy vehicles’ crawl speed as the flow rate increased. Consequently, there was no way to obtain the average mixed flow travel speed from the speed-flow curve using a single PCE value. Figure 2-11 illustrates this potential issue for a 5-mile long freeway segment with a 6 percent upgrade, 30 percent heavy vehicle mix, and 70 mi/h passenger car FFS. The solid blue line represents the passenger car speed-flow relationship in the HCM (Transportation Research Board, 2010). The light blue region represents the speed-flow relationship for the mixed flow condition obtained from Vissim simulations (Dowling et al., 2014). A density-based PCE can get the analyst to point A, but there is still a difference of 25 mi/h between point A and point B. An additional PCE would be required to get the analyst to point B. It is also worth noting that the mixed speed- flow relationship is highly variable for low flow rates, unlike that for passenger-car-only flows. A single PCE value is also unable to account for this variability.

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 43 Figure 2-11. Discrepancy between speed-flow patterns for passenger car only and mixed flows Adapted from Exhibit 59, NCFRP Report 31 (Dowling et al., 2014) and Chapter 11, 2010 Highway Capacity Manual It could be argued that the situation depicted in Figure 2-11, while valid in theory, is unlikely to occur in reality. The type of freeway in this example would likely exist in a rural area (grades in urban areas are usually fairly level) where the observed flow rates are low. Therefore, passenger cars would still have the ability to maneuver around the heavy vehicles, and the ATS would not approach the heavy vehicles’ crawl speed. This situation could, however, become more realistic when applied to a two-lane highway with 100 percent no-passing zones. In this case, passenger cars would not have the ability to maneuver around the heavy vehicles. They would be forced to travel at the heavy vehicles’ reduced speed. This makes the situation depicted in Figure 2-11 more plausible for two-lane highways than freeways. PCE Tables While the concept of PCEs is simple, the tables for these values have created some issues. In the HCM 2000 (Transportation Research Board, 2000), the demand flow rates in the tables were in units of passenger cars per hour. This proved to be awkward, since the PCE values were needed to convert the demand flow rate from units of vehicles per hour to passenger cars per hour. Users had to first assume a passenger car flow rate range, which they used to obtain the PCE value(s) from

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 44 the table. The PCE value(s) were then used to convert the demand flow rate into units of passenger cars. If the demand flow rate was not within the assumed range of demand flow rates, the process was repeated with a new demand flow rate range. The process ended when the calculated flow rate was within the demand flow rate range used for the PCE value(s). This process was not only awkward, but also created a situation where an endless cycle of iterations could occur in certain cases. No matter what demand flow rate range was assumed, the calculated flow rate would not be within the assumed range used for the PCE value(s). This issue was “corrected” in the HCM 2010 (Transportation Research Board, 2010) by creating additional demand flow rate categories and changing the demand flow rate units in the table from passenger cars per hour to vehicles per hour (Roess and Prassas, 2014). However, this “correction” was not based on any theoretical or observed relationships. The tables also proved to be inconvenient when implementing the two-lane highway methodology into an analysis tool. Arrays of PCE values had to be coded in the tool, rather than using a simple equation. This inconvenience was furthered by having different PCE tables for the different service measures (i.e., ATS or PTSF). While tables were likely more convenient a few decades ago, equations are now more convenient given advances in computing technology. Equations are also easier to interpret with respect to relationships between variables. Specific Downgrades The current HCM methodology accounted for the effect of trucks operating at crawl speeds on specific downgrades when estimating ATS, as shown by Equation (2-14). It did not, however, provide guidance on how to estimate the truck crawl speed or the proportion of trucks operating at their crawl speed. These two values are critical for estimating the heavy vehicle adjustment factor. The original research that developed the methodology did provide some guidance on estimating the proportion. It stated, “Where more specific data are not available, the percentage of trucks that use crawl speeds (PTC) can be estimated as equal to the percentage of all trucks that are tractor- trailer combinations” (Harwood et al., 1999, p. 141). This guidance was printed in the HCM 2000 (Transportation Research Board, 2000), but was removed in the HCM 2010 (Transportation Research Board, 2010). The methodology also did not account for the effect of trucks operating at crawl speed when estimating PTSF. It is not clear why this effect was excluded for PTSF. The original research stated that trucks operating at crawl speeds “are likely to impede other vehicles and will decrease ATS and increase PTSF” (Harwood et al., 1999, p. 140). Therefore, it seems logical to include PCEs for trucks operating at crawl speeds when estimating PTSF for specific downgrades. 2.5.3. Alternative Methodologies Other methodologies have been developed to account for the impact of heavy vehicles on two-lane highway traffic operations. Some of these methodologies are adaptions of the PCE approach in the HCM, while others vary significantly from the HCM methodology. Each of the methodologies presented in this section addresses one or more of the limitations of the current HCM methodology.

