A Collaborative Transit Signal Priority Method Considering Gaming among Traffic Participants

Wu, Bing; Wang, Haishan; Wang, Yanli; Zhai, Ben; Xue, TanXing

doi:https://doi.org/10.1155/2023/1974771

Journal of Advanced Transportation

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Abstract Introduction Evaluation Conclusions Data Availability Conflicts of Interest Acknowledgments References Copyright Related Articles

Research Article | Open Access

Volume 2023 | Article ID 1974771 | https://doi.org/10.1155/2023/1974771

A Collaborative Transit Signal Priority Method Considering Gaming among Traffic Participants

Bing Wu,¹Haishan Wang,¹Yanli Wang,¹Ben Zhai,¹and TanXing Xue¹

Academic Editor: Giulio E. Cantarella

Received24 Nov 2022

Revised05 Mar 2023

Accepted22 Mar 2023

Published21 Apr 2023

Abstract

How to realize the game equilibrium between bus and nontransit vehicle is a hot topic in the field of transit signal priority (TSP). To this end, a collaborative transit signal priority (Co-TSP) method is proposed. The core of Co-TSP is a two-objective optimization problem which takes the expected delays of buses and the average delays of nontransit vehicles as the objectives. Different from previous studies, Co-TSP uses game theory to realize collaborative optimization, instead of transforming the problem into a single objective optimization problem by weighting. A finite state machine-based algorithm is developed to estimate the average delays of nontransit vehicles. The stochasticity of bus arrival time is also considered in the estimation of bus delays to improve the robustness. Candidate timing plans obtained by the nondominated sorting genetic algorithm (NSGA) are divided into three priority levels based on the delays of buses. The final timing plans can be picked intuitively from the candidates by rules representing expert knowledge and demands to control the priority level. Co-TSP guarantees theoretically by preliminary screening that the expected delays of bus after optimization must be no higher than that before optimization. Simulation experiments are conducted in Shanghai, China, to verify the performance. Results show that Co-TSP reduces the delays of buses by 27.7%∼41.0% and still performs well under low and high congestion levels, while the conventional TSP (CTSP) fails in some cases. Priority control proves to be effective at last. The research provides a new idea for the benefit allocation among participants at intersections.

1. Introduction

Traffic congestion has plagued many cities for years [1]. Public transport with large passenger capacity is considered to be an effective way to alleviate traffic congestion [2], which has been vigorously promoted worldwide [3]. Limited by low speed and punctuality, bus competitiveness is difficult to improve in many cities [4, 5]. Transit signal priority (TSP) is the most cost-effective way to increase bus speed [6, 7]. With limited resources (such as capacity), competition among traffic participants is zero-sum [8]. Therefore, TSP is generally considered to be detrimental to the interests of the nontransit vehicle [9, 10]. How to realize the game equilibrium between bus and nontransit vehicle is a hot topic in the field of TSP.

TSP is classified into three types by Transit Cooperative Research Program (TCPR) [11], namely, passive, active, and adaptive TSP. Passive TSP usually makes static timing plans on the basis of bus schedules or other information [12, 13]. Active and adaptive TSP can dynamically adjust the timing plans according to the real-time arrival of buses to achieve bus priority [14] and can be further divided into rule-based TSP and model-based TSP [15, 16]. Rule-based TSP has good interpretability, but its generalization ability is weak [17]. It usually cannot adapt to the dynamic changes of traffic conditions well, and it is very complicated to formulate rules when the timing plan is complex. Model-based TSP is attracting more attention in recent years [18, 19].

Model-based TSP is usually formulated as an optimization problem. If the priority requirements are embodied in the constraints, it usually means that the bus has absolute priority. If minimizing bus delays are only set as an optimization goal, then buses enjoy conditional priority. Absolute priority methods usually have significant negative impacts on intersection operations [20], so they are only used in special scenarios such as trams [21]. In fact, the essential difference between absolute and conditional TSP lies in the level of priority, which is also a hot topic in current research.

