1. Introduction
Toll roads provide a great convenience in the road transportation system. In China, toll collection mainly relies on the toll plazas; they are a crucial component of toll roads. By the end of 2021, the quantity of toll plazas in China had increased to 972 [
1]. Since electronic payments have not been fully popularized yet, the majority of toll plazas in China are traditional mainline toll plazas (TMTPs), which consist of both electronic toll collection (ETC) and manual toll collection (MTC) methods.
In the TMTP, drivers using electronic payment can pass through the ETC lanes at low speeds (20 km/h in China), but those paying with cash must stop at MTC lanes to finish the payment. Previous research has shown that there is a considerable speed differential between ETC and MTC vehicles in the diverging area of toll plazas [
2]. However, vehicles with different toll collection types are not restricted by lane markings or separation facilities in the diverging area of the TMTP. Vehicles need to complete the diversion and select their matching toll collection lanes within a limited distance. Complex distribution of toll collection lanes and speed difference of ETC and MTC vehicles result in the diverging area becoming a hot spot of frequent crossing behaviors and rapid decelerations [
3,
4,
5,
6]. These aggressive driving behaviors caused a large number of conflicts [
2,
7]. There is an urgent need to explore the conflict mechanism in the diverging area of toll plazas so a corresponding effective policy can be developed.
Modeling the relationship between traffic conflict risk and contributing factors can help us understand how these factors cause conflict risks [
8,
9,
10]. Numerous robust econometric models have been employed to investigate the possible association between conflict risk and influencing factors. Nevertheless, there may be some unobserved and unmeasured heterogeneity variables that make the existing factors less effective in explaining the observed results [
11,
12]. Especially on complex road nodes like toll plazas, drivers need to process more information simultaneously than on the road sections, such as choosing a matching toll lane with shorter waiting time. Ignoring such heterogeneity and assuming the effect of a contributing factor across all observations as the same will lead to biased and incorrect parameter estimation [
13]. The random parameter approach is applied to solve the problem of unobserved heterogeneity. As one of the random parameter approaches, the heterogeneity in the means and variances of the random parameters has been used to explore the mechanism of crash frequency and severity and obtained remarkable results [
14,
15,
16,
17].
In previous studies, the safety analysis of toll plazas is mainly based on historical crash data [
18,
19]. However, due to their insufficient quantity, crash data need to be collected for a long time before they can be used for analysis. Meanwhile, since most traffic conflicts have not further developed to crashes, it is not comprehensive to judge the traffic safety status of a region based only on crash data. With the development of information techniques, a growing number of devices are used to record vehicle traveling information, such as GPS, high-definition cameras, and unmanned aerial vehicles (UAVs). Vehicles’ high-precision trajectory data are extracted in large quantities and are being utilized more frequently to analyze traffic safety. Potential conflicts captured from trajectory data overcome the limitation of insufficient quantity and incomplete assessment of historical crash data. This study analyzes the characteristics of conflicts in the toll plaza diverging area based on the trajectory data collected by UAV.
Although several studies have assessed toll plaza conflict risks based on trajectory data [
2,
5,
7], they do not consider the conflict characteristics and influencing mechanism between vehicles with different toll collection types. Unlike driving on road segments, vehicles are additionally grouped with their toll collection types at toll plaza diverging areas that they need to drive to their matching toll booths. As mentioned above, the frequent crossing behavior between vehicles with different toll collection types is one of the key factors contributing to conflicts in the toll plaza diverging area. Therefore, this study aims to explore the influencing mechanism of vehicle conflict risks in the toll plaza diverging area from the perspective of different vehicle-following patterns with different toll collection types. To achieve this goal, trajectory data of vehicles were collected from a typical toll plaza diversion area in Nanjing, China, and the collision risk between vehicles at any angle was calculated by using the index of extended time-to-collision (ETTC). The conflicts between two vehicles are divided into four categories based on their toll collection types: (1) ETC-ETC, (2) ETC-MTC, (3) MTC-MTC, and (4) MTC-ETC, as shown in
Figure 1. Each combination indicates the toll collection type of the leading vehicle followed by the toll collection type of the following vehicle. Considering the ordinal nature of conflict risks and the unobserved heterogeneity of influencing factors, a heterogeneous random parameters ordered logit model is employed to analyze the causes of conflicts among vehicles with different payment methods.
This study focuses on the following directions for the traffic safety analysis in toll plaza diverging areas: (1) comparing the characteristics of conflict risks between vehicles with different toll collection types, and (2) analyzing the differences in the formation mechanism of vehicle conflict risks between vehicles with different toll collection types. The remainder of the paper is organized as follows.
Section 2, review studies, is about conflict risk modeling. In
Section 3 and
Section 4, major methodologies and data description are presented, respectively, followed by likelihood ratio tests in
Section 5. The results and discussion are presented in
Section 6. The paper concludes in
Section 7.