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 45 PCEs in Other Countries Many countries have adopted the HCM as a traffic analysis tool. Unfortunately, these countries cannot always use the same values for adjustment factors (e.g., PCEs, grade, no-passing), since traffic operations in these countries differ from those in the United States. Some countries have developed their own values for adjustment factors based on field data from their respective countries. One of the most calibrated adjustment factors is the PCE. This factor has been locally calibrated in Canada, China, Indonesia, Brazil, Japan, India, Thailand, and Singapore (Dowling et al., 2014). All of these countries, except Brazil, Japan, and India, subdivided heavy vehicles into three or more classes and determined PCE values for each class (Dowling et al., 2014). While this is not a significant departure from the HCM methodology, it is a fairly simple adjustment that has the potential to increase the accuracy of the analysis results. German Capacity Handbook Germany released the first edition of its own traffic analysis handbook in 2001. Called Handbuch für die Bemessung von Straßenverkehrsanlagen, it is referred to as the German Capacity Handbook in English and abbreviated as HBS. This handbook contained a two-lane highway analysis methodology that departed significantly from the methodology in the HCM. The HBS 2001 methodology utilized a set of speed-flow curves rather than PCE values (Handbuch für die Bemessung, 2001). These curves differed for various combinations of heavy vehicle percentages, horizontal alignment, and vertical alignment. Similar to the HCM, roadways were divided into smaller pieces to facilitate analyses. The HBS classified these smaller pieces as subsegments. The speed-flow curves were therefore used to describe the traffic operations on each subsegment. The HBS 2001 performed analyses for the combination of both directions, but similar to the change from the HCM 2000 to the HCM 2010, the HBS 2015 moved to a purely directional analysis (Handbuch für die Bemessung, 2015). The speed-flow curves were updated in the HBS 2015 to reflect this change. Each subsegment was attributed a bendiness and grade class. Bendiness was used to describe the horizontal alignment of a subsegment. It was defined as the average degree of curvature contained in the subsegment, in units of deg/km. The grade class was used to describe the vertical alignment of the subsegment. The HBS 2015 assigned this class based on the length and slope of the subsegment. Subsegments could fall into four different classes of bendiness and four different classes of grade. Table 2-7 and Table 2-8 show the classifications used for horizontal and vertical alignment, respectively. Table 2-7. HBS Classifications for Horizontal Alignment Bendiness (KU) (deg/km) Class KU ≤ 50 1 50 < KU ≤ 100 2 100 < KU ≤ 150 3 KU > 150 4 Source: HBS 2015

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 46 Table 2-8. HBS Classifications for Vertical Alignment Grade Length (L) (m) Grade Class s ≤ 3% s ≤ 4% s ≤ 5% s ≤ 6% s ≤ 7% s > 8% L ≤ 600 1 (1) 1 (1) 2 (1) 2 (1) 2 (1) 3 (3) 600 < L ≤ 900 1 (1) 2 (1) 2 (1) 2 (1) 2 (2) 3 (3) 900 < L ≤ 1800 1 (1) 2 (1) 2 (1) 2 (2) 3 (3) 4 (3) L > 1800 1 (1) 2 (1) 2 (2) 3 (3) 3 (3) 4 (4) * s refers to the slope of the grade; downgrade classifications in parentheses Source: HBS 2015 A different set of speed-flow curves was used for each combination of bendiness and grade class. Each set contained curves for various percentages of heavy vehicles. Figure 2-12 shows the set of speed-flow curves for a subsegment that falls within class 1 for both bendiness and grade. Figure 2-12. HBS 2015 speed-flow curves for subsegment with bendiness class 1 and grade class 1 * VF is the average speed of passenger cars; q is the flow rate in veh/h; SV is heavy vehicles; top curve corresponds to 0% heavy vehicles Source: HBS 2015 The figure shows that the average speed of passenger cars generally decreased with an increase in flow rate and heavy vehicle percentage, as expected. Unlike the curves in the HCM, the curves in the HBS did not differ for posted speed. The research used to develop the HBS showed that posted speed did not influence the traffic quality on two-lane highways (Weiser, Date Unknown a). Therefore, this parameter was excluded from the methodology. The speed-flow curve corresponding to the subsegment was used to obtain the ATS. This speed and flow rate were used to calculate the density, which was the service measure for two- lane highways in the HBS. The HBS used density as the service measure because it was easier to

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 47 define levels of service that applied to all subsegment conditions (i.e., all combinations of bendiness class, grade class, and heavy vehicle percentage) for density as compared to ATS. The benefit to using multiple speed-flow curves was that they directly captured the relationships between speed, flow, and heavy vehicles for a variety of roadway geometry. This geometry included horizontal and vertical alignment, whereas the HCM methodology only considered vertical alignment. A disadvantage to using multiple speed-flow curves was that users had to sort through multiple figures, which can be cumbersome. Additionally, the curves could not be defined for every heavy vehicle percentage value, so some interpolation had to be done between curves. The speed-flow curves in the HBS 2015 also did not consider the effect of no-passing zones, unlike the HCM. The decision to not include this effect was due to the difficulties of defining no-passing zones for the German roadways as well as a change in German drivers’ attitude to not want to pass in the opposing lane (Weiser, Date Unknown b). Previously, the HBS 2001 included this effect through an additional term in the bendiness equation. Mixed-Flow Model The mixed-flow model was developed to more accurately estimate the performance of freeways with steep upgrades and high heavy vehicle percentages. For these scenarios, a single PCE value was unable to capture the impact of heavy vehicles on freeway operations (Dowling et al., 2014). This limitation was described in more detail in the previous section titled ‘Simplicity of PCE approach’. The model was included in the HCM 6th Edition (Transportation Research Board, 2016). Although the model was developed for freeways, its underlying concepts could be applied to two- lane highways. An overview of the model is provided below. The objective of the model was to develop a general speed-flow curve that described the mixed flow of traffic. The curve was calibrated to the traffic and roadway conditions of the analysis segment. Since the flow rate was described in units of veh/h/ln, the need for PCE values was eliminated. The speed-flow curve was used to obtain the speed of the mixed-flow, which was then used to calculate the mixed-flow density. The mixed-flow density dictated the LOS of the segment/facility, rather than the automobile-only density. The remaining parts of this section describe the process used to develop the general speed-flow curve. The first step in developing the general speed-flow curve was to define its general shape. The speed-flow curve for freeways had two parts, as shown in Figure 2-12. The first part was linear and defined the range of flow rates at which vehicles could maintain their FFS. The second part was concave in shape and defined how rapidly the speed dropped as the flow rate increased. The general functional form for this curve is shown in Equation ((2-14). = ≤− − , −− > (2-14) where

