Bus Priority Signal Control Considering Delays of Passengers and Pedestrians of Adjacent Intersections

,


Introduction
In order to alleviate urban tra c congestion and tra c pollution, it is particularly important and urgent to develop urban transit and to give transit priority accordingly. BPSC is one of the useful measures that has been widely used. For example, BPSC can be used to reduce bus delays to ensure the e ciency of bus operation and to improve the quality of bus service. BPSC is divided into three categories: passive bus priority control, active bus priority control, and adaptive bus priority control. BPSC could not only reduce the delay of buses, but also impact social vehicles and pedestrians at intersections. When a large number of vehicles and pedestrians are at an intersection, if the change of their delays which due to BPSC cannot be fully considered, the bus priority cannot be regarded as successful. erefore, the impacts of the control scheme on pedestrians and vehicles of the upstream intersection and downstream intersection should be considered. Speci cally, in the green wave coordinated control system, when the upstream intersection adopts the BPSC, the bus and some vehicles can smoothly pass through the intersection. However, if the operation of the priority vehicles at the downstream intersection is not taken into consideration, it could increase the delay of pedestrians and vehicles at the downstream intersection. In order to protect the rights and interests of vehicles and pedestrians at adjacent intersections, this paper proposes a BPSC method considering the total delay of vehicles and pedestrians of adjacent intersections. delay on arterials composed of the delay of social vehicles and buses, and presented a real-time signal control system that optimizes signal settings based on minimization of passenger delay on arterials [1]. Zeng et al. proposed a stochastic mixed-integer nonlinear programming (SMINP) model to produce a good transit signal priority (TSP) timing considering the bus stop dwell time and the delay caused by standing vehicle queues [2]. Ghanim and Abu-Lebdeh developed a realtime tra c signal control method integrating tra c signal timing optimization and TSP control using genetic algorithms (GA) and arti cial neural networks (ANN) [3]. Wu et al. proposed to optimize the holding time at bus stops, signal timings, and bus speed in order to minimize bus delay so that buses can pass through signalized intersections without stopping [4]. Li and Jin regarded intersection and the downstream bus stop as a control unit and established an optimization model of bus priority green signal duration considering passenger delay at intersection and bus stops [5]. Considering the in uence of bus priority strategy on nonpriority phase, Wang et al. established a bi-level programming model with the upper-level model aiming at minimizing the vehicle delay in the nonpriority direction and the lower-level model aiming at minimizing the average passenger delay in the entire intersection [6]. Shu et al. discussed the tra c conditions of bus and social vehicles at near-saturated intersections, and established a model for BPSC based on vehicle delay [7]. Shaaban and Ghanim used VISSIM multimodal microscopic simulation to study the e ect of early green and green extension on major urban arterials [8]. According to the operation characteristics of buses and the actual road conditions which aim at the maximum green wave band, Gao established a transit priority control model to obtain the signal timing scheme of arterial intersections and the speed of buses. Consequently she adjusted the speed of buses through the bus detection technology and information transmission technology to control the green wave [9]. Based on the kinematic wave model and vehicle delay, Chow et al. proposed an optimization model aiming at minimizing the bus schedule discrepancies and the total squared headway deviations to adjust the signal timing of arterial intersections. In addition, they also analyzed di erent control strategies for improving bus service reliability [10,11]. Hu et al. calculated vehicle delays according to the deviation distribution of vehicle running time, and built a bi-level programming model. e upper level aimed to optimize the e ciency of intersections under the guidance of vehicle speed, while the lower level aimed to optimize the total delay at intersections [12]. Ma et al. took intersection group as the research object, and minimized the travel delay deviation of bus passing through intersection group. For late and early arriving bus, he proposed two optimization strategies "increasing bus delay strategy" and "decreasing bus delay strategy" respectively [13,14]. Li et al. presented a TSP model that considered the delays at the upstream and downstream intersections along arterial roads based on the strategy of green light extension and red light compression. e model ensured transit priority at upstream intersection and reduced its in uence on green wave of social vehicles and downstream intersections [15]. Some scholars have established bi-level optimization models of bus signal priority by analyzing bus delay and person delay. e upper level aims at obtaining optimized public cycle, split and o set, while the lower level optimized the bus signal priority signal with the upper and lower limits of green wave band as constraints [16][17][18]. In general, most of the existing BPSC methods only considered the queuing and delay of bus and social vehicles at intersections, ignoring the impact of BPSC on pedestrians crossing the street, which easily contribute to increase pedestrian delay.
For the research on the delay of pedestrians, Feng and Pei analyzed moving features and traversing features of vehicles and pedestrians, depicted the sketch map of pedestrians assembling and scattering, and proposed the calculation of average delay and established models according to the delay [19,20]. Marisamynathan and Vedagiri proposed a pedestrian delay model considering waiting time delay, crossing time delay, and pedestrian-vehicular interaction delay to evaluate the pedestrian level of services at signalized intersections [21]. Ma et al. analyzed the safety and delay of vehicles and pedestrians between the two pedestrian phase patterns, the exclusive pedestrian phase (EPP) and normal two-way crossing (TWC) [22]. For large intersections with center transit lanes, Zhao and Ma studied the passing and stopping situations of pedestrians at intersections (including one-stage crosswalk intersections and two-stage crosswalk intersections), and optimized signal timing scheme according to vehicle and pedestrian delays [23]. Considering pedestrian and vehicle delays at intersections under unsaturated tra c conditions, Yu et al. put forward a method of signal timing for an isolated intersection with one-stage crossing and two-stage crossing [24]. Dai et al. analyzed the pedestrian delay of unsignalized intersections and signalized intersections respectively, and proposed the model considering the delay of signal controlling and vehicle stream disturbance [25]. e previous studies of pedestrian delay only focused on isolated signalized intersections and did not consider multiple intersections with implementing BPSC. is paper establishes a coordinated control method of BPSC considering passenger delays and pedestrian delays at adjacent intersections. e total changes of delays caused by BPSC are analyzed. e changes include the delay of bus passengers, social vehicle users and pedestrians at the upstream intersection and the increase of stop delay of priority vehicles at downstream intersections.

