# Optimization Method for Transit Signal Priority considering Multirequest under Connected Vehicle Environment

Authors: Song Xianmin; Yuan Mili; Liang Di; Ma Lin
Journal: Journal of Advanced Transportation
 (2018)

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## Abstract

Aiming at reducing per person delay, this paper presents an optimization method for Transit Signal Priority (TSP) considering multirequest under connected vehicle environment, which is based on the travel time prediction model. Conventional arrival time of transit depended on the detection information and the front road state, which restricted the effect of priority seriously. According to the bidirectional and real-time information transmission under connected vehicle environment, this paper establishes a more accurate forecasting model of bus travel time. Based on minimizing the total person delay at the intersection, the decision mechanism of multirequest is devised to meet the priority needs of buses with different arrival times. And the green time compensation algorithm is developed after considering the arrival information of the buses in the next cycle of compensational phase. Finally, the paper combines the COM interface of VISSIM and Matlab to achieve the proposed method under connected vehicle environment. Four control methods were tested when the VCR was 0.5, 0.7, and 0.9. The results illustrated that the proposed method reduced per person delay by 18.57%, 11.88%, and 18.96% and decreased the private vehicle delay by 3.73%, 7.62%, and 13.10%, respectively.


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## Body

## 1. Introduction

Transit Signal Priority (TSP) is significant to alleviate traffic congestion in urban areas. Transit Signal Priority (TSP) can be divided into conventional TSP and TSP under connected vehicle environment. In order to coordinate the multidirection buses with multirequest, various strategies were developed such as the first-come-first-service, the priority under sole factor, and the priority considering multiple factors. Furth et al. pointed out that the relative priority can effectively reduce the average vehicle delay of the intersection with comparing no priority, absolute priority, and relative priority [1]. Liu et al. presented a weight model to determine the priority of the buses, and the method was based on the bus arrival time [2].Head et al. noted that the first-come-first-service policy may not provide the best service sequence [3]. The logical framework was designed to determine transit priority level, and an optimization algorithm was formulated by minimizing total person delay. After that, Ma and Bai used the decision tree method to determine the service sequence of multiple priority requests [4]. The above methods overemphasized the reduction of the vehicle delay. However, the main purpose of TSP is to ensure punctuality and avoid the deviation from the schedule. Kim et al. considered the delay of all buses in a region, proposed a strategy under conflicting priority requests based on regional coordination, and then analyzed the impact of transit priority on the whole region [5]. A mixed-integer linear programming model based on multipriority request was proposed by He et al. [6]. Zlatkovic et al. considered the current green phase as the highest priority and proposed a transit priority method based on the new rule [7]. Ma et al. established the optimal service sequence of conflicting priority requests and the corresponding signal timing through a dynamic programming model [8]. By acquiring the information of passengers and adjusting the weight in the objective function, Christofa et al. established a person-based signal control system with TSP [9]. Xu et al. built a multiple requests decision model by considering the per person delay and the waiting time of passengers at bus station [10]. After considering the randomness of the bus arrival time, Zeng et al. developed a stochastic mixed-integer nonlinear programming (SMINP) to find the optimal green time for real-time TSP control [11].With the development of connected vehicles, Transit Signal Priority (TSP) has aroused the attention to scholars. The information about speed, position, direction, acceleration, and so on is transferred between vehicle and vehicle under connected vehicle environment. Owing to this feature, it is possible to predict the travel time accurately. More importantly, both the transit delay and the private vehicle delay can be taken into account. He et al. proposed a multimodal signal control called PAMSCOD in connected vehicle environment and used the powerful optimization solver to solve complex optimization problems [12]. In order to ensure the accuracy of the bus arrival time and minimize the adverse effects on the general traffic, a new priority sequence between the two successive stations was proposed by Hao et al. [13]. To resolve conflicting priority requests among social vehicles, pedestrians, buses, and emergency vehicles, Zamanipour et al. designed a priority decision framework with multiple models under connected vehicle environment and used the weights of all kinds of vehicles as the basis for determining the priority decision [14]. He et al. formulated a mixed-integer linear program (MILP) under multirequest which explicitly accommodated multiple priority requests from different modes of vehicles and pedestrians while simultaneously considering coordination and vehicle actuation [15]. In the premise of not increasing the green time, Hu et al. established a transit priority algorithm under connected vehicle which aimed at minimizing total delays [16–18]. Wu et al. developed the speed guidance model and the signal priority control model under CV environment. Different control strategies were adopted for delayed buses and buses ahead of schedule [19].Our work focuses on developing the decision mechanism of multirequest and the green time compensation algorithm based on minimizing total person delay at the intersection. In order to meet the priority needs of multibuses with different arrival times, the decision mechanism of multirequest is established. And the green time compensation algorithm is developed after considering the arrival times of the buses in the next cycle of compensational phase.The rest of this paper is organized as follows. Section2 shows the logical framework of the proposed method. Section 3 elaborates the signal control strategy. In Section 4, an optimization method for Transit Signal Priority (TSP) considering multirequest under connected vehicle environment is put forward, which is based on the travel time prediction model. Meanwhile, the decision mechanism of multirequest and the green time compensation algorithm are established by minimizing person delay at the intersection. In Section 5, four priority control methods are tested by using the COM interface of VISSIM simulation platform and Matlab.