In existing studies [12, 22–24], the final optimization objective is usually the weighted sum of several subobjectives. In this way, the priority level is reflected by the weights. These weights are determined subjectively and lack practical physical meaning, especially when the dimensions are different. Therefore, managers cannot intuitively understand the relationship between weights and priority levels, which makes it difficult to control the priority level. In fact, it is not only difficult to tune these weights in application but also expensive to test. More damningly, since minimizing bus delays are not a direct optimization goal, these methods cannot ensure theoretically that buses always get priority after optimization. Pareto optimization is a better way to solve this problem.

What is more, the background timing plans for intersections is usually static, while traffic conditions (such as volumes) change dynamically. This means that most of the time, the background timing plans may not be the best choice for real-time traffic conditions. Therefore, it is even possible for the delays of nontransit vehicles and buses to be optimized simultaneously.

Every TSP method needs to adopt at least one priority strategy, such as the commonly used green extension [25], red truncation [26], and phase insertion [27], as well as the relatively novel phase rotation [28], green reallocation [29, 30], cycle extension [31], and the variable cycle length strategy adopted in this study. The green extension and red truncation are the strategies adopted in the conventional TSP [29, 30] (i.e., CTSP) and many current studies [16, 25, 32]. Different from the strategies listed above, the variable cycle length strategy reallocates signal splits over a wider range to cope with more extreme situations and random arrival times of buses.

In this study, an adaptive signal priority method based on the variable cycle length strategy is proposed, and dedicated bus lanes are required for good implementation conditions [33]. The method takes the expected delays of buses and the average delays of nontransit vehicles as the optimization objectives, adopts the stochastic optimization and Pareto optimization concepts, and divides the priority intensity into three levels. Finally, the collaborative optimization of buses and nontransit vehicles under a specific priority level is realized. Therefore, the method is named as Co-TSP (i.e., collaborative transit signal priority). Postprocessing with good interpretability makes the priority level control a white box process, and explicitly guarantees theoretically that the expected delays of bus after optimization must be no higher than that before optimization. The contributions of this study are listed as follows.(i)Develop a finite state machine-based method to estimate the delays of nontransit vehicles(ii)Propose a TSP method considering gaming among traffic participants(iii)Provide a new idea for the benefit allocation among participants at intersections

The remainder of the study is organized as follows: the formulations of Co-TSP and postprocessing are introduced in the methodology section. The performance of Co-TSP is evaluated in the EVALUATION section. Conclusions and recommendations for future research are shown at last.

2. Methodology

The proposed collaborative transit signal priority (Co-TSP) method consists of an algorithm and corresponding hardware. The key hardware includes traffic volume detectors, bus arrival detectors, and processors. Traffic volume data are used to estimate the delays of nontransit vehicles, arrival detectors are used to initiate priority requests, and processors are used to optimize timing plans. When a bus is detected, the whole process shown in Figure 1 will be triggered. Once the processor receives a TSP request, a multiobjective nonlinear optimization problem will be constructed. The problem will be solved by nondominated sorting genetic algorithm (NSGA). The processor will get solutions on Pareto frontier, and the optimal timing plans will be further determined by a preset evaluation method. Priority strategy adopted in Co-TSP is variable cycle length for the continuity of the objective functions. Stochasticity of the dwell time of bus is taken into consideration to improve the robustness of the method. It should be noted that this study aims to reduce signal delays, that is, it does not consider the effect of transit signal priority on the accuracy of bus schedule. If the schedule deviation is not acceptable, priority can be granted only to later-arriving buses.

2.1. Assumptions

The assumptions of Co-TSP are shown as follows:(1)Buses run on dedicated bus lanes(2)Buses move at a constant speed except when waiting in line and dwelling in station(3)The acceleration and deceleration of buses are negligible(4)Communication delays are negligible(5)The method provides TSP to at most one bus in each cycle on a first come/first serve basis(6)The distribution of dwell time is well updated and maintained(7)All hardware are reliable

2.2. Variable Cycle Length Strategy

The variable cycle length strategy is developed on the basis of cycle extension. Both the cycle lengths and the green time ratios can be modified in the variable cycle length strategy. Compared with traditional strategies that expect buses to pass the intersection within a specific window of time such as green extension, red truncation, and phase insertion, the variable cycle length strategy can be well adapted to the scenario where the arrival time of buses is stochastic as shown in Figure 2. Buses are not guaranteed to be released immediately after optimization, but delays of buses will be reduced in most cases.