5. Likelihood Ratio Tests
To examine the differences in conflict severity outcomes between different ETC and MTC vehicle-following patterns and the spatial dependence in sub-segments, four groups of likelihood ratio tests were conducted.
To compare the models developed for four different vehicle-following patterns between MTC and ETC vehicles, the first series of likelihood ratio tests were conducted, which can be expressed as follows [
19,
29]:
where
is the log-likelihood at the convergence of the model estimated with all data,
,
,
and
represent the log-likelihood values at the convergence of the estimated models using different ETC and MTC vehicle-following patterns.
Moreover, to investigate the spatial stability of variables between different sub-segments of the diverging area, three sub-models were developed for three parts of the diverging area (denoted as D
1, D
2, and D
3; D
1 represents the downstream of the diverging area, including sub-segment 1–4; D
2 represents the midstream of the diverging area, including sub-segment 5–8; D
3 represents the upstream of the diverging area, including sub-segment 9–12, as shown in
Figure 4). The second series of likelihood ratio tests were utilized [
11]:
where
is the log-likelihood at convergence of a model containing parameters from y
2 while using data subset y
1, and
is the log-likelihood at convergence of the model using data subset y
1.
Table 2,
Table 3,
Table 4 and
Table 5 present whether the null hypothesis that the parameters are stable in the three parts of the diverging area can be rejected based on the results. For example, as shown in
Table 2, using the converged parameters of the D
2 model (y
2) as the initial values and applying them to the D
1 data (y
1) yields
with 9 degrees of freedom, indicating that the null hypothesis that the two parts of the diverging area are the same can be rejected at a 99.88% confidence level. Likewise, using the converged parameters of the D
1 model as the starting values and applying them to the D
2 data gave
with 8 degrees of freedom, demonstrating that the null hypothesis that the parts of the diverging area are the same can be rejected at a 99.65% confidence level. Other subsections have similar results that the null hypotheses can be rejected at a high confidence level.
6. Results and Discussions
A total of 24 variables are considered. All dummy variables are transformed to binary indicator variables, and numbers are appended to the variable names to distinguish the indicator variables (e.g., , ). Prior to modeling, the correlations between the variables are analyzed, and those with high correlations are removed. In addition, Z-score is used to standardize continuous data in order to eliminate the effects of dimension and make them comparable with other variables.
The results of the best-fitted random parameters ordered logit (RPOL) models and RPOL models with heterogeneity in means (RPOLMH) are shown in
Table 6,
Table 7,
Table 8,
Table 9 and
Table 10, as the variance heterogeneity is not statistically significant. These results consist of the estimation of parameter, t-statistics, and goodness-of-fit statistics (simulated log-likelihood at convergence, restricted log-likelihood, McFadden’s pseudo R
2, and AIC). On the basis of the RPOLMH models, likelihood ratio tests show that the null hypothesis of the performance of four models (
Table 7,
Table 8,
Table 9 and
Table 10) are the same with that of the combined model (
Table 6) which is rejected with over 99.9% confidence, indicating the separation of different vehicle-following patterns is reasonable.
For four vehicle-following patterns, the AIC values of the RPOL models are larger than those of RPOLMH, which demonstrates the RPOLMH models have better performance. The values of McFadden’s pseudo R
2 of four RPOLMH models also indicate the same result. The number of significant variables is almost the same in models for different vehicle-following patterns (
Table 7,
Table 8,
Table 9 and
Table 10). Specifically, nine variables, including the average traffic volume of the sub-segment (
), overall acceleration standard deviation (
), lane-marking indicator (
), the average acceleration within 3 s (
), the average speed within 3 s (
), the speed standard deviation of the following vehicle within 3 s (
), the standard deviation of ETTC of all vehicles in sub-segment (
), the mix measure of MTC and ETC vehicles (
), the percentage of vehicles with ETTC less than 4 s in sub-segment (
) are significantly associated with risk status in the toll plaza diverging area. Moreover, three variables are identified to be random parameters with heterogeneity in means (
,
, and
).
6.1. Traffic Condition Related Characteristics
According to the results of four RPOLMH models presented in
Table 7,
Table 8,
Table 9 and
Table 10, the coefficients of the proportion of risky vehicles around the vehicles (
) are positive, indicating that an increase in
has significant positive effects on the conflict risk for all vehicle-following patterns. One possible reason might be that when approaching the toll collection lanes, vehicles usually have an increase in lane-changing behaviors and acceleration and deceleration due to the toll booth restriction and speed limitation [
47].