Research Object Setting.
Suppose that two adjacent intersections are shown in Figure 1. e direction of the green wave is from west to east and the bus runs from west to east.

Notation.
To facilitate the presentation, all de nitions and notations used herea er are summarized in Table 1. e existing BPSC strategies mainly include three categories: passive priority, active priority, and real-time priority. In practice, most studies focus on strategies of active priority, which have the merits of convenience, exibility, and simple operation compared to the other strategies. e commonly used active priority strategies include green light extension, shortening red lights, and inserting phase etc. According to the time when the bus arrives at the intersection and the status of tra c lights, di erent priority control strategies could be adopted.
In order to facilitate the study, this paper makes the following hypotheses.
(1) When the bus arrives at the upstream intersection, the green time is over, that is g v ( , ) < v ( ). It is necessary to extend the green time for the th phase of the upstream intersection to ensure the smooth passage of the bus and the extension of the green light is Δ ( , ).
(2) e tra c ow is unsaturated and the number of phases and phase sequence in each cycle are unchanged. (3) e vehicles are moving at a uniform speed at the intersection.
(4) e extended green time for the th phase is compensated by the th phase.
If the strategy of green light extension is adopted at the upstream intersection, by analyzing the operation of buses and social vehicles, the following situations shown in Figure 2 will occur when the bus reaches the downstream intersection.
(2) When the upstream bus reaches the downstream intersection, the downstream intersection is in the red phase. e bus and the tail of the eet are blocked at the downstream intersection, that is (3) When the upstream bus reaches the downstream intersection, the downstream intersection is in red T 1: Symbols and parameters.

Symbol
De nition

( , )
Green time for the th phase at intersection , is the priority phase ( , ) Red time for the th phase at intersection , is the priority phase ( + 1, ℎ) Green time for the ℎ th phase at intersection + 1, ℎ is the phase when the priority vehicle arrives at intersection + 1 ( + 1, ℎ) Red time for the ℎ th phase at intersection + 1, ℎ is the phase when the priority vehicle arrives at intersection + 1 ( , ) Red time for the th phase at intersection , is the compensation phase for bus priority Step 4: When the green phase of the upstream intersection is extended by Δ ( , ), the system will analyze the hindered status of the upstream vehicles reaching the downstream intersection and calculate the delay of vehicles and pedestrians at the upstream and downstream intersection. en, the system will establish models to obtain the optimal timing scheme of the upstream intersection.
Step 5: If the bus could arrive at the upstream intersection within the extended green time, which is , the signal timing scheme needs to be adjusted. Otherwise if the original signal timing plan should be used.