2.3. Notations

Notations used in this study are listed in Table 1.

2.4. Formulations of Co-TSP

2.4.1. Decision Variables

The green durations (i.e., ) in the control horizon are chosen as the decision variables in Co-TSP. The control horizon is a time window consisting of a predefined number of consecutive cycles. The variable cycle length strategy allows the green time in the control horizon to be allocated to phases which need it more. What is more, adopting only one TSP strategy avoids the integer programming which is more difficult to solve.

2.4.2. Objective Functions

The core of the Co-TSP is a two-objective optimization problem. The first objective is the delays of the bus, and the second one is the average delays of nontransit vehicles in the whole intersection.

Considering that there may be a bus stop between the detector and the stop line, the bus delays are replaced by the expected bus delays. “No bus station” can be interpreted as “the bus will dwell at a (virtual) station.” Then, the dwell time follows a single-point distribution, which is not fundamentally different from any other distribution. It should also be noted that continuous distribution (such as Gaussian distribution) should be discretized.

The delays of nontransit vehicles in a single cycle can be easily estimated by the time-space diagram method. However, the delays of nontransit vehicles in multicycles cannot be obtained easily. A finite state machine-based algorithm, which will be introduced later, is adopted in this study.

In summary, the objective of Co-TSP can be expressed as in the following equations.

2.4.3. Constrains

Different from other methods, Co-TSP already takes the delays of nontransit vehicles as an optimization objective, so the constraints only need to ensure the feasibility of the solution. There are five types of constraints in Co-TSP.(i)The green duration has a lower bound Too short green duration is not only unfriendly to pedestrians crossing the street but also a safety hazard. The constraint is shown as(ii)The cycle length is bounded According to Webster delay formula, both too long and too short cycle length mean high signal delays. Therefore, this study requires that the cycle length should neither be too long nor too short, as shown in the following equation.(iii)Overall degree of saturation is controlled The degree of saturation is generally considered to be directly related to the signal delays of vehicles. However, in the Co-TSP, the delays of nontransit vehicles have been taken as an optimization objective, so there is no need to limit the degree of saturation of a single cycle. It is enough to control the degree of saturation in the whole control horizon as shown in the following equations.(iv)Passed moment cannot be modified If the green stage of a phase has ended, the start and end times of the green stage of that phase cannot be modified. If the green stage of a phase has started, the start and end times of the green stage of and before that phase cannot be modified. This is determined by the laws of physics. As shown in equations (7)∼(13), the expression of this constraint is somewhat complex.(v)Duration of control horizon is fixed For the stability of intersection operation, the duration of control horizon should be fixed as the following equation shows.

2.5. Delay Estimation

2.5.1. The Delay Estimation of Buses

A bus is detected in cycle and in leg . If it is known that the bus will dwell at the station for seconds, then, as shown in Figure 3, the moment when the bus reaches the stop line can be calculated accord. A bus is detected in cycle and in leg . If it is known that the bus will dwell at the station for seconds, then, as shown in Figure 3, the moment when the bus reaches the stop line can be calculated according to equations (15)∼(16).

The time of buses dwell at stations is considered stochastic in this study. Therefore, as mentioned above, the expected bus delays are chosen as an optimization objective, which can be estimated by the following equation.

If there is no station between the detector and the stop line, just set the position of the station to zero and set the bus must stop at the station for zero seconds as equations (18)∼(19) show.