## 2. Logical Framework

As shown in Figure1, the road is under connected vehicle environment. The information is transferred among vehicles, as well as vehicles and infrastructures. The TSP mechanism starts when the buses arrive at the section XA of the road. The buses are detected by the infrastructure next to the bus station when buses get to the bus station upstream. The time to reach the stop line is real-time predicted. And the corresponding TSP the green time is calculated in the process of driving. Taking into account the arrival time of all buses and general vehicles on the road, the optimal timing plan is generated.Figure 1
Layout of the intersection.In this study, a Transit Signal Priority method with the multiple requests under connected vehicle environment consists of three components: the detection and status discrimination component, the prediction component, and the priority signal control component. The logical framework is shown in Figure2.Figure 2
Logical framework.


## 3. Signal Control Strategy

The signal controller obtains multiple priority requests simultaneously at a signalized intersection under connected vehicle environment. In this paper, four different signal control strategies are discussed in this section: NTSP, CVTSP, CVTSP-GD, and CVTSP-CC. NTSP indicates that the intersection adopts the original signal timing, and it is nonpriority timing plan. The control strategy of Transit Signal Priority under connected vehicle (CVTSP) was proposed by He et al. [12]: for the sake of serving the conflicting requests of multidirectional buses, the optimal signal timing plan is generated by minimizing the total delay at the intersection. However, the green time will be not compensated in the next cycle. The green time reallocation strategy (CVTSP-GD) is to insert the green time in the first cycle to make sure the buses priority requests are served, and the green time is reallocated in the next cycle to keep the total green time in two cycles the same. Aiming at minimizing total person delay at the intersection, an optimization method for Transit Signal Priority considering multirequest under connected vehicle environment is presented, which also implies the green time compensation algorithm. The central idea of CVTSP-CC is to insert the TSP green time in a cycle to provide buses priority. Considering arrival information about transit in the competition direction, the green time is inserted into the appropriate position of the competitive phase in the next cycle, and the optimal signal timing plan for the next cycle is generated.This section takes a three-phase signalized intersection as an example to explain these four strategies in Figure3. The original plan is shown in Figure 3(a). Buses A, B, C, D, E, and F arrive at the intersection at the first cycle, and buses G, H, I, and J arrive at the second cycle. According to the total person delay, the controller decides that buses D and E and buses I and J acquire signal priority at the first cycle and second cycle, respectively, and the timing plan is showed in Figure 3(b). CVTSP-GD is shown in Figure 3(c). After serving requests for bus D and E in the first cycle, green time is reallocated in the second cycle. As a result, green time of the third phase is extended. CVTSP-CC is as illustrated in Figure 3(d). Bus H priority request is served after calculating the total person delay for giving priority to bus H. The green time occupied by the first phase in the first cycle is compensated for the time when bus H arrives at the intersection. It can guarantee the priority of buses in all directions without compromising the interests of private vehicles.Figure 3
Timing plans for NTSP, CVTSP, CVTSP-GD, and CVTSP-CC.
(a)
NTSP (b)
CVTSP (c)
CVTSP-GD (d)
CVTSP-CCThe goal of this strategy is not to meet priority requests to all buses, because the priority requests from different directions conflict with each other and cannot be met simultaneously. When the buses call for requests priority, the total delay of the intersection can be calculated by the algorithm, and the plan which owns the least delay will be chosen. This plan can meet one or more bus priority requests in one phase.