BPSC Delay Model
is paper takes the upstream and downstream intersections with large crossing pedestrian volume as an example. To ensure the tra c conditions of the crossing pedestrians, models aiming at maximizing the reduced total delay are developed by considering the delays of bus passengers, social vehicle users and crossing pedestrians at upstream and downstream intersections. In order to calculate the delay of the bus, it is assumed that the bus will arrive at the intersection by the end of the extended green light.

BPSC Process
e control system could obtain the arrival time of the bus through the detector at the upstream intersection, establish models to analyze the delay of pedestrians and vehicles at the upstream and downstream intersections, and obtain the speci c priority schemes of the upstream intersection. e speci c control process is shown in Figure 3.
Step 1: When the detector detects the bus, the system predicts that the bus will arrive at the stop line at the upstream intersection at time v ( ).
Step 2: According to the arrival time of the bus and the end of the green light at the upstream intersection, the system evaluates whether the signal timing scheme should be adjusted. If g v ( , ) ≥ v ( ), keep the timing scheme, otherwise the green time should be extended by Δ ( , ).
Step 3: According to the average ow of pedestrians and tra c at the intersection, the system analyzes the delay of pedestrians and passengers at the intersection a er the green light extension at the upstream intersection. (2) e reduced delay of social vehicle users is shown in Figure 4. Social vehicles can pass the intersection without stopping in the extended green time Δ ( , ). e reduced delay of passengers of social vehicles can be calculated by Equation (2): (3) e reduced delay of crossing pedestrians is shown in Figure 5. e waiting time of pedestrians is reduced by Δg ( , ), and the reduced delay can be calculated by Equation (3):

Analysis of Delay at Upstream Intersection.
When the green phase extension strategy is adopted at the upstream intersection, the green time for priority phase is extended and the green time for nonpriority phase is shortened. Hence, the delay of priority phase is reduced, which includes the delays of bus passengers, social vehicle users and crossing pedestrians. e speci c analysis is as follows: (1) By adopting the green light extension strategy, buses can pass the intersection without stopping, which reduces the delay of stopping and waiting, so the reduced delay of bus passengers can be calculated by Equation (1) e delay of nonpriority phase increases, which includes the delays of social vehicle users and crossing pedestrians. e speci c analysis is as follows: (1) e increased delay of social vehicles is shown in Figure 6. e red light time is extended and the waiting time of vehicles increases. e vehicles that could have passed need to stop and wait. erefore, the increased delay of social vehicles is represented by the area of shadows in the Figure 6, and the increased delay of users can be calculated by Equation (4): Journal of Advanced Transportation 6 (4) (2) e increased delay of crossing pedestrians is represented by the area of shadows in the Figure 7, which can be calculated by Equation (5):

Analysis of Delay at Downstream Intersection.
When the green light extension strategy is adopted at the upstream intersection, the analysis of delay at the downstream intersection is discussed according to three cases in Figure 2.
(1) When the priority vehicles reach the downstream intersection, as described in situation 1 of Figure 2, it is during green phase and the vehicles can directly pass through. e total delay model of the upstream and downstream intersection is established as Equation (6). (2) When the priority vehicles reach the downstream intersection, as described in situation 2 of Figure 2, some of the priority social vehicles can pass through the intersection, but the bus and the tail of the social vehicles are hindered. e delays of downstream intersection increase, and the increased delays are as follow.
e increased delay of bus passengers can be calculated by Equation (7) e increased delay of social vehicle passengers is represented by the area of shadows in Figure 8, which can be calculated by Equation (8)   e increased delay of bus passengers can be calculated by Equation (10): e increased delay of social vehicle passengers is represented by the area of shadows in Figure 9, which can be calculated by Equation (11): The total delay model considering delays at the upstream and downstream intersection is established as Equation (12).

Optimization Algorithms.
e models mentioned above are multi-objective optimization models. ese models are solved using three di erent algorithms namely, the multiobjective genetic algorithm function gamultiobj, multiobjective particle swarm optimization (MOPSO) and goal attainment method function fgoalattain.
(3) When the priority vehicles reach the downstream intersection, as described in situation 3 of Figure 2, the bus and all the priority social vehicles are hindered. e delays of downstream intersection increase, and the increased delays are as follow.