2.5.2. The Delay Estimation of Nontransit Vehicles

The average delays of nontransit vehicles are an optimization objective of Co-TSP. To calculate the average signal delays, the total delays in the control horizon should be calculated first. The delays of nontransit vehicles in a single cycle can be calculated based on the time-space diagram. However, due to the potential queue residual phenomenon, the calculation of the delays of nontransit vehicles over multiple cycles becomes much more complicated. A finite state machine is introduced to solve this problem. As shown in Figure 4, this finite state machine contains four states: Start, Queue NOT cleared, Queue cleared, and End. The number of uncleared vehicles at the end of each cycle is used to determine the next state. When the finite state machine ends, the sum of the delays in each cycle is the total delays of the nontransit vehicles in the control horizon. Among the four states, state “Queue NOT cleared” and state “Queue cleared” are the keys to the delay estimation and will be described in detail.

(1) Queue Cleared. State “Queue cleared” indicates that no vehicle remains at the end of the previous cycle. As shown in Figure 4, there are two outcomes to this state.

In the first case, all vehicles arriving in the current cycle (i.e., cycle ) and in the current leg (i.e., leg ) can be emptied, so the total delays of nontransit vehicles in cycle and in leg are the areas of triangle ABC in Figure 5(a). The number of residual vehicles (i.e., ) is 0. In mathematics, the total delays can be calculated by the following equations.

(a)

(b)

In the second case, not all vehicles in cycle and in leg can be emptied. Therefore, the total delay of nontransit vehicles in cycle and in leg is the difference of the areas of the triangle ABE and triangle CDE in Figure 5(b). In mathematics, the total delays can be calculated by equation (23), and the number of residual vehicles (i.e., ) can be determined by equation (24).

(2) Queue NOT Cleared. State “Queue NOT cleared” indicates that not all vehicles are cleared at the end of the previous cycle. As shown in Figure 4, there are also two outcomes to this state.

In the first case, all vehicles arriving in the current cycle (i.e., cycle ) and in the current leg (i.e., leg ) can be emptied, so the total delay of nontransit vehicles in cycle and in leg is the difference of the areas of trapezoid ABCE and triangle CDE in Figure 6(a). The number of residual vehicles (i.e., ) is 0. In mathematics, the total delays can be calculated by the following equations.

(a)

(b)

In the second case, not all vehicles in cycle and in leg can be emptied. Therefore, the total delay of nontransit vehicles in cycle and in leg is the difference of the areas of the trapezoid ABCF and triangle DEF in Figure 6(b). In mathematics, the total delays can be calculated by equation (28) and the number of residual vehicles (i.e., ) can be determined by equation (29).

Once the state is determined, and are determined by and . Then, the average delays of nontransit vehicles are determined by the following equation.

Numerical analysis shows that the prediction error of this finite state machine-based delay estimation algorithm is about 20% in low degree of saturation (<0.25) condition and less than 10% in middle and high degree of saturation condition. The average relative prediction error is about 2.5%, which is accurate enough for this study.

2.6. Pareto Optimality and Decision Making

2.6.1. Pareto Optimality

There are two approaches to solve the multiobjective optimization problem: the first is to weight the objectives and the second is to use the Pareto optimization theory. For the first approach, it is tedious to assign proper weight to each subobjective. In other words, the expert knowledge can hardly be applied to guide the optimization. As the interests of nontransit vehicles need to be taken into account, the TSP problem is a multiobjective optimization problem. Thus, the objective is definitely not bus delays. Consequently, TSP methods based on this idea cannot ensure the priority of buses. The second approach handles those problems well.

In a multiobjective optimization problem, a solution is said to be a Pareto optimality if it is superior to any other solution in at least one subobjective and not inferior to any other solution in the rest subobjectives. The Pareto solution set is a set of all Pareto optimality solutions. The surface in the objective space formed by the Pareto solution set is called the Pareto frontier. Decision makers can intuitively select the appropriate solution in the Pareto frontier according to their demands. In the field of TSP, this ensures that the bus will not suffer from the TSP.

2.6.2. Decision Making

Decision making which is also the postprocessing mentioned above refers to the process of selecting the optimal solution in the Pareto solution set according to preset rules by users. As mentioned above, the core of the Co-TSP is a two-objective optimization problem, so its Pareto frontier is a curve rather than a surface. For the Co-TSP, each solution on the Pareto frontier implies a different level of TSP priority. Co-TSP provides a simple way to switch signal priorities by a set of preset rules. The decision making of Co-TSP is divided into three steps: truncation, division, and selection.