## 4. Algorithm

### 4.1. Assumption

The following assumptions need to be created in the sake of establishing a method for Transit Signal Priority considering multirequest under connected vehicle environment:( 1 ) The entire road is under connected vehicle environment and the information is transferred between vehicles and vehicles, vehicles and infrastructures.( 2 ) The original signal timing plan is reasonable, and it can effectively allocate the traffic rights of vehicles in all directions.


### 4.2. Notation

To illustrate the description of the proposed model, the summary of the model notation is presented in Notations.


### 4.3. Detection and Status Discrimination Component

When the buses get to the sectionXA, Transit Signal Priority mechanism begins to work. If a bus passes XA during a signal cycle, we mark that ψ is equal to 1, namely, ψ=1; otherwise ψ=0. In this component, it is necessary to distinguish whether the bus kdeviates from the schedule. If the bus is on schedule, the signal controller runs the original signal plan. If the bus deviates from schedule and the delay is greater than the acceptable delay, the signal controller should determine whether to provide the bus k priority according to the actual situation.


### 4.4. Prediction Component

This part takes a three-phase signalized intersection as an example to describe the prediction algorithm. When the first bus passes through the stop line, the green phase is presented asj=1. According to the order of the green phase, the other phases are defined as j=2, j=3. The mechanism defines the beginning of the cycle as t0 and the time when the bus k arrives the section XA as T(i,j,k)A. In the prediction component, the mechanism needs to predict the time when the bus k arrives at the end of the queue, the time when the bus k starts again T(i+1,j,k)B′, and the time when the bus k reaches the stop line T(i+1,j,k)O.


#### 4.4.1. The Time When the Busk Arrives at the End of the Queue

If the busk arrives at the intersection in the red time of phase j for cycle i, the system starts to predict the location of the bus k when it arrives at the end of the queue according to the number of vehicles before the bus k. As shown in Figure 5, if the bus k arrives at the intersection in the green time phase j for cycle i, not all vehicles between the bus k and the stop line will line up. If P vehicles before the bus k meet g(i,j)s≤X(i,j,k,P)/V(k,P)≤g(i,j)e and P+1 vehicles before the bus k meet X(j,k,P+1)/V(k,P)>g(i,j)e, there will be P vehicles in line. The position where the bus k arrives at the end of the queue is(1)Xi,j,kB=∑p=1NALpgi,js≤Ti,j,kA≤gi,je∑p=1PLpTi,j,kA<gi,jsorTi,j,kA>gi,je.The time when the busk arrives at the end of the queue is(2)Ti,j,kB=XA-Xi,j,kBvk+Ti,j,kA.


#### 4.4.2. The Time When the Busk Starts Again

When red time for phasep during cycle k begins, the vehicles line up. Define velocity of queue wave at this time as V1. The queue begins to dissipate when the green time starts, and speed of discharging shockwave is V2. The bus k starts up when discharging shockwave is transmitted to the bus k, and the time is(3)Ti+1,j,kB′=Xi,j,kBV2+i·C+t0.