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 48 Smix = mixed-flow speed (mi/h) FFSmix = mixed-flow FFS (mi/h) Scalib,cap = mixed-flow speed at capacity (mi/h) vmix = flow rate of mixed traffic (veh/h/ln) BPmix = breakpoint for mixed flow (veh/h/ln) Cmix = mixed-flow capacity (veh/h/ln) φmix = exponent for the speed-flow curve (decimal) After the general shape of the speed-flow function was defined, equations for the shape parameters were developed. The shape parameters for the freeway speed-flow curve were FFSmix, Scalib,cap, BPmix, Cmix, and φmix. Equations for these parameters were based on field and/or simulation data from a variety of traffic and roadway conditions. The speed-related shape parameters (FFSmix and Scalib,cap) were based on vehicles’ travel rates, which were expressed in units of s/mi. Travel rates were computed separately for automobiles, SUTs, and TTs. The travel rates for SUTs and TTs were based on travel time-versus-distance curves (e.g., Figure 2-13), while the automobile travel rate was a function of the truck travel rates, percentage of trucks, and flow rate of mixed traffic (vmix). The vehicle-specific travel rates were used along with the vehicle percentages to calculate the mixed-flow travel rate. This mixed-flow travel rate was converted to a mixed-flow speed. The mixed-flow speed was equal to FFSmix when vmix = 1 veh/h/ln and equal to Scalib,cap when vmix = Cmix. Figure 2-13. Travel time-versus-distance curves for a single-unit truck with an initial speed of 70 mi/h Source: Exhibit 26-5 from HCM 6th Edition (Transportation Research Board, 2016).

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 49 The flow-related shape parameters (BPmix and Cmix) were based on the shape parameters for the auto-only flow condition (BPao and Cao). The equations for BPmix and Cmix applied adjustment factors to BPao and Cao, respectively, in order to account for the effect of truck percentage, grade, and grade length on these values. The remaining parameter (φmix) defined how rapidly speed decreased with an increase in flow rate. The equation for this parameter depended on FFSmix, Scalib,cap, mixed-flow speed at 90 percent of capacity (Scalib,90cap), Cmix, and BPmix. The final set of shape parameter equations allowed users to construct a speed-flow curve that described the mixed-flow conditions on their analysis segment. While the shape parameter equations and general form of the speed-flow curve differ for freeways and two-lane highways, the approach described in this section can be adapted to two-lane highways. 2.5.4. Modeling Speeds of Heavy Vehicles for Simulation Microscopic traffic simulation tools are frequently used to model traffic operations and assess traffic performance. These tools enable traffic analysts to produce large amounts of data at a much smaller cost compared to collecting data in the field. While field data collection should not be eliminated entirely, simulation data can supplement limited field data that results from project and/or environmental constraints. As the transportation profession begins to take advantage of these simulation tools, it is important that engineers assess the accuracy of these tools to reproduce traffic conditions in the field. The accuracy of a simulation tool largely depends on the models and algorithms implemented within the software. One of the critical aspects of modeling traffic operations on two-lane highways is the performance of vehicles on various roadway geometry (e.g., upgrades, downgrades, horizontal curves). Accurately modeling the effect of this geometry on the speeds and accelerations of heavy vehicles is especially crucial when using the simulation tool to estimate the impact of heavy vehicles on traffic operations. Appendix D provides an overview of the research on heavy vehicle speeds and accelerations on different two-lane highway geometry. 2.5.5. Estimating the Impact of Heavy Vehicles on Traffic Operations Three approaches were considered in the development of the methodology to estimate the impact of heavy vehicles on two-lane highway traffic operations: 1) PCE values, 2) speed-flow curves for various combinations of roadway alignment and heavy vehicle percentages (similar to those in the German HBS), and 3) a general speed-flow function (similar to that in the mixed-flow model). The PCE approach has been the subject of some criticism. A preliminary evaluation was performed on this approach to assess its ability to estimate heavy vehicle impacts on two-lane highways. The results of this evaluation combined with a comparison of the other two approaches were used to guide the proposed methodology. This section describes the evaluation of the PCE approach, comparison of the German HBS and mixed-flow methodologies, development of the proposed methodology, and the corresponding experimental design. Evaluation of PCE Methodology An investigation was conducted on the use of PCE values to estimate the impact of heavy vehicles on two-lane highway traffic operations. Four scenarios were simulated in the simulation tool for this investigation. The roadway network for each scenario consisted of three straight links. The

