Platoon-Based Assessment of Two-Way Two-Lane Roads Performance Measure: A Classification Method

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Introduction
Two-lane roads make up the majority of road networks, encompassing both urban and suburban areas. In fact, the quantity of these roads surpasses that of any other road type, not only in the United States but also in numerous countries worldwide [1]. According to the report of Road Maintenance and Transportation Organization [2,3], about 29% of the roads in Iran are two-way roads. If we exclude the roads that provide access to villages, approximately 85% of Iran's rural road network consists of arterial roads and collector roads, which are predominantly two-way two-lane roads [2,3].
Two-way two-lane roads play an important role in road transportation facilities. Te creation of platoons on twolane roads is one of the factors that afect the characteristics and quality of trafc fow such as the average travel speed (ATS) on two-lane roads. For instance, the creation of a platoon results in an increase in the density of vehicles (ρ) and the number of overtaking (NO). On the other hand, it leads to a decline in the trafc performance of two-lane roads and the level of service (LOS) [4][5][6]. Te decline in the trafc performance of two-lane roads due to the creation of platoons has a negative efect on drivers' safety [7]. Te Highway Capacity Manual 6th [8] provides two performance indicators, namely, the percent time spent following (PTSF) and the average travel speed (ATS) which can be used for determining the LOS of the two-lane roads. Al-Kaisy and Durbin [9] defned ATS (average time spent) as the average percentage of travel time for vehicles traveling in platoons at a speed lower than the average travel speed. HCM [8] defnes PTSF as a function of the percentage of follower vehicles with time intervals which are less than 3 seconds. Hence, by determining the extent to which the relationship between ATS, PTSF, and platoon characteristics impacts the trafc performance of two-lane roads, it becomes feasible to enhance the estimation and prediction of the trafc fow and LOS.
Tis study aimed to provide a model for evaluating the impact of platoon characteristics including time headway (H t ), number of overtaking (NO), average platoon speed (APS), platoon size (PS), percentage of heavy vehicle (HV), and number of follower vehicles (NF) on the trafc fow of two-lane roads. Moreover, we tried to provide a classifcation of LOS based on the developed model. Considering these objectives, the study examined the creation of trafc platoons on two-lane roads which stemmed from the leader and follower vehicles including light or heavy vehicles. A nonlinear regression equation was obtained and was used for predicting the trafc fow by evaluating the variables of platoon characteristics and trafc fow and establishing a relationship between the variables. First, the number of followers per capacity (NFPC) parameter [10] was defned using the nonlinear model and the NF. Next, the LOS of the examined roads was checked and evaluated based on the model which was developed on the basis of NFPC and PTSF. Finally, the LOS was categorized based on the NFPC-HCMplatoon relationship using the k-nearest neighbor (KNN) algorithm.

Literature Review
An examination of the previous studies on the capacity of two-lane roads reveals that these studies have primarily concentrated on three key aspects: LOS and capacity, platoon changes, and time headway and spacing headway. In the frst group of the aforementioned studies, several research works have investigated the infuence of various parameters, such as the number of platoons formed by vehicles [11], the HV [12][13][14] [15], the NFPC [16,17], speed of followers and critical H t as functional characteristics [18,19], the PTSF and the ATS [20][21][22], geometric parameters (longitudinal slope and superelevation of the road) [23,24], geometric features of the road and trafc conditions (density, speed, and the trafc fow rate) [25][26][27], and density [28] and travel speed using passenger car equivalent [29] on the LOS and road capacity.
In the second group of the previously mentioned studies, specifc research works have emphasized parameters related to platoon formation, such as identifying the timing of platoon creation based on the volume of vehicles passing through [30], H t [31][32][33], the speed of followers, the average time and spacing headway [34], HV [35], and the NO [36,37]. Finally, in the third group of the abovementioned studies, a number of studies have investigated the impact of certain parameters such as density and speed and trafc fow rate on time and spacing headway [38,39];. Among these studies, the works conducted by Penmetsa et al. [16], Al-Kaisy et al. [40], and Jain et al. [10] carried out more comprehensive investigations than other studies. Penmetsa et al. introduced an auxiliary parameter known as NFPC. Tis parameter addressed the attributes of follower vehicles and road capacity. Te calculated value of NFPC is utilized to determine a parameter known as the percentage of followers (PF) [41]. According to the HCM [42], PF is considered as an alternative measure that can be employed to calculate PTSF. Te equation of NFPC, which was provided by Penmetsa et al., examines the volume value based on 6 parameters, namely, ATS, ATSPC, ATS/FFS (free fow speed), ATSPC/ FFSPC, PF, and FD (follower density). Te examination of the abovementioned categories of studies shows that various studies have investigated one or several parameters of the platoon characteristics or the trafc fow.
In recent years, none of the relevant studies has comprehensively examined the efect of platoon characteristics including H t , ATS, PS, APS, HV, PTSF, NO, and ρ on the volume and quality of trafc fow. Te present study examined the impact of platoon characteristics on the quality of trafc fow on two-lane roads. Moreover, it developed a model based on capacity and LOS. Finally, the study compared the efect of platoon characteristics on the LOS (in the form of PF) and PTSF based on HCM [8]. Te last objective of the study constituted one of its innovative aspects. Moreover, this study carries out LOS classifcation based on all platoon parameters using the KNN algorithm for the frst time.

