OPERATIONAL CONSIDERATIONS OF PASSING ZONES FOR TWO-LANE HIGHWAYS: SPANISH CASE STUDY

The U.S. Highway Capacity Manual (HCM 2010) methodology is used in Spain to evaluate traffic operation and quality of service. In two-lane undivided highways, the effect of limiting where drivers could pass slower vehicles, or passing restrictions, is considered through the percentage of no-passing zones. This measure does not account for how passing opportunities are distributed along the road. The objective of this research was to evaluate the effect percentage of no-passing zones and average passing zone length on a two-lane highway and, if significant, incorporate them in the analysis methodology,. The TWOPAS microsimulation program was calibrated and validated to the Spanish conditions. Passing restrictions had little effect on average traffic speed (ATS), with differences lower than 6 km/h between a road segment with no passing restrictions and a road segment with a passing restriction on 100% of its length. Con-versely, passing restrictions can increase the percent time spent following (PTSF) up to 30%. Increasing the passing zone length beyond 2,000 m does not improve PTSF. The new models could be used to better estimate traffic operation on Spanish two-lane highways.


INTRODUCTION
Two-lane undivided highways have a level of interaction between vehicles traveling in the same and opposite directions which results in unique operational characteristics. This is mainly because faster vehicles wishing to travel at their desired speed must use the oncoming lane to pass slower vehicles (where a passing lane is not present). To ensure road safety, design guidelines allow passing only in those zones where available sight distance is long enough to perform passing maneuvers and where oncoming traffic permits [1,2].
Passing behavior has been largely studied with different purposes. Most of the studies are centered on determining adequate passing sight distance criteria [3][4][5] and quantifying the number of passing maneuvers at isolated passing zones [6][7][8][9][10][11]. Rare are studies that explicitly link passing zone characteristics to traffic operations.

Evaluation of quality of service on two-lane highways
In order to analyze traffic efficiency, Spanish standards [2] rely on the procedures of the U.S. Highway Capacity Manual (HCM) [12]. For two-lane highways, the level of service is based on one or more of three performance measures, depending on highway classification [24]. However, they were removed on the current version [23] because its impact on speed was marginal compared to differences on roadway alignment [25]. As a result, actual characteristics and distribution of passing zones (number and length) are not used in any analysis procedure.

Effects of passing restrictions on traffic performance
Passing zone length may affect traffic operations. According to experimental data collected by Harwood et al. [4,26] to determine U.S. passing sight distance criteria, short passing zones with lengths of 120 to 240 m contribute little to the traffic operational efficiency of two-lane roads, with observed 0.77 passes per hour compared to 2.95 passes per hour at longer passing zones (passing zone length from 300 to 1,650 m). Additionally, Harwood et al. used the simulation program TWOPAS to evaluate the contribution of short passing zones. The results indicated that short passing zones had little effect on ATS or PTSF, compared to the total passing restriction [4].
Similar results on isolated passing zones were obtained in Spain [10] and Uganda [11]. Experimental data from external observations showed that increasing the passing zone length over 1,100 m did not improve the passing rate much [10]. Simulations in Aimsun with the same scenarios as Harwood et al. [4] indicated that passing zones shorter than 250 m add very little to operational efficiency compared to 100% no-passing zones, in terms of ATS and PTSF improvement [27].