(1) Truncation. After a TSP is responded to, the signal delays of the bus should be at least no higher than the current situation. Truncation refers to the process of removing the Pareto optimality whose bus delays are higher than the current situation. As shown in Figure 7, solutions with higher bus delays than the current one are discarded.

(2) Division. Division refers to dividing the Pareto frontier into several regions for subsequent search of optimal solutions in each subregion. As shown in Figure 7, Co-TSP divides the Pareto frontier into three regions of approximately equal size which stands for low, middle, and high priority levels. The critical points are 30% and 70% quantiles.

(3) Selection. Selection is to select the optimal solution in the corresponding region according to the preselected priority level. In Co-TSP, the evaluation criteria of selection are delays per vehicle. However, delays per vehicle do not really need to be calculated. This is because the control horizon is fixed in the Co-TSP, so the number of nontransit vehicles and buses are all fixed. However, as equations (31)∼(32) show, the number of buses is far less than the number of nontransit vehicles, so the delays per vehicle is dominated by the average delays of nontransit vehicles.

The constrained two-objective optimization problem can be solved by NSGA solver. By the way, the background timing plans should be placed in the initial population of NSGA to accelerate solving.

3. Evaluation

3.1. Study Area and Data

To evaluate the performance of the Co-TSP, Hongde Road intersection of Huyi Highway in Shanghai, China, as shown in Figure 8, is selected as the simulation study area. There are two bus routes passing through the study area. The two bus stations are both set up approximately 100 meters from the stop line. The intersection in the experiment is about 200 meters away from the upstream and downstream intersections. Considering that long response time is conducive to reducing the negative impact on nontransit vehicles, in the experiment, detectors are both set 180 meters away from the stop line. Volumes, large vehicle rates, and the background timing plans obtained by field investigation are shown in Tables 2∼3, respectively. The degree of saturation is about 0.44. Bus headways are both set to 6 minutes. The dwell time of buses is assumed to follow a discrete uniform distribution with 4 outcomes [32]. The outcomes are 20, 30, 40, and 50 seconds in the following experiments. The CTSP assumes that the bus will dwell for 35 seconds, which is the mathematical expectation of the distribution mentioned above.

3.2. Experiments Design

Two types of simulation experiments are carried out to illustrate the performance of Co-TSP in this study. The first experiment uses the volume and timing plans collected by field investigation to verify the effectiveness of Co-TSP. In the second experiment, the volume data collected in the field are scaled by 0.5 and 2 to verify the applicability of Co-TSP under low and high congestion levels.

All three experiments adopted the timing plans obtained by field investigation as shown in Table 3. The control horizons are all set to three cycles. All experiments were performed on the VISSIM 7 simulation platform. Co-TSP is implemented by secondary development based on Com interface. Evaluation result files generated by VISSIM 7 are used for subsequent analysis. All experiments were repeated three times.

3.3. Results and Discussion

As shown in Figure 9, in the effectiveness experiment, Co-TSP performed well in all the three priority levels. Compared with the no priority scenario, Co-TSP under low, middle, and high priority levels reduces bus average delays by 27.7%, 33.3%, and 41.0%, respectively. Although, these improvements cause an increase in the average vehicle delays in conflict directions, Co-TSP reduces the delay of nontransit vehicles by 13.4%, which is beneficial to the whole intersection. This further proves that it is possible to reduce the delays of both nontransit vehicles and buses. Due to the stochasticity of bus arrival time, CTSP performs terribly, because delays of both buses and nontransit vehicles are increased.

Performance of the three control methods under different congestion levels is shown in Figure 10. Co-TSP reduces bus delays by 35%∼45% and 33%∼47% under low and high congestion levels, respectively. Although the average vehicle delays in the direction of conflict increases slightly, the average delays of nontransit vehicles are also decreased, which is beneficial to the whole intersection. In addition, the bus delays reduction of Co-TSP under different priority levels varies significantly, which preliminary illustrates the effectiveness of priority control.