Journal of Advanced Transportation 8
In order to reduce the impact on straight tra c, a er prolonging the green time of the east-west straight phase of upstream intersection, the green time of the le -turn phase in the north-south direction would be appropriately reduced to compensate. e speed limit of urban roads is 60 km/h. If the eet can run at an average speed of 60 km/h, Situation 1 and Situation 2 shown in Figure 2 may appear a er the green light extension of the upstream intersection. If the eet runs slowly, the average speed can only reach 50 km/h, Situation 3 may appear. e three situations are discussed below.
(1) Situation 1, when ( , ) + Δ ( , ) + ( ( , + 1)/v) mod ( ) ≤ ( + 1, ℎ) + ( , + 1), the priority vehicles can pass through the intersection + 1 without stopping. A delay model is developed, and the three algorithms are used to obtain the solutions. e results of the model in situation 1 during the peak period are shown in Table 4. e green light extension time obtained by three algorithms are 2.86 s, 2.89 s, and 2.70 s, respectively. e results of the model in situation 1 during the nonpeak period are shown in Table 5. e green light Genetic algorithm is a search algorithm to solve the optimization problem, which draws lessons from the phenomena of heredity, mutation, natural selection and hybridization in the process of biological evolution. e algorithm of function gamultiobj is a variant of NSGA-II (Nondominated sorting and sharing genetic algorithm II), which can e ectively solve multi-objective optimization problems.
Particle swarm optimization (PSO) is a random search algorithm based on group cooperation, which is developed by simulating the foraging behavior of birds. e multi-objective particle swarm optimization algorithm is based on the single objective particle swarm optimization and Pareto optimization, so that the particle swarm optimization algorithm can deal with the multi-objective problems.
Function fgoalattain is a multi-objective optimization function in MATLAB. e algorithm used in this function is goal attainment method. e principle of goal attainment method to solve the multi-objective model is to nd the minimum deviation between all objective functions and goals, so as to obtain the extreme value of the objective function. e goal of this method is clear and the calculation speed is fast, but it may only give the local optimal solutions.

Case Study
In order to illustrate the e ectiveness of the BPSC model considering the delays of passengers and pedestrians at adjacent intersections, the adjacent intersections on Shenghe Road in Chengdu, China are used as an example. e intersection of Shenghe Road and the northern section of Yizhou Avenue is regarded as upstream intersection . e intersection of Shenghe Road and Duhui Road is regarded as downstream intersection + 1. ese intersections are close to the Chengdunan Railway Station. e bus ow and the pedestrian ow are large. e tra c parameters of upstream intersections during peak and nonpeak periods are shown in Tables 2 and 3. e saturated ow rates of both east and west straight approach at the intersection + 1 are 2000 (pcu·h −1 ).
Assuming the two intersections are coordinated control intersections, the signal timing scheme is shown in Figure 10.    Table 6. e green light extension time obtained by three algorithms are 4.83 s, 4.59 s, and 4.42 s, respectively.   e results of the model in situation 3 during the nonpeak period are shown in Table 9. e green light extension time obtained by three algorithms are 4.68 s, 4.68 s, and 4.71 s, respectively.
Considering the results of three algorithms, the calculation speed of function gamultiobj and function fgoalattain are faster than that of MOPSO. Taking the result of genetic algorithm as an example, the e ect of BPSC considering the delay of crossing pedestrians and the e ect of conventional control without considering pedestrians are compared in Tables 10  and 11. (1) Situation 1, during the peak period, if delay of crossing pedestrians is not taken into consideration, the green time at intersection can be extended by 2.61 s. However, if delay of crossing pedestrians is considered, the green time at intersection can be extended by 2.86 s. e bus delay increases less than 1%, while the delays of social vehicles and pedestrians are both reduced by 9%. During the nonpeak period, if delay

Conclusion
Based on the previous analysis, we make following conclusions.
(1) A case study is performed using the green phase extension method as an example. e numerical results confirm the effectiveness of the proposed method. is method could reduce the delay of pedestrians significantly without increasing the delay of bus passengers and social vehicle users. (2) e study only uses the green phase as an example for demonstration. In the future, all combinations of various priority control strategies can be further studied. In addition, this paper only focuses on the two adjacent intersections. In the future, focus can be placed on multiple adjacent intersections or intersections in a region.
Data Availability e data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare that there is no conflict of interests regarding the publication of this paper.