Research statement
The HCM analysis procedure accounts for the effect of passing restrictions through the percentage of no-passing zones. Consequently, two highways with the same length, but the first with one passing zone of 2,500 m and the second with ten passing zones of 250 m, will have the same results, which is quite unrealistic, as previous studies concluded that very short passing zones contribute little to traffic operations [4,10,11]. To overcome this shortcoming, we added one second parameter: average passing zone length. Moreover, passing behavior field data used for the development of the HCM analysis methodology was from the 1970s [13,14], and it is not clear what changes in motorist passing behavior may have taken place in the subsequent years.
Therefore, there is a need to document current passing behavior and relate it to traffic performance, in order to determine when passing restrictions would limit traffic efficiency. Unfortunately, field measurements can be expensive, and, even more importantly, they rarely provide sufficient repeatability for the full range of traffic demands and passing restrictions. At this point, traffic microsimulation must be considered. [2,12]: average travel speed (ATS), percent time spent following (PTSF), and percent 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. PTSF is difficult to measure in the field, and the HCM recommends to use percent followers as the surrogate measure for field estimation of PTSF. The HCM procedure starts with estimating traffic performance for the base scenario (i.e., passing is allowed along the entire length of the segment), adjusting traffic demands to account for heavy vehicles and grade impacts. Then, passing restriction effects are considered through adjustment factors to the performance measures of specific segment. ATS has a linear relationship with directional and opposing traffic flow, while PTSF varies exponentially with directional traffic flow. Passing restriction adjustments depend on the percentage of no-passing zones and directional split. This ratio is complementary to the percentage of length on which vehicles can pass. However, this measure does not account for how passing opportunities are distributed along the road. Consequently, two highways with equal percentage of no-passing zones will produce the same operational results.
The adjustments to account for passing restrictions are based in large part on simulation results from the microsimulation program TWOPAS [13,14]. TWOPAS was originally developed by the Midwest Research Institute (between 1971 and 1974), and had occasional updates through the late 1990s. TWOPAS is currently packaged with the Traffic Analysis Module of the Interactive Highway Safety Design Model (IHSDM) from the Federal Highway Administration (FHWA). To develop the HCM procedure, field data collected in the 1990s was used to calibrate TWOPAS results on ATS and PTSF, although passing behavior was not updated [13]. Moreover, no indications on the precision of the adjustment or how passing zones were distributed were given [14].
Local adaptations of the HCM analysis procedure for two-lane highways were performed in Finland [15,16,17], Brazil [18,19], Argentina [20], India [21], and Spain [22], while Germany has its own analysis procedure [23,24]. The most commonly used performance measures (in all countries' two-lane highway analysis procedures) are ATS and PTSF, with notable exceptions being that Germany uses density; Finland does not consider PTSF, and the ATS of interest is just for passenger cars; and India includes the number of followers as a proportion of capacity. The effect of passing restrictions is considered through the percentage of no-passing zones in the U.S., Finland, Brazil, Argentina, and Spain. In India, passing restrictions are not considered because there are no delimited passing zones [21]. In Germany, passing restrictions were considered on the previous analysis procedure 4) Modeling traffic operations for the base conditions (i.e., no passing restrictions). 5) Modeling traffic operations for scenarios with passing restrictions. Tasks 1 and 2 were carried out as a part of a previous study that feeds into this research [22]. They are summarized in the following sections.

Field data
Data was collected across four passing zones located along the two-lane highway N-225 in Spain. The characteristics of the passing zones are summarized in Table 1.
Video recordings were made at the beginning and end of the passing zones. The videos were individually analyzed to obtain the time stamp of each vehicle. Directional traffic volume, traffic composition, average travel time, and time headway were obtained. The HCM recommends a 3-second headway threshold for the purpose of estimating percent followers (PF) [12]. The number of passing maneuvers was calculated by comparing the vehicles' order at the beginning and end of the passing zone. Variations on the order indicated the performance of passing maneuvers. Changes in two or more positions of the same vehicle were considered as one multiple passing maneuver. A total of 52 hours of video data was collected on N-225. Data was collected during daytime hours under good weather conditions, and the pavement was in good condition.
Passing behavior on N-225 was validated with observations from 12 additional passing zones [10] ( Table 2). Passing rate was used as a validation parameter. The results indicated that the observed passing behavior on N-225 did not differ much from other passing zones.

Calibration and validation of TWOPAS
The N-225 highway was created in TWOPAS. The posted speed equals 100 km/h, and it has 3.5 m lane width and 1.5 m shoulder width. Mean desired speed and standard deviation were estimated based on the unimpeded speed distributions, considering headways longer than 6 seconds [28]. Percentage of each vehicle type was assigned based on the observations. For passenger cars, maximum acceleration and overall The objective of this study was to analyze the effect of passing restrictions on two-lane highway traffic performance. Based on the results, criteria to analyze traffic operations on two-lane highways are proposed.

Basic hypotheses
Based on the literature review, the following hypotheses have been established: -Distribution of passing restrictions will influence traffic operations. Given the same percentage of no-passing zones, configurations with few long passing zones will perform better than configurations with many short passing zones. -Operational improvement due to passing will be minimized at high traffic volumes or at unbalanced traffic flows. Under those conditions, the number of passes would decrease as the gap sizes on the opposing traffic stream decrease. -The effect of passing restrictions will be higher on PTSF than ATS. The inability to pass directly affects PTSF, as this variable starts being computed when vehicles are not traveling at their desired speed. Nevertheless, the inability to pass reduces speed compared to the desired speed. Given that speed dispersion is not extremely high, the overall effect would be low.