Research Methodology
For this study, four case study sites in Iran were chosen to assess the impact of platoon characteristics on the quality of trafc fow on two-lane roads. Te platoon parameters were assessed using the videography analysis methodology. Following the initial investigation, a Pearson correlation statistical analysis was conducted to validate the data, examining the relationship between each platoon variable and trafc fow. Subsequently, a nonlinear regression model was developed to explore the impact of platoon characteristics on trafc fow. After establishing the nonlinear regression model for trafc fow on two-lane roads, an alternative parameter was proposed as a substitute for ATS and PTSF, as indicated in HCM [8], to evaluate LOS. Lastly, the KNN model was employed to classify the LOS by assessing the extent to which the relationship between platoon characteristics infuenced the obtained NFPC. Figure 1 provides an overview of the steps undertaken in this study.

Case Study Sites and Data Collection.
To investigate the impact of vehicle platoon characteristics on the quality of trafc fow on two-lane roads, four road sections were selected in Iran: Fuman-Saravan (site 1), Rasht-Jirdeh (site 2), Rasht-Somesara (site 3), and Kiasar-Sari (site 4). Tese road sections belong to the rural class I road category. Figure 2(a)-2(d) (obtained from the free online resources of Google Earth (GE)) displays the selected sites. Te trafc fow volume varied from relatively high to low, with a mix of light and heavy vehicles. Consequently, a straight and longitudinal stretch of 60 meters was chosen as the measurement location for fow, ATS, and platoon characteristics. Videography analysis was conducted at a frame rate of 30 frames per second to extract feld data. Te weather conditions during the analysis were daylight, clear, and sunny, with the pavement in good condition. Furthermore, the study disregarded the efects of the longitudinal slope, intersections, and horizontal alignments in the straight sections of the road. Te speed limit on the examined roads was 90 km/h, and each lane had a width of 3.65 meters. Figure 2 provides an overview of the case study sites.
As shown in Table 1, the data, which were used in this study, were the data on the fow and platoon characteristics such as ATS, H t , ρ, HV, PTSF, NO, PS, and APS. Te data were collected in a 5-minute interval during an 8-hour period of time. As shown in Table 1, the minimum trafc fow had 70 Veh/h. On the other hand, the maximum trafc fow had 1810 Veh/h with a maximum density of 55 Veh/km. Furthermore, while the ATS of passing vehicles was 67 km/h with the minimum H t of 2 seconds, the maximum H t of the vehicles was 35 seconds and the average value of all of the examined roads was 7.69 seconds. Te maximum and the minimum speeds of the platoons were 68 and 25 km/h, respectively. Te maximum observed NO was 96 N/h. In