#### 4.4.3. The Time When the Busk Reaches the Stop Line

After the busk starts, it continues to drive at the speed of Vk. The time when the bus k reaches the stop line is(4)Ti+1,j,kO=Xi,j,kBV2+i·C+Xi,j,kBVk+t0.


### 4.5. Priority Signal Control Component

In this component, the TSP signal plan is calculated to serve priority to buses. The bus which gain priority can pass through the intersection unimpeded and would not be stopped by the queue.


#### 4.5.1. The Green Time Required for Multiple Requests

As shown in Figure4, queue of vehicles should be dissipated before the bus k reaches the end of the queue, so the green time required to serve a single transit priority request is(5)Gi,j,ks=Ti,j,kB-Xi,j,kBV2=XA-Xi,j,kBVk+Ti,j,kA-Xi,j,kBV2Gi,j,ke=Ti,j,kA+XAVkGi,j,k=Xi,j,kBVk+Xi,j,kBV2.Figure 4
Space-time map.Figure 5
Four situations for busK getting to the stop line.
(a)
Busk arrived at the intersection in red time (b)
Busk arrived at the end of the queue in red time (c)
Busk arrived at the intersection in green time (d)
Busk arrived at the end of the queue in green timeOn the basis of calculating the green time required for giving the busk priority, the green time required for the N buses is calculated. The buses in the same phase are reordered as k′,…,kn. And the green time required to provide the requests for N buses headed by the bus k is solved by iterative method.Step  1 ( N = 1 ) (6) G i , j , k s 1 = G i , j , k s G i , j , k e 1 = G i , j , k e G i , j , k 1 = G k .Step  2 ( N = N + 1 ) (7) G i , j , k s N = m i n G i , j , k s N - 1 , G i , j , k N s G i , j , k e N = m a x G i , j , k e N - 1 , G i , j , k N e G i , j , k N = G i , j , k e N - G i , j , k s N .Step  3. If N=n, the iteration ends.


#### 4.5.2. Signal Timing Plan

Three control strategies are adopted to avoid the green time diffuse, which are green extension, red truncation, and green insertion. WhenG(i,j,k)s(N)-g(i,j)e≤θ1, green extension is adopted; when r(i,j)e-G(i,j,k)s(N)≤θ2, red truncation is adopted, or green insertion is adopted. The start and end moments of the new TSP the green time are as follows:(8)Gi,j,ks,newN=gi,jeGi,j,ksN-gi,je≤θ1Gi,j,ksNGi,j,ksN-gi,je>θ1,ri,je-Gi,j,ksN>θ2Gi,j,ksNri,je-Gi,j,ksN≤θ2Gi,j,ke,newN=Gi,j,keNGi,j,ksN-gi,je≤θ1Gi,j,keNGi,j,ksN-gi,je>θ1,ri,je-Gi,j,ksN>θ2ri,jeri,je-Gi,j,ksN≤θ2.TSP green time is inserted in the phasej when phase j′ is green duration originally, so phase j′ should be inserted into a red time whose length is equal as TSP green time.(9)Ri,j′s=Gi,j,ks,newNRi,j′e=Gi,j,ke,newN.In order to obtain the optimal signal plan, a mixed-integer linear programming equation based on the minimum total delays of intersection is proposed to get the optimal TSP green time. The objective function is set as(10)Minimize∑mDm·Occm+∑kDk·Occk.The constraint equation is(11)Gi,j,knew≥GminGi,j,knew≤Gmax.


