A new method has been developed for estimating the capacity of an exclusive left lane with a permitted phase under nonstrict priority. Different from maneuvers under strict priority, these left-turning vehicles were released in the form of a left-turn group. A field survey was first conducted to explore the maximum number of vehicles in a left-turn group, and the releasing process of the permitted left turns. The observations revealed that (1) the maximum number is related to the intersection geometry and (2) the releasing process includes two stages: the first left-turn group crossing at the beginning of a permitted phase and the following left-turn groups crossing using gaps provided by opposing right turns. Next, a method based on probability theory and these observation results were applied to estimate the capacity of an exclusive left lane. The procedure contains two stages and eight steps. Finally, the estimation of the left-turn capacity using the proposed model was validated by comparing the capacity from the strict priority and actual maximum volumes.
At a signalized intersection, permitted left turns, either from shared lanes or from exclusive lanes, will have serious impacts on intersection operations. According to traffic laws, vehicular traffic turning left and facing a permitted phase must yield the right-of-way to oncoming traffic; however, this situation is not the case in some countries, including China, Norway, and Finland. Drivers in these countries may not follow the full compliance with the official priority rules and instead fail to yield [
In addition, scholars and engineers who study autonomous vehicles should also focus on the nonstrict priority behaviors of left-turning vehicles, especially for mixed traffic flow with human-driving and autonomous vehicles. At an intersection with permitted left-turning phase, through autonomous vehicles must pay close attention to opposed left-turning vehicles by human-driving and then decide whether it can cross the intersection. According to the capacity model under nonstrict priority, the significant factors will be obtained as well. Then, it can provide reference on optimizing the coordination strategy of the autonomous vehicles, to improve the capacity of the intersection with a permitted left-turning phase.
Many scholars have conducted studies on intersection capacity under a permitted phase. Existing methods can be categorized into two aspects: traditional method for two traffic flows with strict priority and platoon method for two flows with the same priority.
The traditional methods used to compute the capacity of a permitted left-turn lane mostly follow a strict priority [
The platoon method was first proposed by Wang [
According to Bai’s empirical study on permitted left-turning maneuvers, left-turning vehicles would release in the form of a left-turn group under nonstrict priority. In his study, a left-turn group is comprised of all the vehicles turning at the same time without interruption by through-vehicles (saturation flow) or all those turning without interruption and with a time headway of no more than four seconds (unsaturation flow), as shown in Figure
The definition of a left-turn group.
The objective of this study was to develop the capacity model of an exclusive left lane with a permitted phase under a nonstrict priority. A field survey was first conducted to explore the maximum number of vehicles in a left-turn group and the releasing process of permitted left turns. Next, methodologies for measuring exclusive left-lane capacity were proposed on the basis of survey results. The following section describes sensitivity analysis and a comparison analysis with the model under strict priority. The final section presents the conclusions.
To gain a better understanding of the permitted left-turn operations under a nonstrict priority, a field survey was conducted at 19 approaches from 8 intersections in the city of Changchun, China, during the months of April through September 2014. The survey was conducted during peak hour periods because a high left-turning flow rate is more likely to occur during those periods. Finally, a total of 648 cycles were observed.
Table
Description of field sites.
Intersection | Approach | Cycle length (seconds) | Number of surveyed cycles | Extension distance (meters) | Maximum volume of a left-turn group (pcu) |
---|---|---|---|---|---|
Feiyue rd.-Dongfeng str. | E. | 155 | 20 | 10 | 4 |
W. | 155 | 20 | 15 | 5 | |
Heping rd.-Haoyue str. | N. | 140 | 52 | 19 | 6 |
S. | 140 | 52 | 21 | 8 | |
W. | 140 | 52 | 23 | 7 | |
E. | 140 | 52 | 27 | 8 | |
Jianshe str.-Bei’an rd. | E. | 130 | 30 | 16 | 5 |
W. | 130 | 30 | 16 | 5 | |
Tongzhi str.-Chaoyang rd. | W. | 133 | 30 | 16 | 5 |
E. | 133 | 30 | 16 | 6 | |
Tongzhi str.-Zhonghua rd. | W. | 133 | 30 | 19 | 6 |
E. | 133 | 30 | 19 | 7 | |
Tongzhi str.-Xi’an rd. | S. | 175 | 20 | 36 | 9 |
Tongzhi str.-Ziyou rd. | N. | 187 | 30 | 19 | 6 |
S. | 187 | 30 | 20 | 7 | |
Zhuhai rd.-Huizhan str. | N. | 105 | 35 | 15 | 5 |
E. | 105 | 35 | 17 | 6 | |
S. | 105 | 35 | 17 | 6 | |
W. | 105 | 35 | 20 | 7 |
The definition of the extension distance.
Two significant results will be obtained from the field survey: the maximum number of vehicles in a left-turn group and the releasing process of permitted left turns. These survey results will offer the basis for measuring the capacity of an exclusive left lane with a permitted phase under nonstrict priority.
It is found that a left-turn group will accommodate more left-turning vehicles with the increase of the extension distance. The logarithmic model is found to provide a better fitting result, with an
The maximum left-turning volume for various extension distances.
The extension distance at these sites ranges from 10 m to 36 m. Because of the good-fit of the regression model, a length of 40 m was thought to be the maximum length for the application of equation (
Under nonstrict priority, permitted left-turning vehicles will cross the intersection in a left-turn group, which may lead to a severe delay for the opposed crossing flow. Thus, these vehicles will strive to maintain a small time headway to prevent being disturbed by the conflicting traffic flow, especially at peak hours. It is difficult for left-turning vehicles to find an acceptable gap in a continuous through-flow. Using the field survey, it was found that permitted left turns will release in two stages.