Journal of Advanced Transportation
Fuman-Saravan

Results and Discussion
In order to determine the efect of the platoon characteristics on the quality of trafc fow, the results of Pearson's correlation analysis were examined. Tese results expounded on the efect of each of the variables on the other variables. Moreover, they showed the impact of each of the relevant variables on the trafc fow. Te researchers used nonlinear regression modeling to improve the accuracy of the developed trafc fow model based on the Pearson correlation results regarding the relationships between the platoon characteristics and the trafc fow and the relationships between each of the platoon characteristics and the other platoon characteristics. Figure 3 illustrates the distribution of feld data collected from the examined sites, categorized by trafc fow. Tis fgure showcases the variations in platoon parameters based on the trafc fow. Figures 3(a)-(3e) specifcally depict the changes in Ht, PS, NO, PTSF, and APS, respectively. Heavy vehicles have the potential to generate more platoons within the trafc fow due to their tendency to assume leadership positions. Given the composition of heavy vehicles in the trafc fow across the four examined road sites, it was observed that a signifcant portion of the trafc fow was attributed to heavy vehicles. Consequently, the creation of platoons and an increase in the trafc fow led to an increase in PS (Figure 3(b)). Tis increase in PS, in turn, contributed to an increase in PTSF (Figure 3(d)). In addition, the rise in PTSF resulted in a decrease in APS and Ht (Figures 3(a) and (3e)). Ultimately, these changes in the trafc fow led to an increase in NO (Figure 3(c)). Pearson's correlation test was used to check the significance of feld statistics for platoon characteristics and to determine their relationships with trafc fow. Table 2 shows the results of Pearson's correlation test regarding the relationships between the platoon characteristics and the trafc fow and the relationships between all of the platoon characteristics. A negative correlation indicates an inverse relationship between the parameters. For example, as APS increases, NO decreases (r � −0.876). According to the distribution of feld data, the highest correlation between the fow and platoon characteristics was related to APS. On the other hand, the lowest correlation was related to H t .

Analysis of Platoon Characteristics on Trafc Flow.
Te most positive correlation was established between ATS and APS. It can be stated that the increase in the ATS was accompanied by the increase in the APS. Moreover, the highest negative correlation was the correlation between ρ and APS. Consequently, it can be argued that the decrease in the average platoon speed was accompanied by an increase in the density. Figure 4 shows the efect of vehicle density on trafc fow in the 4 examined sites. Te results showed that the increase in the density of vehicles was accompanied by an increase in the rate of trafc fow. Te increase in this rate continued until the fow reached its maximum value. After passing the maximum point, the trafc fow rate decreased. Figure 5 shows the efect of vehicle density on ATS. Moreover, it shows that the increase in the density of vehicles was accompanied by the decrease in the ATS of vehicles.

Nonlinear Regression Model.
Pearson's correlation test was used to determine the correlation between the independent variables. Te examination of the results of this test showed that the relationships between some of these variables were not signifcant. Moreover, based on the results, the aforementioned correlations were not linear. For example, in Table 2, the signifcance level of the correlation between the fow and APS was 0.046. Tis level is not acceptable at the 99% confdence level. Moreover, the direction of the data (positive or negative) regarding a certain independent variable difered from the direction of the data regarding the other indirect variables. For instance, there were negative correlation between the trafc fow, and H t , APS, and ATS. Terefore, in this section, nonlinear regression was used to increase the accuracy of the model (equation (1)). Te data on platoon as an independent variable and the data on fow as a dependent variable were entered into SPSS in order to develop the model. Te R 2 value of the developed model was equal to 0.87. Consequently, there were good correlations between the relevant variables.
where f is the trafc fow (Veh/h), ATS is average travel speed (km/h), HV is heavy vehicles (%), PS is the platoon size of vehicles (N/h), NO is the number of overtaking (N/h), APS is the average platoon speed (km/h), H t is the time headway (s), PTSF is the percent time spent following (%), and ρ is the density (Veh/km).

Model Validation.
Two statistical tests were employed to validate the developed nonlinear model of trafc fow and the independent variables (equation (1)). Te frst test aimed to demonstrate the absence of collinearity among the independent variables of the nonlinear regression model, while the second test was conducted to assess the accuracy of the  (1)), the tolerance value was calculated using the equation T � 1 − R 2 , and the VIF value was determined using the equation VIF � 1/T. In the regression model, T �1−0.87 � 0.13, resulting in a VIF value of 7.69. Tus, the model did not exhibit any issues of data collinearity. According to Figure 6, the proposed nonlinear regression model gives a good performance in terms of regression coefcients (R 2 ) in the prediction model. Te proposed model was able to predict the trafc fow on twolane roads in a satisfactory way. Moreover, the regression coefcient of the model was approximately 0.928 compared to the actual data.