(a)

(b)

The above results are obtained from the complete simulation. To better illustrate the effect of priority control, Figure 11 shows two typical Pareto frontier modes when the bus dwells for 35 seconds (i.e., single-point distribution) in the simulation. As shown in Figure 11(a), the average delays of buses and nontransit vehicles among candidate solutions have no significant difference, which usually occurs when the degree of saturation is high. In this case, the effect of choice under different congestion levels will not be significant. Meanwhile, as shown in Figure 11(b), the differences among different solutions are obvious, which usually occurs when the degree of saturation is not too high and the bus delays under the original timing plans are not too low. In this case, the effect of priority control is obvious and bus priority may increase delays of nontransit vehicles. This further illustrates the effectiveness of priority control.

(a)

(b)

4. Conclusions

In this study, a collaborative transit signal priority method (Co-TSP) considering gaming among traffic participants is put forward. The core of Co-TSP is a two-objective optimization problem which takes the expected delays of buses and the average delays of nontransit vehicles as the objectives. The delays of nontransit vehicles are estimated by a finite state machine-based algorithm with four critical states. The stochasticity of bus arrival time is considered in the estimation of bus delays. The nondominated sorting genetic algorithm (NSGA) is selected as the solver to obtain candidate timing plans. Terrible solutions will be abandoned first, and then, the remaining candidates will be divided into three types according to 30% and 70% quantiles. The final timing plans will be picked from the corresponding type according to user-defined rules to realize the control of priority. Therefore, Co-TSP guarantees theoretically that the expected delays of bus after optimization must be no higher than that before optimization.

To verify the performance of Co-TSP, a simulation case study is conducted on Hongde Road intersection of Huyi Highway in Shanghai, China. The results show that CTSP increases the average delays of both buses and nontransit vehicles in some case, while Co-TSP reduces bus delays by 27.7%∼41.0% and reduces delays of nontransit vehicles by about 13.4% with slight increasement of delays of vehicles moving in conflicting directions. In addition, Co-TSP performs well under low and high congestion levels with a 33%∼47% drop in the average delays, which shows excellent applicability. Finally, numerical analysis demonstrates the difference of Co-TSP among different priority levels can be striking, which further illustrates the effectiveness of priority control.

However, Co-TSP grants priority to only one bus in a single cycle. Multiple buses competing for priority have not been considered. More expert knowledge can be applied to guide the determination of the final timing plans. What is more, more traffic participants such as pedestrian and passengers waiting at the station can be introduced into the collaborative optimization in the future. Fuel consumption is also a meaningful factor reserved to be studied.

Data Availability

All necessary data that support the findings of this study are listed in the manuscripts. Road network can be found in Google maps.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

The research was supported by the National Natural Science Foundation of China (Grant no. 52172331).