METHODOLOGY
This study is based on microsimulation results from the TWOPAS program. TWOPAS was selected because it was previously used to develop the HCM analysis procedure, and it was the only program available at the time of the research that was calibrated using field data.
The methodology is as follows: 1) Documenting current passing behavior on Spanish two-lane highways. 2) Calibrating and validating TWOPAS by using a genetic algorithm. Passing behavior is also calibrated, as passing rate was included within the fitness function. 3) Generating and simulating multiple scenarios in TWOPAS with varying directional traffic flow, directional split, heavy vehicles percentage, and passing restrictions. Given that there were more speed-related variables than passing-related variables within the fitness function, assignment of equal weighting to all variables would likely produce suboptimal outcomes. Therefore, three combinations of weights were tested for the fitness function variables. The sensitivity analysis considered four generations for each combination. Ultimately, the combination that minimized the average error and individual variable error was: weighted passes 86%, percent followers 6%, and speeds 8%.
The genetic algorithm was executed for 80 generations of 40 individuals, 5 random seeds, and 30 traffic scenarios. Each simulation run was 15 minutes long, with a 15-minute warm-up period. The mean average square error was reduced from 7.9% (default values) to 3.8% (calibrated values). The 25 best calibration parameter combinations were validated with additional field data (60 traffic scenarios). The mean average square error was 4.3%, very close to the calibration error; compared to 7.9% for the default values.
Further details on the calibration can be found in [22].

Case study scenarios
The case study included a 10-km long straight segment, with percent grade equal to 0.5%. Passing restrictions varied as follows ( Figure 1 The goal of the calibration is to find the combination of parameters that minimizes the differences (ATS, PTSF, passing rate) between the simulation and field data. For this research, the genetic algorithm from Bessa and Setti [18,19] was utilized.
The genetic algorithm's objective is to minimize the fitness function. This function was defined as the mean average square error between the simulated results and field data (Equation 1). It depended on 20 parameters (10 per direction).
where: F -fitness function; M -number of road segments; N -number of demand periods; K -number of parameters. They include, per travel direction: number of passes, percent followers at the end of the segment (3 second headway criterion); average speed of passenger cars and trucks; standard deviation of speed of passenger cars and trucks; 15 th percentile from speed distribution of passenger cars; 15 th percentile from speed distribution of trucks; 85 th percentile from speed distribution of passenger cars; 85 th percentile from speed distribution of trucks; w k -weight of the parameter; V OBS -observed value; V SIM -simulated value.
where PTSF base is the percent time spent following for base conditions (i.e., 0% no-passing zones) [%]; a and b are coefficients. Other terms are as previously defined. The total number of simulations was 128,700 (257,400 directional scenarios). The maximum directional traffic flow was 1,540 veh/h (with 0% heavy vehicles), as higher traffic flows stalled TWOPAS. Therefore, the number of valid directional scenarios was reduced to 249,150.

Modeling base conditions
Two performance measures are analyzed: ATS and PTSF. Passenger car units from the HCM are not used. Instead, the effect of heavy vehicles is applied through the percentage of heavy vehicles, similar to the German procedure, but classified as a continuous variable. The values are obtained from the TWOPAS output file (*.OUT).
Base conditions (i.e., no passing restrictions) are modeled first for ATS and PTSF. They correspond to scenario 000-01. The statistical summary of the models is provided on the supplementary materials. The resulting best model for ATS is the same type as HCM 2010, i.e., linear model considering directional traffic flow rate, opposing traffic flow rate, and percent where ATS NPZ is the ATS adjustment factor for percentage of no-passing zones [km/h]; P NPZ is the percentage of no-passing zones [%]. Other terms are as previously defined. ATS decreases as the percentage of no-passing zones (NPZ) increases ( Figure 2). The effect of passing restrictions is very small in unbalanced directional splits (lower than 40/60), with reductions lower than 2 km/h. As directional split becomes more balanced, the effect is greater, up to 5 km/h. The maximum effect is produced at directional traffic volumes between 200 and 400 veh/h, where the passing rate is relatively high.
For all directional splits, the differences are practically zero at high directional traffic volumes. Passing zones are essentially no longer effective for balanced flows with directional traffic volume higher than 800 veh/h.