#### 4.5.3. Compensation Signal Plan

As shown in Figure3, the adopted mechanism is the way to compensate the green time for the occupied phase in the next cycle if the green time is occupied in the previous cycle. The green time which meets the priority needs of buses with different arrival times is inserted to the previous cycle, which is based on minimizing the total person delay at the intersection. And the compensational green time is inserted to the next cycle after considering the arrival information of the buses of the compensational phase. The length of the green time occupied in the previous cycle is equal to the green time compensated in the next period, which means that the total green times and the total red times of each phase in the two cycles are equal. It also represents that the length of each cycle is the same.For compensating the green time, the time when buses arrive at the intersection in phasej′ and the green time required for priority will be predicted. If there is no bus at the intersection in phase j′ of cycle i+1, then the signal plan of cycle i+1 meets(12)gi,j+Gi,j,knew=gi+1,j-Gi+1,j′,k′final.If there is a bus to the intersection in phasej′ of cycle i+1, then the signal plan of cycle i+1 meets(13)Gi+1,j′,k′s,com=Gi+1,j′,k′s,newGi+1,j′,k′new≤Gi,j,knewGi+1,j′,k′e,new-Gi+1,j′,k′newGi+1,j′,k′new>Gi,j,knewGi+1,j′,k′e,com=Gi+1,j′,k′e,new.After obtaining the compensation signal plan by (12) and (13), the compensational signal plan which owns the minimum total delay will be selected according to (10) and (11).


## 4.1. Assumption

The following assumptions need to be created in the sake of establishing a method for Transit Signal Priority considering multirequest under connected vehicle environment:( 1 ) The entire road is under connected vehicle environment and the information is transferred between vehicles and vehicles, vehicles and infrastructures.( 2 ) The original signal timing plan is reasonable, and it can effectively allocate the traffic rights of vehicles in all directions.


## 4.2. Notation

To illustrate the description of the proposed model, the summary of the model notation is presented in Notations.


## 4.3. Detection and Status Discrimination Component

When the buses get to the sectionXA, Transit Signal Priority mechanism begins to work. If a bus passes XA during a signal cycle, we mark that ψ is equal to 1, namely, ψ=1; otherwise ψ=0. In this component, it is necessary to distinguish whether the bus kdeviates from the schedule. If the bus is on schedule, the signal controller runs the original signal plan. If the bus deviates from schedule and the delay is greater than the acceptable delay, the signal controller should determine whether to provide the bus k priority according to the actual situation.


## 4.4. Prediction Component

This part takes a three-phase signalized intersection as an example to describe the prediction algorithm. When the first bus passes through the stop line, the green phase is presented asj=1. According to the order of the green phase, the other phases are defined as j=2, j=3. The mechanism defines the beginning of the cycle as t0 and the time when the bus k arrives the section XA as T(i,j,k)A. In the prediction component, the mechanism needs to predict the time when the bus k arrives at the end of the queue, the time when the bus k starts again T(i+1,j,k)B′, and the time when the bus k reaches the stop line T(i+1,j,k)O.


### 4.4.1. The Time When the Busk Arrives at the End of the Queue

If the busk arrives at the intersection in the red time of phase j for cycle i, the system starts to predict the location of the bus k when it arrives at the end of the queue according to the number of vehicles before the bus k. As shown in Figure 5, if the bus k arrives at the intersection in the green time phase j for cycle i, not all vehicles between the bus k and the stop line will line up. If P vehicles before the bus k meet g(i,j)s≤X(i,j,k,P)/V(k,P)≤g(i,j)e and P+1 vehicles before the bus k meet X(j,k,P+1)/V(k,P)>g(i,j)e, there will be P vehicles in line. The position where the bus k arrives at the end of the queue is(1)Xi,j,kB=∑p=1NALpgi,js≤Ti,j,kA≤gi,je∑p=1PLpTi,j,kA<gi,jsorTi,j,kA>gi,je.The time when the busk arrives at the end of the queue is(2)Ti,j,kB=XA-Xi,j,kBvk+Ti,j,kA.


### 4.4.2. The Time When the Busk Starts Again

When red time for phasep during cycle k begins, the vehicles line up. Define velocity of queue wave at this time as V1. The queue begins to dissipate when the green time starts, and speed of discharging shockwave is V2. The bus k starts up when discharging shockwave is transmitted to the bus k, and the time is(3)Ti+1,j,kB′=Xi,j,kBV2+i·C+t0.