References

K. Wu, M. Lu, and S. I. Guler, “Modeling and optimizing bus transit priority along an arterial: a moving bottleneck approach,” Transportation Research Part C: Emerging Technologies, vol. 121, Article ID 102873, 2020.
View at: Publisher Site | Google Scholar
F. Li, X. Guo, L. Zhou, J. Wu, and T. Li, “A capacity matching model in a collaborative urban public transport system: integrating passenger and freight transportation,” International Journal of Production Research, vol. 60, no. 20, pp. 1–26, 2022.
View at: Publisher Site | Google Scholar
T. D. Camacho, M. Foth, and A. Rakotonirainy, “Pervasive technology and public transport: opportunities beyond telematics,” IEEE Pervasive Computing, vol. 12, no. 1, pp. 18–25, 2013.
View at: Publisher Site | Google Scholar
D. J. Lee, “A multi-criteria approach for prioritizing advanced public transport modes (APTM) considering urban types in Korea,” Transportation Research Part A: Policy and Practice, vol. 111, pp. 148–161, 2018.
View at: Publisher Site | Google Scholar
D. Okuda, T. Watanabe, N. Fukasawa, T. Suzuki, H. Sakakibara, and Y. Nakamura, “Method for evaluating the level of convenience of public transportation networks in regional small and middle sized cities,” Quarterly Report of RTRI, vol. 60, no. 3, pp. 178–183, 2019.
View at: Publisher Site | Google Scholar
F. A. Consoli, A. H. Alomari, H. Al-Deek et al., “Evaluation of conditional transit signal priority technology for regional implementation,” Transportation Research Record, vol. 2484, no. 1, pp. 140–148, 2015.
View at: Publisher Site | Google Scholar
Y. Lin, X. Yang, N. Zou, and M. Franz, “Transit signal priority control at signalized intersections: a comprehensive review,” Transportation Letters, vol. 7, no. 3, pp. 168–180, 2015.
View at: Publisher Site | Google Scholar
D. Lin and S. E. Jabari, “Pay for intersection priority: a free market mechanism for connected vehicles,” IEEE Transactions on Intelligent Transportation Systems, vol. 23, no. 6, pp. 5138–5149, 2022.
View at: Publisher Site | Google Scholar
L. T. Truong, G. Currie, M. Wallace, C. De Gruyter, and K. An, “Coordinated transit signal priority model considering stochastic bus arrival time,” IEEE Transactions on Intelligent Transportation Systems, vol. 20, no. 4, pp. 1269–1277, 2019.
View at: Publisher Site | Google Scholar
J. Li, Y. Liu, N. Zheng, L. Tang, and H. Yi, “Regional coordinated bus priority signal control considering pedestrian and vehicle delays at urban intersections,” IEEE Transactions on Intelligent Transportation Systems, vol. 23, no. 9, pp. 16690–16700, 2022.
View at: Publisher Site | Google Scholar
Kittelson, Associates transit cooperative research Program United States transit development corporation, and National Research Council (U S), Transit Capacity and Quality of Service Manual, Transportation Research Board, Washington, DC, USA, 2nd edition, 2003.
B. Moghimi and C. Kamga, “Transit signal priority in smart cities,” in Models And Technologies For Smart, Sustainable And Safe Transportation Systems, IntechOpen, London, UK, 2020.
View at: Publisher Site | Google Scholar
Y. Ren, J. Zhao, and X. Zhou, “Optimal design of scheduling for bus rapid transit by combining with passive signal priority control,” International Journal of Sustainable Transportation, vol. 15, no. 5, pp. 407–418, 2021.
View at: Publisher Site | Google Scholar
H. Liu, K. Teng, L. Rai, and J. Xing, “Transit signal priority controlling method considering non-transit traffic benefits and coordinated phase states for multi-rings timing plan at isolated intersections,” IEEE Transactions on Intelligent Transportation Systems, vol. 22, no. 2, pp. 913–936, 2021.
View at: Publisher Site | Google Scholar
Q. Wang, X. T. Yang, and Y. Yuan, “Transit signal progression algorithm for supporting redwood road transit signal priority (tsp),” 2020, https://trid.trb.org/view/1770734.
View at: Google Scholar
X. Zeng, Y. Zhang, J. Jiao, and K. Yin, “Route-based transit signal priority using connected vehicle technology to promote bus schedule adherence,” IEEE Transactions on Intelligent Transportation Systems, vol. 22, no. 2, pp. 1174–1184, 2021.
View at: Publisher Site | Google Scholar
A. Likmeta, A. M. Metelli, A. Tirinzoni, R. Giol, M. Restelli, and D. Romano, “Combining reinforcement learning with rule-based controllers for transparent and general decision-making in autonomous driving,” Robotics and Autonomous Systems, vol. 131, Article ID 103568, 2020.