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 50 first, second, and third links were 5280 ft, 3960 ft, and 2640 ft long, respectively. The first and third links had a 0 percent grade with 100 percent no-passing allowed. The second link was the analysis segment for which the PCE values were estimated. The grade and percent no-passing allowed for this link varied depending on the scenario being analyzed. The opposing flow rate also varied for each scenario. Table 2-9 lists the input values used for each scenario. All links had a FFS of 65 mi/h. PCE values for ATS were developed using Webster and Elefteriadou’s methodology (1999), the same methodology used to develop the current set of PCE values in the HCM. This methodology is the same as that originally proposed by Sumner et al. (1984), just applied to a different performance measure. This PCE estimation methodology is just referred to as ‘the PCE estimation methodology’ hereafter. The first step in the methodology is to develop speed-flow curves for the base and mixed traffic conditions. The base vehicle flow consists of 100 percent passenger cars. A 10 percent heavy vehicle mix was selected for the mixed vehicle flow. This heavy vehicle mix included 50 percent SUTs (FHWA classes 5, 6, and 7) and 50 percent IMSTs (FHWA class 8). The following flow rates were simulated to develop the base and mixed speed- flow curves: 350, 700, 1050, 1400, and 1750 veh/h. Six replications were simulated for each flow rate value. Table 2-9. Network Information for Scenarios Used in PCE Evaluation Scenario Number Grade of Analysis Segment (%) Percent No-Passing Allowed on Analysis Segment (%) Opposing Flow Rate (veh/h) 1 6 0 0 2 6 0 350 3 6 100 N/A 4 3 100 N/A The second step in the PCE estimation methodology is to develop the speed-flow curve for the subject traffic conditions. Per Webster and Elefteriadou’s (1999) suggestion, five percent of the passenger cars in the mixed vehicle flow were replaced by the subject vehicle (i.e., vehicle for which the PCE values were being estimated) to develop the subject vehicle flow. The following flow rates were simulated to develop the subject speed-flow curve: 400, 725, 1050, 1375, and 1700 veh/h. Six replications were simulated for each flow rate value. PCE values were initially estimated for IMSTs. Figure 2-14 presents the base, mixed, and subject speed-flow curves for scenarios 1 through 4. The speed-flow relationships in these figures are all as expected.

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 51 (A) (B) (C) (D) Figure 2-14. Speed-flow curves for PCE evaluation. A) Scenario 1. B) Scenario 2. C) Scenario 3. D) Scenario 4 The final step in the methodology is to obtain the base and mixed flow rates that yield ATS values equivalent to those produced by the subject flow rates. This was done through interpolation of the mean speed-flow curves as depicted in Figure 2-15 for scenario 2. 0 10 20 30 40 50 60 70 0 300 600 900 1200 1500 1800 Av er ag e Tr av el S pe ed (m i/h ) Flow Rate (veh/h) Base Mixed Subject 0 10 20 30 40 50 60 70 0 300 600 900 1200 1500 1800 Av er ag e Tr av el S pe ed (m i/h ) Flow Rate (veh/h) Base Mixed Subject 0 10 20 30 40 50 60 70 0 300 600 900 1200 1500 1800 Av er ag e Tr av el S pe ed (m i/h ) Flow Rate (veh/h) Base Mixed Subject 0 10 20 30 40 50 60 70 0 300 600 900 1200 1500 1800 Av er ag e Tr av el S pe ed (m i/h ) Flow Rate (veh/h) Base Mixed Subject

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 52 Figure 2-15. Flow interpolation issues with scenario 2 in PCE evaluation As shown in Figure 2-15, it was only possible to interpolate the base flow rate for the lowest subject flow rate in scenario 2. The remaining subject flow rates produced ATS values that were lower than the lowest ATS for the base vehicle flow. Consequently, it was not possible to calculate the PCE values for these subject flow rates. This result supports Dowling et al.’s (2014) findings (described in an earlier section of this document) and provides evidence to the argument that the PCE estimation methodology is too simplistic for situations with steep grades (or even long moderate grades) where there is any significant percentage of heavy vehicles. This interpolation issue was encountered in all of the remaining scenarios. For those cases where both the base and mixed flow rates could be interpolated, Equation (2-15) was used to estimate the PCE value. = 1∆ − + 1 (2-15) where PCES = the PCE value of the subject vehicle Δp = the proportion of the subject vehicle that is added to the mixed vehicle flow and subtracted from the base vehicle flow to obtain the subject vehicle flow (equal to 0.05 for scenarios 1 through 4) qB = the base vehicle flow (veh/h) qM = the mixed vehicle flow (veh/h) qS = the subject vehicle flow (veh/h) Table 2-10 shows the final set of PCE values obtained for each scenario. A value of “N/A” indicates that it was not possible to calculate the PCE value because the base and/or mixed flow 45 50 55 60 65 0 300 600 900 1200 1500 1800 M ea n Av er ag e Tr av el S pe ed (m i/h ) Mean Flow Rate (veh/h) Base Mixed Subject ?