Percent time spent following
The best model to estimate the effect of NPZ on PTSF includes the directional traffic flow rate, opposing traffic flow rate, and percentage of no-passing zones (Equation 5). The correlation between the fitted and simulation values is 85%.
The adjustment factors for ATS and PTSF depending on NPZ (ATS NPZ and PTSF NPZ ) are modeled as the difference between simulation results and estimates for the reference scenario (000-01). Different combinations of independent variables and functional forms are executed in the R statistical software tool using the NLS package [29]. AIC (Akaike Information Criterion), correlation between fitted values and simulation values, beta parameters, p-value of the variables, and number of parameters are then used to determine the best model at each case. Coefficient of determinations and pseudo R 2 are added only to linear regression models. The statistical summary of the best model for each case is provided on the supplementary materials.

Average travel speed
The best model to estimate the effect of NPZ on ATS is polynomic and considers directional traffic volume, opposing traffic volume, percentage of heavy vehicles and percentage of no-passing zones (Equation 4). Pseudo R 2 is 33.7%, and the correlation between the fitted and simulation values is 58%. Directional   factors for PTSF are modeled because the influence of passing restrictions on ATS is quite low and comparable to the dispersion of the variable. As in Section 2.5, the adjustment factor for PTSF depending on PZL (PTSF PZL ) is calculated as the difference between simulation results and estimates for the reference scenario (050-01). Then, different combinations of independent variables and functional forms are tested.
The best model for PTSF PZL includes the directional traffic flow rate, opposing traffic flow rate, and average passing zone length (Equation 6). The correlation between the fitted and simulation values is 63%. The difference to the reference scenario (050-01, one passing zone of 5,000 m) was used to evaluate the effect of reducing the passing zone length.
where PTSF PZL is the PTSF adjustment factor for average passing zone length [%], and L PZ is the average passing zone length [m]. Other terms are as previously defined. Additionally, the difference between the model estimations for 50% NPZ and for 100% NPZ is calculated to compare with total passing restrictions ( Figure 4) where PTSF NPZ is the PTSF adjustment factor for percentage of no-passing zones [%]. Other terms are as previously defined. The effect of NPZ is higher for PTSF than for ATS (Figure 3). For low traffic volumes, increasing NPZ can increase PTSF up to 40 %. The differences increase as the directional split is more balanced. For directional splits below 40/60, PTSF is practically equal on the base conditions and 50% NPZ, and the difference is up to 20% for 100% NPZ. For balanced flows, the influence is maximized for directional traffic volume of 200 veh/h: 7% and 23% increases in PTSF for 50% and 100% NPZ, respectively. As the directional split is less balanced, the differences are greater, and the maximum influence moves to higher directional volumes, between 250 and 350 veh/h.
On the other hand, the PTSF-improving effect of passing zones disappears at high traffic volumes. The exact value depends on the directional split: 400 veh/h for 30/70, 800 veh/h for 50/50, and 1,250 veh/h for 70/30.

Modeling the effect of average passing zone length
Given the high differences on PTSF between 50% NPZ and 100% NPZ, the effect of average passing zone length (PZL) is also analyzed. Only adjustment is around 5 km/h. Therefore, the influence of average passing zone length is not evaluated as the effect will be close to the dispersion of the variable. Simulation results are compared to HCM estimates for ATS. Average differences are calculated and plotted depending on directional traffic volume, directional split, and average passing zone length ( Figure 5). Differences are lower than 2 km/h on average for passing zones longer than 1,250 m and directional splits over 60/40. For different conditions, differences can be up to 8 km/h.
The PTSF-improving effect of passing zones disappears at high traffic volumes or when opposing traffic volume is significantly higher than directional traffic volume. The model estimates differences greater than zero for average passing zone lengths shorter than 2,000 m. Therefore, increasing passing zone length beyond 2,000 m does not improve operational efficiency, regardless of directional split. For balanced flows, reducing passing zones from 5,000 m to 1,000 m only increases PTSF up to 5%. PTSF increases by 11.7% for passing zones of 500 m, compared to passing zones of 5,000 m. Conversely, very short passing zones contribute very little to traffic efficiency and have similar results as total passing restrictions.
Simulation results are compared to HCM estimates for PTSF. Similar to ATS, average differences are calculated and plotted ( Figure 6). Differences between to 20%, even though they have the same percentage of no-passing zones. On the other hand, the difference between 2,500 and 5,000 m is practically zero. Therefore, increasing the passing zone length beyond 2,500 m does not improve traffic performance.
Similarly to NPZ, differences disappear at high traffic volumes. The value depends on the directional split and increases as it becomes more favorable. As seen, the difference decreases as the directional traffic flow rate increases, as passing opportunities decrease on the opposing lane. From that traffic demand, increasing average passing zone length will not improve traffic performance. The exact traffic demand where passing zones are no longer effective depends on directional split: 400 veh/h for 30/70; 800 veh/h for 50/50, and 1,250 veh/h for 70/30.