NFPC-PTSF Model.
After providing the nonlinear regression model, equation (2) was proposed as a function of NF and capacity on two-lane roads to examine the infuence of the vehicle platoon characteristics on the quality of trafc fow and to determine the LOS based on the NF and capacity. Equation (2) was obtained by substituting the NF for the maximum fow function as the NFPC variable.    Journal of Advanced Transportation where NFPC is the number of followers per capacity in twolane roads, NF is the number of followers (Veh/h), and f max is the maximum trafc fow (Veh/h). Furthermore, Figure 7 shows the results of the efect of platoon characteristics on the LOS as a function of NFPC and PTSF by substituting equation (2) in equation (3). According to equation (3) and Figure 7, the LOS was classifed into fve categories ranging from category A to category E based on the NFPC and PTSF in the examined roads. It can be observed that the increase in the NFPC was accompanied by the increase in the PTSF and platoon and the reduction in the LOS.
PTSF � 120.07NFPC + 54.32. (3) According to the results, which are shown in Figure 7, in order to provide a model for evaluating the LOS on two-lane roads under the infuence of platoon, there was a need to examine NFPC. Table 3 provides the results regarding NFPC. According to Figure 7 and Table 3, LOS classifcation was divided into 5 parts from LOS A to LOS E as a percentage. As shown in Table 3, the proposed method was able   In order to use the proposed model in the examined roads, the capacity and LOS of the two-lane roads were compared with these values in HCM [8] and the study by Penmetsa et al. based on the NFPC and PTSF. Table 4 shows the results of this comparison. In site 1, the capacity was obtained as LOS E according to the NFPC. However, in site 4, the capacity was determined as LOS B. Moreover, the examination of the infuence of the PTSF on road capacity (according to Table 4 and equation (2)) showed that the proposed two-lane road capacity became 1810 Veh/h (equivalent to 2080 pcu/h) due to the 65% increase in the average PTSF which was accompanied by 21% reduction in capacity compared to the capacity of two-lane roads in HCM [8] which was equal to 2650 Veh/h.
In addition, the investigation of HCM [8] for two-lane roads in the examined roads indicated that HCM [8] classifed LOS on these roads under three categories ranging from C to E by means of ATS and PTSF, respectively. Nonetheless, in the present study, the LOS was classifed into three categories ranging from A to E according to NFPC and PTSF. Furthermore, the examination of the classifcation based on the LOS of each road relative to HCM [8] showed that the LOS of site 2 was B on the basis of the proposed method. Nonetheless, in HCM [8], the LOS was C. Consequently, the proposed method was able to classify the LOS properly under unsaturated-to-saturated conditions and high PTSF by taking account of the efect of the capacity of each road in comparison with HCM [8] which used ATS and PTSF.
In site 3 (where the trafc fow was high), the LOS did not change compared to HCM [8]. Accordingly, the proposed method was able to predict the LOS under the unsaturated-to-saturated conditions on two-lane roads in a more satisfactory way compared to HCM [8]. Nonetheless, LOS was the same in the saturated and oversaturated conditions in comparison with HCM [8]. Terefore, it can be concluded that on the examined class I roads, the NFPC measure was able to predict the LOS of the two-lane roads in a more satisfactory way in the unsaturated-to-saturated conditions compared to the two measures of HCM [8] including PTSF and ATS.
Comparing the present study with the study of Penmetsa et al. in Table 4, it can be shown that in the unsaturated and saturated conditions, the present study is able to consider the LOS B and LOS C for the unsaturated condition and LOS E for the saturated condition considering the platoon characteristics on the trafc fow. However, in the study of Penmetsa et al., the comparison between the results of the present study and the results of the study by Penmetsa et al. in Table 4 show that in the unsaturated and saturated conditions, the present study was able to provide LOS B and LOS C in the unsaturated condition and LOS E in the saturated condition considering the efect of the platoon characteristics on the trafc fow. Notwithstanding, in the study by Penmetsa et al. [16], LOS A and LOS B were provided for the unsaturated condition and LOS C was provided for the saturated condition without considering the efect of platoon characteristics on the trafc fow. According to the roads which were examined in this study, the LOS that was provided by Penmetsa et al. based on the trafc fow and NF was overestimated in the unsaturated condition and was underestimated in the unsaturated condition. Consequently, the LOS did not match the conditions of the two-lane roads. Tis inappropriate assessment stemmed from the failure to determine the conditions of platoon characteristics which afected the trafc fow on two-lane roads in the study by Penmetsa et al., but the present study was able to evaluate the efect of the platoon characteristics on the trafc fow using the nonlinear regression model and the measures which contributed to NFPC and PTSF and provided the LOS in a satisfactory way in the unsaturated and saturated conditions.