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 53 rate could not be interpolated. Scenario 4 yielded the most PCE values, which can be attributed to the smaller grade used in this scenario. The research team used this scenario to continue its assessment of the PCE methodology. Table 2-10. Passenger Car Equivalent Values for Intermediate Semi-Trailer Trucks Flow Rate (veh/h) Scenario Number 1 2 3 4 390 N/A 19.099 N/A 8.909 690 N/A N/A N/A 5.839 940 N/A N/A N/A 4.861 1190 N/A N/A N/A N/A 1340 N/A N/A N/A N/A The next objective was to use the PCE values to estimate the ATS for the mixed flow rates in Table 2-10. Before this could be done, PCE values for the SUTs had to be estimated. These PCE values were then used along with the PCEs for the IMSTs to calculate a heavy vehicle adjustment factor for each flow rate, per the equation in the HCM. These adjustment factors were used to calculate the equivalent passenger car flow rates. The base speed-flow curve was then used to obtain the ATS corresponding to each of these flow rates. Table 2-11 presents the results of this calculation process. Table 2-11. ATS Estimations for Scenario 4 Using PCE Methodology Mixed Flow Rate (veh/h) Mixed ATS (mi/h) SUT PCE IMST PCE Heavy Vehicle Adjustment Factor (fHV) PCa Flow Rate (pc/h) PCa ATS (mi/h) Error in PCE Estimation of ATS (%) 372 61.04 7.243 8.909 0.5856 635 59.73 −2.14 659 59.68 3.781 5.839 0.7241 910 58.20 −2.48 923 57.87 3.509 4.861 0.7584 1217 57.03 −1.45 a. Passenger car The percent error between the ATS estimated using the PCE estimation methodology and the actual travel speeds obtained from the simulation tool were all less than 3 percent, as shown in Table 2-11. This indicates that the PCE methodology can provide reasonable estimations of the impact of heavy vehicles on two-lane highway travel speeds, so long as it is possible to obtain the PCE values. Since it is not possible to obtain PCE values for all two-lane highway scenarios, an alternative approach should be adopted. This approach should directly utilize the speed-flow curves for the mixed traffic, rather than translating the mixed flow into a base, passenger-car-only flow.

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 54 Comparison of German HBS and Mixed-Flow Model Methodologies The general idea behind the methodologies in the German HBS and mixed-flow model are the same. Both attempt to capture the interaction between passenger cars and heavy vehicles for a variety of roadway alignment and heavy vehicle percentages using speed-flow relationships. Where the two methodologies differ is on how to develop these speed-flow relationships. The HBS methodology does not use a functional form for the speed-flow relationship. Instead, figures depicting general speed-flow relationships are used for various combinations of horizontal and vertical alignment. The mixed-flow methodology does use a general functional form, which is calibrated to the local roadway conditions (e.g., heavy vehicle percentage, grade slope, and grade length). This methodology is much more complicated than the HBS methodology, since multiple calculations are required to calibrate the speed-flow function. It does, however, have the potential benefit of achieving a higher level of accuracy. The HBS methodology relies on a general classification of horizontal and vertical alignment to estimate the speed-flow relationship. Conversely, the mixed-flow model uses continuous values for the slope and length of the grade and heavy vehicle percentages. Therefore, for any given grade and heavy vehicle percentage, the mixed-flow model may produce more accurate estimations of the speed-flow relationship. It cannot, however, account for speed reductions due to horizontal alignment, since it was developed for freeways, where horizontal alignment is of little to no concern. Another benefit of the mixed-flow methodology is that it accounts for different distributions of the heavy vehicle mix. The relative percentages of SUTs to TTs, along with their travel rates, affect the calibration coefficients, which in turn affect the shape of the speed-flow function. The speed-flow curves in the HBS do not differ with the relative heavy vehicle distribution. Instead, the curves were developed using a typical distribution of heavy vehicles. The final difference between the HBS and mixed-flow methodologies is the average speed used in the speed-flow relationship. The HBS methodology uses an average speed of the passenger cars, whereas the mixed-flow methodology uses an average speed of the entire traffic stream. Both methodologies use these speeds to obtain a density value, which dictates the level of service of the segment. Proposed Methodology The methodology proposed for this study fuses components of the HBS and mixed-flow methodologies, while also adding a new segmentation approach that facilitates the analysis of a two-lane highway facility. The relatively simple classification of horizontal and vertical alignment from the HBS is combined with a general speed-flow relationship to produce a methodology that is easy to use and offers reasonable accuracy for an HCM analysis. Detailed information about the various components of this methodology are provided in their respective sections. 2.5.6. Classification of Horizontal and Vertical Alignment Similar to the HBS methodology, horizontal and vertical alignment were each divided into five classifications. These classifications were based on the reduction in FFS of a typical heavy vehicle