DISCUSSION
The effect of passing restrictions on ATS is quite low. This result suggests a marginal effect on ATS, compared to other variables that directly affect speeds along curves, such as higher presence of curves with smaller radii. The result agrees with the simulation results in Germany [25]. Moreover, the difference between 50% of passing zones and no passing at all is lower than 3 km/h, and the dispersion of the variable   level terrain, straight segments, and good pavement conditions. Other highways with higher presence of curves or considerable passing restrictions may need local adaptation. The extrapolation of these results to other geographical areas should be undertaken with caution, since drivers' behavior may vary. Other software could provide different results derived from their specific structure and their passing acceptance model. It is beyond the scope of this paper to compare calibrated traffic microsimulation software and its results on traffic performance measures. By using the same software as Harwood et al. [13,14], we minimized the impact of such limitation. Finally, the most appropriate performance measure for two-lane highways is still open for discussion. Field studies indicated that follower density was the most promising performance measure, as it presented the highest correlation to traffic variables. Further research will be needed to model alternative performance measure(s), such as density, follower density, or percent impeded, and under different geometric conditions, such as posted speed limit, terrain, or horizontal alignment.

CONCLUSION
The research evaluates the influence of passing restrictions on two-lane traffic performance. Current passing behavior was collected in passing zones with a posted speed limit of 100 km/h. The TWOPAS microsimulation program was calibrated with a genetic algorithm and validated with additional field data. Then it was applied to different scenarios with varying directional traffic flow, directional split, percentage of heavy vehicles, and passing restrictions.
The passing zone length should be included in the analysis to evaluate PTSF. Increasing the passing zone length beyond 2,000 m does not improve PTSF, while passing zones shorter than 250 m do not contribute to operational efficiency and produce the same traffic performance as total passing restriction. Based on these conclusions, the recommendations of the study are: -ATS can be calculated using Equations 2 and 4.
PTSF can be calculated using Equations 3, 5, and 6. This methodology is simpler than the HCM methodology and accounts for the effect of average passing zone length in PTSF. -Application of HCM equations to the analysis of Spanish two-lane highways is not recommended. Minor differences were observed for ATS. While the use of simulation provides sufficient repeatability for the full range of traffic demands and passing restrictions, the results are subject to some degree of uncertainty. They could be derived from the structure of the model, the values of the model parameters, or methodological choices, such as case study scenario definition. Calibration and validation of the model are crucial to reduce the degree of uncertainty, as well as using multiple random seeds. The conclusions of the study are limited to the observed and generated simulation scenarios in TWOPAS: twolane highways with 100 km/h posted speed limit,

CONSIDERACIONES OPERACIONALES DE LAS ZONAS DE ADELANTAMIENTO EN CARRETERA CONVENCION-AL: CASO DE ESPAÑA RESUMEN
La metodología que se emplea en España para la evaluación de la funcionalidad del tráfico y la determinación del nivel de servicio es el Manual de Capacidad de Estados Unidos (Highway Capacity Manual -HCM 2010). En carreteras convencionales, las restricciones al adelantamiento se consideran a partir del porcentaje de zonas de adelantamiento no permitido. Esta medida no tiene en cuenta la distrución de las zonas de adelantamiento en el segmento. El objectivo de la investigación es la evaluación del efecto del porcentaje de adelantamiento no permitido y la longitud media de las zonas de adelantamiento en la funcionalidad del tráfico, y, en caso de ser significativos, incorporarlos a la metodología. El programa de microsimulación TWOPAS se ha calibrado y validado para las condiciones españolas. Las restricciones al adelantamiento tienen escaso efecto en la velocidad media, con unas diferencias inferiores a 6 km/h entre un segmento sin restricciones al adelantamiento y otro con restricción total. Por otro lado, las restricciones al adelantamiento pueden incrementar el porcentaje de tiempo en cola hasta un 30%. Aumentar la longitud media de las zonas de adelantamiento a partir de 2,000 m no mejora el porcentaje de tiempo en cola. Los nuevos modelos se pueden emplear para estimar la funcionalidad del tráfico en carreteras convencionales españolas.