View at: Publisher Site | Google Scholar
Y. Zhang, T. Yang, J. Tan, and T. Z. Qiu, “Research on transit signal priority strategy of single intersection based on v2x environment,” in Proceedings of the 2019 5th International Conference on Transportation Information and Safety (ICTIS), pp. 356–363, Liverpool, UK, July 2019.
View at: Publisher Site | Google Scholar
P. Anderson and C. F. Daganzo, “Effect of transit signal priority on bus service reliability,” Transportation Research Part B: Methodological, vol. 132, pp. 2–14, 2020.
View at: Publisher Site | Google Scholar
Y. Xiao, M. S. Ali, E. I. Kaisar, and M. Hadi, “Development of planning-level guidelines for deploying transit signal priority,” IEEE Transactions on Intelligent Transportation Systems, vol. 23, no. 9, pp. 14731–14740, 2022.
View at: Publisher Site | Google Scholar
W. Zhou, Y. Bai, J. Li, Y. Zhou, and T. Li, “Integrated optimization of tram schedule and signal priority at intersections to minimize person delay,” Journal of Advanced Transportation, vol. 2019, Article ID 4802967, 18 pages, 2019.
View at: Publisher Site | Google Scholar
S. Shu, J. Zhao, and Y. Han, “Signal timing optimization for transit priority at near-saturated intersections,” Journal of Advanced Transportation, vol. 2018, Article ID 8502804, 14 pages, 2018.
View at: Publisher Site | Google Scholar
K. Yang, M. Menendez, and S. I. Guler, “Implementing transit signal priority in a connected vehicle environment with and without bus stops,” Transportation Business: Transport Dynamics, vol. 7, no. 1, pp. 423–445, 2019.
View at: Publisher Site | Google Scholar
W.-H. Lee and H.-C. Wang, “A person-based adaptive traffic signal control method with cooperative transit signal priority,” Journal of Advanced Transportation, vol. 2022, Article ID 2205292, 17 pages, 2022.
View at: Publisher Site | Google Scholar
A. Girijan, L. D. Vanajakshi, and B. R. Chilukuri, “Dynamic thresholds identification for green extension and red truncation strategies for bus priority,” IEEE Access, vol. 9, pp. 64291–64305, 2021.
View at: Publisher Site | Google Scholar
J. Hu, Z. Zhang, Y. Feng, Z. Sun, X. Li, and X. Yang, “Transit signal priority enabling connected and automated buses to cut through traffic,” IEEE Transactions on Intelligent Transportation Systems, vol. 23, no. 7, pp. 8782–8792, 2022.
View at: Publisher Site | Google Scholar
K. Teng, H. Liu, and L. Rai, “Transit priority signal control scheme considering the coordinated phase for single-ring sequential phasing under connected vehicle environment,” IEEE Access, vol. 7, pp. 61057–61069, 2019.
View at: Publisher Site | Google Scholar
Z. Yu, V. V. Gayah, and E. Christofa, “Implementing phase rotation in a person-based signal timing optimization framework,” in Proceedings of the 2018 21st International Conference on Intelligent Transportation Systems (ITSC), pp. 20–25, Maui, HI, USA, November 2018.
View at: Publisher Site | Google Scholar
J. Hu, B. B. Park, and Y. J. Lee, “Coordinated transit signal priority supporting transit progression under Connected Vehicle Technology,” Transportation Research Part C: Emerging Technologies, vol. 55, pp. 393–408, 2015.
View at: Publisher Site | Google Scholar
J. Hu, B. B. Park, and Y. J. Lee, “Transit signal priority accommodating conflicting requests under Connected Vehicles technology,” Transportation Research Part C: Emerging Technologies, vol. 69, pp. 173–192, 2016.
View at: Publisher Site | Google Scholar
W. Ekeila, T. Sayed, and M. E. Esawey, “Development of dynamic transit signal priority strategy,” Transportation Research Record, vol. 2111, no. 1, pp. 1–9, 2009.
View at: Publisher Site | Google Scholar
X. Zeng, Y. Zhang, K. N. Balke, and K. Yin, “A real-time transit signal priority control model considering stochastic bus arrival time,” IEEE Transactions on Intelligent Transportation Systems, vol. 15, no. 4, pp. 1657–1666, 2014.
View at: Publisher Site | Google Scholar
J. Zhao and X. Zhou, “Improving the operational efficiency of buses with dynamic use of exclusive bus lane at isolated intersections,” IEEE Transactions on Intelligent Transportation Systems, vol. 20, no. 2, pp. 642–653, 2019.
View at: Publisher Site | Google Scholar

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Copyright © 2023 Bing Wu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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