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 55 due to the alignment. Table 2-12 presents the reductions in FFS used to define the classifications of both horizontal and vertical alignment. Table 2-12. Reductions in Heavy Vehicle FFS Used to Classify Horizontal and Vertical Alignment Classification Reduction in Heavy Vehicle FFS (mi/h) 1 < 7 2 ≥ 7 < 14 3 ≥ 14 < 21 4 ≥ 21 < 28 5 ≥ 28 An ISST with a weight-to-power ratio of 110 lb/hp and an initial speed of 65 mi/h was chosen as a typical heavy vehicle. The upgrade speed versus distance curves and horizontal curve speed models discussed in the previous section ‘Modeling Speeds of Heavy Vehicle’ were used to estimate the reductions in FFS for this vehicle type. Horizontal and vertical alignment were divided into a range of conditions, and the largest speed reduction for each range was used to assign the classification value. Table 2-13 and Table 2-14 present the classification values for horizontal and vertical alignment, respectively. Speed-flow relationships were developed for each of these general horizontal and vertical alignment classes, which are presented in detail in Appendix F.

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 56 Table 2-13. Classifications for Horizontal Alignment. Radius (ft) Superelevation (%) <1 ≥1 <2 ≥2 <3 ≥3 <4 ≥4 <5 ≥5 <6 ≥6 <7 ≥7 <350 5 5 5 5 5 5 5 5 ≥350 <500 4 4 4 4 4 4 4 4 ≥500 <650 3 3 3 3 3 3 3 3 ≥650 <800 3 3 3 3 3 3 2 2 ≥800 <950 3 2 2 2 2 2 2 2 ≥950 <1100 2 2 2 2 2 2 2 2 ≥1100 <1250 2 2 2 2 2 2 2 1 ≥1250 <1400 2 2 2 2 2 1 1 1 ≥1400 <1550 2 2 2 1 1 1 1 1 ≥1550 <1700 2 1 1 1 1 1 1 1 ≥1700 1 1 1 1 1 1 1 1

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 57 Table 2-14. Classifications for Vertical Alignment (Downgrades in Parentheses). Segment Length (mi) Segment Slope (%) ≤1 >1 ≤2 >2 ≤3 >3 ≤4 >4 ≤5 >5 ≤6 >6 ≤7 >7 ≤8 >8 ≤9 >9 ≤0.1 1 (1) 1 (1) 1 (1) 1 (1) 1 (1) 1 (1) 1 (1) 2 (1) 2 (2) 2 (2) >0.1 ≤0.2 1 (1) 1 (1) 1 (1) 1 (1) 2 (1) 2 (2) 2 (2) 3 (2) 3 (3) 3 (3) >0.2 ≤0.3 1 (1) 1 (1) 1 (1) 2 (1) 2 (2) 3 (2) 3 (3) 4 (3) 4 (4) 5 (5) >0.3 ≤0.4 1 (1) 1 (1) 2 (1) 2 (2) 3 (2) 3 (3) 4 (4) 5 (4) 5 (5) 5 (5) >0.4 ≤0.5 1 (1) 1 (1) 2 (1) 2 (2) 3 (3) 4 (3) 5 (4) 5 (5) 5 (5) 5 (5) >0.5 ≤0.6 1 (1) 1 (1) 2 (1) 3 (2) 3 (3) 4 (4) 5 (5) 5 (5) 5 (5) 5 (5) >0.6 ≤0.7 1 (1) 1 (1) 2 (1) 3 (2) 4 (3) 4 (4) 5 (5) 5 (5) 5 (5) 5 (5) >0.7 ≤0.8 1 (1) 1 (1) 2 (1) 3 (3) 4 (4) 5 (4) 5 (5) 5 (5) 5 (5) 5 (5) >0.8 ≤0.9 1 (1) 1 (1) 2 (1) 3 (3) 4 (4) 5 (5) 5 (5) 5 (5) 5 (5) 5 (5) >0.9 ≤1.0 1 (1) 1 (1) 2 (2) 3 (3) 4 (4) 5 (5) 5 (5) 5 (5) 5 (5) 5 (5) >1.0 ≤1.1 1 (1) 1 (1) 2 (2) 3 (3) 4 (4) 5 (5) 5 (5) 5 (5) 5 (5) 5 (5) >1.1 1 (1) 1 (1) 2 (2) 4 (4) 4 (4) 5 (5) 5 (5) 5 (5) 5 (5) 5 (5)