According to a significant body of studies, the collision risk level increases as traffic volume rises. In our investigation, the coefficient of the average traffic volume of the diverging area () is found to be a random parameter with heterogeneity in means in all vehicle-following patterns, indicating that, in some cases, the collision risk level increases with low traffic volume. Such a result is reasonable since drivers are more likely to compensate for the increased traffic volume with more cautious behavior in the toll plaza diverging area. Similarly, another possible explanation for this outcome is that vehicles must wait in line to pass the toll lane when the traffic volume is high, thereby reducing the conflict risk.
6.2. Driving Behavior Related Characteristics
In terms of the variables related to initial lane and vehicle lane changes, interesting results have been found from the model estimation. Only
have significant effects on conflict risk level in ETC-MTC (
Table 8) and MTC-MTC models (
Table 9). However, the results are significantly different when the following is an ETC vehicle (
Table 7 and
Table 10). In ETC-ETC and MTC-ETC models, all effects of variables associated with the initial lane (
,
,
) are significant. When the initial lanes of the following ETC vehicles are
,
, or
, the conflict risk increases because ETC vehicles from initial lane 2 may intersect with vehicles coming from inside the diverging area. This implies that different initial lanes chosen by vehicles can result in differences in four vehicle-following patterns.
The average acceleration of the following vehicle within 3 s (
) is found to be a fixed parameter with significantly negative effect on the conflict risk level, indicating that traffic safety status improves as the average acceleration of the following vehicles increases. It is likely because the following vehicle would take an acceleration maneuver only when the driver perceives no collision risk around, and thus the collision risk level between the leading vehicle and following vehicle would decrease. Furthermore, the maximum acceleration in the whole diverging area of the following vehicle (
) also significantly increases the collision risk level of the ETC-MTC (
Table 8) pattern, while decreasing the collision risk level of other patterns.
6.3. Random Parameters with Heterogeneity in Means
Except for the MTC-MTC pattern, the speed standard deviation of the following vehicle within 3 s (
) and the standard deviation of ETTC of all vehicles in sub-segment (
) have random effects on collision risk level. According to
Table 7,
Table 8,
Table 9 and
Table 10, both the means and standard deviations of the two variables are statistically significant, indicating that the effects of the factors vary across different vehicle-following patterns.
Specifically, is identified as statistically significant random parameters in all RPOL models with heterogeneity in means for all vehicle-following patterns, indicating that the effect of has considerable variations across all observations. Overall, the coefficients of are positive, indicating that larger speed changes will result in higher levels of conflict risk. Regarding the standard deviation of ETTC of vehicles in sub-segment (), it produced significant random parameters among models for ETC-ETC, MTC-ETC, and ETC-MTC patterns. The effects of differ greatly across three patterns. To some extent, the larger standard deviation of ETTC reflects the fluctuation of traffic flow near the following vehicle, which may increase the conflict risk level. Nevertheless, a random parameter is not observed in the RPOLMH model for the MTC-MTC vehicle-following pattern. The possible reason is that MTC vehicles are required to stop before toll collection lanes and wait in queues, so the conflict risk of vehicles in the MTC-MTC pattern is quite different from that of other patterns.
Theoretically, vehicles choosing the toll lanes corresponding to their initial lanes directly do not need to change lanes, resulting in fewer conflicts. Interestingly, changing lanes to the left (1) has significant effects on collision risk level in the RPOLMH models for ETC-ETC and MTC-ETC patterns. It indicates that the lane change operation directly affects the collision risk level. If ETC vehicles change to the inner side of the main-line road in advance, there will be less interweaving between ETC and MTC vehicles in the diverging area. The coefficients of variable changing lanes to the right () are significant in the models for ETC-MTC, MTC-ETC, and MTC-MTC patterns. According to the layout of ETC and MTC lanes, MTC vehicles need to operate more lane changes to pass through the diverging area. Therefore, more vehicle-to-vehicle interactions may increase the conflict risk when MTC vehicles are involved in the vehicle-following groups.
Another important issue that cannot be overlooked is that some random parameters are not sufficient in measuring conflict risk alone and should be considered together with the other variables. In
Table 7,
Table 8,
Table 9 and
Table 10, the means of the random parameter for
and
are associated with lane-marking indicator (
) and the percentage of vehicles with ETTC less than 4 s in sub-segment (
). It is noteworthy that
can be regarded as a primary contributor to collision risk level. For example, in the model for the ETC-ETC pattern in
Table 7, when
is involved with
, the mean of the random parameter is 0.165 (0.404 − 0.239 = 0.165). Such a result indicates that the effects of
on the conflict risk level will greatly differ in sub-segments with and without lane markings to a large extent. One possible reason is that the psychology and behaviors of drivers change with the absence of land markings. Apart from the lane-marking indicator,
are also found to have an effect on the mean of the random parameter for TV
STD in the ETC-ETC pattern.