At the beginning of a circular green indication, no conflict traffic flows exist within the intersection. The first left-turning vehicle in the queue prefers a shorter path to cross the intersection to make the potential conflict point with opposed through-flows nearer to itself. This observation indicates that following vehicles in the left-turn group will certainly cross the intersection. As a result, when opposing through-vehicles approach the intersection, they have to stop to accommodate the crossing maneuver of a left-turn group. According to the surveyed data, 81 percent of all 648 cycles exhibit the phenomenon that a left-turn group took precedence over vehicles at the beginning of the permitted phase, as shown in Figure
Field surveyed results. (a) The flow crossing the intersection when the permitted phase start. (b) The reason why an acceptable gap for left-turn appears.
Stage 2 begins after vehicles in the first left-group have finished their turning movements and lasts until the permitted phase ends. After the first left-turn group is released, the opposing through-vehicles will release in a continuous flow. These vehicles will strive to maintain a small time headway to prevent being disturbed by the conflict traffic flow, especially at peak hours. It is difficult for a left-turning vehicle to find an acceptable gap in a continuous through-flow. Once a right-turning vehicle exists, an acceptable gap will appear in the opposing through-stream and a left-turn group will take the opportunity to finish their turns. Thus, the opposing through-vehicles after these right turns have to accommodate their crossing and be severely delayed, as shown in Figure
Opposing right turns provide opportunities for the crossing of left-turning vehicles.
How an acceptable gap appears was carefully observed in the field survey. The result is shown in Figure
According to the aforementioned analysis, the left-turning capacity in stage 1 can be calculated as the maximum number of vehicles in a left-turn group, as shown in the following equation:
Assuming that
In stage 2, the left-turning capacity is closely related to the number of opposing right turns. The arrival characteristics of right-turning vehicles should be first determined. There will be one left-turn group crossing the intersection as long as the opposing right-turning vehicle appears, regardless of how many of these right-turning vehicles are present.
At an entering approach, traffic flows are crowdedand and lane-change behavior is rare. Thus, the binomial distribution is selected to describe the arrival characteristics of right-turning vehicles, as shown in the following equation:
According to the aforementioned logic, each acceptable gap produced by right-turning vehicles could accommodate a left-turn group. In this step, the expectation of the gap number
No right-turning vehicles are arriving and left-turning vehicles cannot cross the intersection during the period. Thus, the expectation of the gap number
All the arriving vehicles are right-turning. The period selected is duration of a releasing time of all the left-turning vehicles in a left-turn group, and there will still be only one left-turn group that can finish turning movements. Thus,
In this case, the number of right-turning vehicles is less than that of the crossing-through vehicles. These
In this case, the number of right-turning vehicles is more than that of the crossing-through vehicles. In addition, the cross-through flow has no more than
The expectation of the gap number can be calculated using the following equation:
In this step, equation (
On the condition that there are
For equation (
Equation (
The left-turning capacity is the sum of CAP1 and CAP2, as shown in the following equation:
Regression analyses were conducted in this study to measure the accuracy of the proposed capacity model. In fact, it is difficult to obtain the actual capacity from a field survey because saturation flow will not last for the whole surveyed period. In addition, if left-turning vehicles always release in saturation flow, a protected phase should be considered at the intersection. In this study, the number of crossing left turns in three adjacent cycles is selected to convert into the observed maximum volumes in an hour. Scatter plots and regression lines for the proposed capacity are shown in Figure
Capacity model validation.
In the figure, the linear form is used to validate the capacity model. If the predicted value is equal to observed value, the regression line for scatter plots will be
Because of some unsaturated flows in the surveyed cycles, it is reasonable that an exclusive left lane cannot reach its capacity in reality. However, the predicted values from the method under strict priority are quite different from the surveyed values. Most of them are smaller than the observed maximum volume. This result indicates that an exclusive left lane can release more vehicles under nonstrict priority than that under strict priority.
There are eight parameters in the proposed capacity model. All these factors will have an impact on the left-lane capacity. Figure
Sensitivity of left-lane capacity to time headway of left turns and crossing through.
Figure
Sensitivity of left-lane capacity to opposed arriving volume and the rate of right turns
The work conducted in this paper is a continuation of the authors’ previous studies regarding nonstrict priority left-turning maneuvers to determine the capacity of an exclusive left-lane with a permitted phase. A new method to estimate the capacity was developed on the basis of the following observation results from field surveys at 19 sites: There are a maximum number of vehicles in a left-turn group that is related to the extension distance of an intersection Permitted left-turning vehicles always have nonyielding maneuvers and cross the intersection before through-vehicles when a green phase starts Left-turn groups will use gaps provided by opposing right-turns to finish their turning movements and severely delay through-vehicles, especially during peak hours
The methodology contained two stages: the first left-turn group crossing at the beginning of a permitted phase (stage 1) and the following left-turn groups crossing using gaps provided by opposing right-turns (stage 2). Probability theory and regression models were used in the computational process. In the model discussion, the time headway of the left-turning vehicles and the rate of opposing right-turning vehicles were proved to be more sensitive to the left-lane capacity. Next, left-turn capacities estimated by the proposed model were compared to the capacity from strict priority and observed maximum left-turning volumes. The results showed the model was valid to estimate the capacity of an exclusive left lane with a permitted phase under nonstrict priority.
The data of this research article are available from the first author upon request.
The authors declare that they have no conflicts of interest.
This research was supported by a project of the National Natural Science Foundation of China (No. 51278220).