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 58 2.6. Approach for Identifying Follower Status The percentage of followers reflects car-following behavior. Car following is a particularly important operational phenomenon on two-lane two-way highways. On these highways, faster vehicles catch up with slower vehicles, resulting in vehicular platoons where vehicle speeds are restricted by the speed of slow-moving platoon leaders. In the process, a vehicle leaves the free- flow state and enters into the following state. Car following has serious implications on operations and safety. In general, car following interactions on two-lane highways are known to be a function of traffic volume in the same direction of travel, opposing traffic volume (where passing zones are present), speed, and speed variation within the traffic stream in relation to traffic mix. Expectedly, these variables include factors that would primarily determine the amount of passing opportunities and platooning for a specific traffic stream. The percentage of followers is a key performance measure in itself, as well as a factor in other performance measures (e.g., follower density), for two-lane highway operations. However, unlike some performance measures that can be measured directly without ambiguity, such as speed and flow rate, the measurement of the percentage of followers involves a potentially subjective determination of what constitutes a vehicle being in a following position. Car following interaction (or lack thereof) is highly dependent on the proximity of successive vehicles in the traffic stream, typically measured using time headway. While the headway at which vehicular interaction starts is believed to be a stochastic variable and is largely dependent on driver characteristics, a single cut-off value has often been used in practice in identifying vehicles in following mode from those in free-flow mode. The percent-time-spent-following (PTSF) measure used in the current HCM methodology is defined as “the average percent of total travel time that vehicles must travel in platoons behind slower vehicles due to inability to pass on a two-lane highway”. Given the challenge of making such as measurement, the HCM states that the percentage of followers can be used as a surrogate measure for PTSF, and recommends using a fixed headway criterion of 3 seconds for identifying vehicles in a following status. Without a comprehensive study that determines follower status directly from driver responses during in-field driving experiments, it is not possible to develop a definitive criterion for follower status. Thus, previously proposed methods for identifying follower status have focused on developing criteria from traffic flow measurements, typically through the use of just headway or the use of headway and speed. The next section briefly discusses previous efforts in this area. 2.6.1. Literature Review First discussed are studies that utilized headways solely in identifying the following status or percent followers. Different headway thresholds have been identified by researchers to separate following vehicles from non-following vehicles. Next discussed are studies that used a combination of speed and headway to identify following status.

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 59 Headway Only Several studies have suggested a headway cut off value between 3 and 4 seconds in identifying vehicles that are in following mode (Van As, 2003; Hoban, 1984; Guell and Virkler, 1988; Pasanen and Salmivaara, 1993; Dijker et al., 1998; Shiomi et al., 2011). Dijker et al. (1998) proposed a headway cut-off value of 5 seconds for identifying trucks in platoon. Wasielewski investigated drivers’ car following patterns on a single lane of an urban freeway. A semi-Poisson model was applied to a database of 42,000 observed headways. It was found that the followers’ headway distribution is independent from the flow with a mean of 1.32 seconds and a standard deviation of 0.52 second (Wasielewski, 1979). Lay (1986) suggested three distinct states in regards to car-following interaction and vehicles’ proximity in the traffic stream. He used 2.5 seconds as a headway threshold for following vehicles, headways between 2.5 and 9 seconds for vehicles that are either in following or free-flow state, and a headway greater than 9 seconds for vehicles in free-flow state. Bennet et al. (1994) investigated critical headways at 58 study sites in New Zealand. Critical headway was defined as “the headway below which a vehicle’s speed is affected by the preceding vehicle”. Different techniques were used to establish the critical headway. Among them, the mean of relative speeds, the mean relative speed ratio and the exponential headway model were identified as the best techniques. Using those techniques, critical headway was found to be in the range of 3 to 4.5 seconds. Van As (2014) investigated the car following behavior using field data in South Africa. A new methodology was proposed. A vehicle was tracked over a length of highway to check if the following gap changed over the observation distance. If the gap remained constant, it was likely that vehicle was following. The study suggested two criteria for classification of vehicles as followers; following gap shorter than 3 seconds, and speed differential less than 20 km/h. The study found an average following headway of 1.2 seconds for light vehicles and 1.8 seconds for heavy vehicles. Penmetsa et al. (2015) studied two-lane intercity highways under mixed traffic conditions in India. The study utilized the clear gap between two consecutive vehicles in analyzing the following status. It was assumed that vehicles traveling in the same lane with a relative speed of 2 km/h or less to be in car-following mode. Then, the probability of not following was plotted against time gap using the 2 km/h rule. The gap corresponding to 50% probability was chosen as the critical gap, which was found to be 2.6 seconds. Al-Kaisy and Durbin (2009) investigated vehicular platoons on two-lane highways in Montana. Average travel speed was plotted against individual time headways at several study sites. The results showed that the increase in speeds is more notable at short headways and it diminishes when headways reach a value in the range of 5 to 7 seconds. Evans and Wasielewski (1983) suggested a headway threshold of 2.5 seconds for vehicles in car-following mode on freeways. The value of 2.5 seconds was suggested for traffic flow of less than 1450 vehicles per hour per lane, while 3.5 s was suggested for higher flow levels. In a study by Vogel (2002), the speed, distance headway and time headway data of more than 100,000 vehicles on urban roads in Sweden were analyzed. The study found that the speed of two successive vehicles are linearly dependent on time headway for headways up to 6 seconds. A