Efect of Platoon Characteristics on LOS Using KNN.
K-nearest neighbor (KNN) is a method used to explore the impact of two independent variables on a dependent variable. In this method, the efect of the independent variables is referred to as the nearest neighbor search (NNS). It is employed to identify the nearest neighbors in metric spaces, such as M, where the set S consists of multiple neighbors and a search neighbor q ∈ M. Te objective is to fnd the closest neighbor to q within S.
Tus, to determine the infuence of two independent variables related to platoon characteristics on the level of service (LOS) of two-lane roads using the proposed NFPC equation, we frst defne the two independent variables of platoon characteristics based on the service level set (S) as M1 and M2, with corresponding search neighbors q1 ∈ M1 and q2 ∈ M2. Next, the variables are evaluated using the NFPC equation according to the proposed LOS classifcations.
To evaluate the LOS under the infuence of platoon characteristics on two-lane roads, equations (2) and (3) and the nearest neighbor (NN) method were utilized. Tese results are depicted in Figures 8(a)-8(e). Figure 8(a) illustrates that higher HV and PTSF were associated with higher NFPC values. Furthermore, an increase in NFPC coincided with an increase in trafc fow and PS, as well as a decrease in LOS. Figure 8(b) displays the correlation between NO and APS, demonstrating the impact of these parameters on NFPC. As depicted in Figure 8(b), a decrease in APS corresponds to an increase in NO and NFPC, leading to a reduction in LOS. Figure 8(c) illustrates the relationship  between Ht, NO, and NFPC. According to Figure 8(c), a decrease in Ht between the vehicles corresponds to an increase in NO and NFPC, resulting in a reduction in LOS. Figure 8(d) illustrates the relationship between ATS and the density of vehicles and its efect on NFPC. As shown in Figure 8(d), an increase in ATS coincides with a decrease in density. Tis reduction in density leads to a decrease in NFPC and an increase in LOS. Figure 8(e) displays the relationship between the platoon and PTSF and its efect on NFPC. As shown in Figure 8(e), an increase in the PS of vehicles is accompanied by an increase in PTSF. In addition, an increase in PTSF corresponds to an increase in NFPC and a reduction in LOS.

. Conclusion
In this study, a model was created considering the impact of vehicle platoon characteristics on the quality of trafc fow on two-lane roads, taking into account the capacity and LOS. Furthermore, the infuence of platoon characteristics on LOS (in terms of follower vehicles) and the percentage of time spent following was examined based on HCM [8]. Te obtained results can be summarized as follows: (1) Te results of the Pearson correlation analysis regarding the impact of platoon characteristics on trafc fow on two-lane roads revealed that the trafc fow exhibited the highest correlations with platoon speed, number of vehicles (NO), platoon size (PS), average travel speed (ATS), density, percent time spent following (PTSF), heavy vehicles (HV), and headway time (Ht). (2) Furthermore, analyzing the direction (negative or positive) and signifcance level of the relationship between platoon characteristics and trafc fow revealed a strong and signifcant nonlinear correlation between them. Tis indicates that the relationship can be accurately calibrated and utilized to predict the trafc fow on various two-lane highways. proposed in HCM [8]. Te results indicated that a 65% increase in the average PTSF resulted in a 21% decrease in the capacity of two-way two-lane roads, thereby improving their LOS.

Data Availability
Te generated or analyzed data used to support the fndings of this study are included within the article.

Conflicts of Interest
Te authors declare that there are no conficts of interest.