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 60 similar finding has been reported in a few other studies (Al-Kaisy and Karjala, 2010; Lobo et al., 2011; Hoogendoorn, 2005). Some other studies have reported the use of 5 seconds as the headway cut-off value for identifying free-flowing vehicles in the traffic stream (Fitzpatrick et al., 2005; Abdul-Mawjoud and Sofia, 2008; Polus et al., 2000; Figueroa and Tarko, 2005; Hashim, 2011). Headway and Speed The use of a headway-only criterion for determining follower status has received some criticism. From a conceptual viewpoint, it is reasonable to think that follower status is a function not just of headway, but also of speed. Furthermore, it is reasonable to think that the thresholds for these values can vary from driver to driver, rather than be constant values. This perspective is supported by a study by Al-Kaisy (2011). This study examined freeway flow and found that some drivers followed other vehicles at headways less than 3 seconds even though flow conditions were low and consequently they had plenty of opportunity to pass. The concept of follower status being a probabilistic function of speed and headway was outlined by Hoogendoorn (2005), which built upon work by Buckley (1968) and Wasielewski (1974), as well as Luttinen (1996). Hoogendoorn’s work was further extended and applied to two- lane highway conditions by Catbagan and Nakamura (2010). The stochastic approach proposed by Catabagan and Nakamura (2009) was evaluated in depth for this project and is discussed in Appendix E. 2.6.2. Following Status on Two-Lane Highways This study aimed to achieve a better understanding of the car-following interaction between vehicles on two-lane two-way highways. Such an understanding is critical for estimating car- following parameters that have been used in practice for identifying vehicles that are in following mode, an important aspect of operational analyses on two-lane highways. Moreover, the knowledge gained from this research is valuable in modeling two-lane two-way traffic operations using microscopic traffic simulation. Car-Following Process Car-following behavior, i.e., the interaction between successive vehicles sharing the same travel lane, has been the focus of research since the early developments in traffic-flow theories. This vehicular interaction becomes especially important on two-lane two-way highways where only one lane is available for each direction of travel. On these facilities, car-following interactions become a major determinant of the quality of service and an indicator of the amount of platooning, i.e., the time during which drivers are forced to travel at a speed less than their desired speed due to being impeded by other vehicles in same travel lane. Those interactions are expected to increase with the increase in traffic demand, increase in the percentage of slow moving vehicles (e.g., trucks), and as more restrictions exist on passing opportunities. It is believed that when the time gap (or headway) between two successive vehicles in the traffic stream gets smaller, the car-following interaction would start at some point and is usually reflected by the following vehicle adjusting its speed as it gets closer to the lead vehicle. This introduces an important parameter, referred to here as critical headway (hcr), and is defined as the time headway at which the car-following interaction starts. As the following vehicle continues to

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 61 approach the lead vehicle, the speed of the following vehicle and the headway between the two vehicles will continue to decrease until a point is reached when the speeds of the two vehicles will be approximately the same. At this point, the headway between the two vehicles represents what is perceived as the minimum safe headway (hmin). In this research, time headway and not gap is used to refer to the physical proximity of successive vehicles in the traffic stream on two-lane highways as it can directly be measured in the field. Like many other traffic phenomena, it is rational to assume that both hcr and hmin are stochastic variables that are mainly a function of driver characteristics. An important question this research attempts to answer is how close the following vehicle needs to be from the lead vehicle for this interaction to take effect; or in other words, what is the value of critical headway on two-lane highways? It is expected that this headway is primarily a function of the driver of the following vehicle. Specifically, more aggressive drivers may start to interact with the lead vehicle and adjust their speeds when they are very close to the lead vehicle (i.e., very small critical headway, hagg), while on the other hand, more conservative drivers may start to interact with the lead vehicle and adjust their speeds at a relatively large distance from the lead vehicle (i.e., very large critical headway, hcon). In following other vehicles, the majority of drivers start interacting with the lead vehicle at headways that fall between the critical headways for the former two driver types; i.e., the very aggressive and the very conservative drivers. This concept is shown in Figure 2-16. This figure clearly demarks the two boundaries: hagg and hcon. Vehicles that travel at headways less than hagg can generally be described as being in following state while those with headways greater than hcon can be described as being independent or in free-flow state. Typical values for the critical headway are expected to be in this range; i.e., between the boundary values hagg and hcon. Figure 2-16. Different headway states between successive vehicles A similar argument can be assumed for the minimum safe headways (hmin) between successive vehicles in platoons that are in following mode (i.e., not in passing mode) traveling roughly at the same speed as that of the platoon leader. Specifically, the “perceived” minimum safe headway is believed to be a stochastic variable generally varying in a range which represents the more aggressive and the more conservative drivers. hagg hcon

NCHRP 17-65 Improved Analysis of Two-Lane Highway Capacity and Operational Performance Final Report 62 The research effort to identify the method for identifying vehicles in a following mode is described in Appendix E. Summary of Findings This study presents an empirical investigation into the car-following interaction and the estimation of percent followers on rural two-lane highways. Field data from 15 study sites in Idaho, Montana, and Oregon were used in this investigation. The most important findings of this study are summarized as follows: 1. Results from the speed-headway investigation suggest that the critical headway (hcr) varies approximately in the range between a lower limit of 1 to 2 seconds and an upper limit of 6 to 7 seconds, with the majority of sites having a range between 1 and 7 seconds. 2. Vehicles traveling at perceived minimum safe headways increase in number as headways get smaller. While pairs of vehicles in free-flow state may still travel at the same speed, the percentage of these vehicles increases steadily as more vehicles enter into the following state. 3. Results from the analysis for determining percent follower headway cut-off value suggest that for class I highway, this value is likely to fall in the range of 1.8 and 2.8 seconds, lower than the current value used by HCM of 3 seconds. For class II and III sites, results suggest values that are slightly higher than 3 seconds. Further research is needed using data from more study sites, particularly on class II and class III highways, to affirm the findings of this study and gain additional insights into car-following parameters on rural two-lane highways. The research team has identified the critical headway value for identifying a vehicle in a following status as 2.5 seconds.