### 4.4.3. The Time When the Busk Reaches the Stop Line

After the busk starts, it continues to drive at the speed of Vk. The time when the bus k reaches the stop line is(4)Ti+1,j,kO=Xi,j,kBV2+i·C+Xi,j,kBVk+t0.


## 4.4.1. The Time When the Busk Arrives at the End of the Queue

If the busk arrives at the intersection in the red time of phase j for cycle i, the system starts to predict the location of the bus k when it arrives at the end of the queue according to the number of vehicles before the bus k. As shown in Figure 5, if the bus k arrives at the intersection in the green time phase j for cycle i, not all vehicles between the bus k and the stop line will line up. If P vehicles before the bus k meet g(i,j)s≤X(i,j,k,P)/V(k,P)≤g(i,j)e and P+1 vehicles before the bus k meet X(j,k,P+1)/V(k,P)>g(i,j)e, there will be P vehicles in line. The position where the bus k arrives at the end of the queue is(1)Xi,j,kB=∑p=1NALpgi,js≤Ti,j,kA≤gi,je∑p=1PLpTi,j,kA<gi,jsorTi,j,kA>gi,je.The time when the busk arrives at the end of the queue is(2)Ti,j,kB=XA-Xi,j,kBvk+Ti,j,kA.


## 4.4.2. The Time When the Busk Starts Again

When red time for phasep during cycle k begins, the vehicles line up. Define velocity of queue wave at this time as V1. The queue begins to dissipate when the green time starts, and speed of discharging shockwave is V2. The bus k starts up when discharging shockwave is transmitted to the bus k, and the time is(3)Ti+1,j,kB′=Xi,j,kBV2+i·C+t0.


## 4.4.3. The Time When the Busk Reaches the Stop Line

After the busk starts, it continues to drive at the speed of Vk. The time when the bus k reaches the stop line is(4)Ti+1,j,kO=Xi,j,kBV2+i·C+Xi,j,kBVk+t0.


## 4.5. Priority Signal Control Component

In this component, the TSP signal plan is calculated to serve priority to buses. The bus which gain priority can pass through the intersection unimpeded and would not be stopped by the queue.


### 4.5.1. The Green Time Required for Multiple Requests

As shown in Figure4, queue of vehicles should be dissipated before the bus k reaches the end of the queue, so the green time required to serve a single transit priority request is(5)Gi,j,ks=Ti,j,kB-Xi,j,kBV2=XA-Xi,j,kBVk+Ti,j,kA-Xi,j,kBV2Gi,j,ke=Ti,j,kA+XAVkGi,j,k=Xi,j,kBVk+Xi,j,kBV2.Figure 4
Space-time map.Figure 5
Four situations for busK getting to the stop line.
(a)
Busk arrived at the intersection in red time (b)
Busk arrived at the end of the queue in red time (c)
Busk arrived at the intersection in green time (d)
Busk arrived at the end of the queue in green timeOn the basis of calculating the green time required for giving the busk priority, the green time required for the N buses is calculated. The buses in the same phase are reordered as k′,…,kn. And the green time required to provide the requests for N buses headed by the bus k is solved by iterative method.Step  1 ( N = 1 ) (6) G i , j , k s 1 = G i , j , k s G i , j , k e 1 = G i , j , k e G i , j , k 1 = G k .Step  2 ( N = N + 1 ) (7) G i , j , k s N = m i n G i , j , k s N - 1 , G i , j , k N s G i , j , k e N = m a x G i , j , k e N - 1 , G i , j , k N e G i , j , k N = G i , j , k e N - G i , j , k s N .Step  3. If N=n, the iteration ends.


### 4.5.2. Signal Timing Plan

Three control strategies are adopted to avoid the green time diffuse, which are green extension, red truncation, and green insertion. WhenG(i,j,k)s(N)-g(i,j)e≤θ1, green extension is adopted; when r(i,j)e-G(i,j,k)s(N)≤θ2, red truncation is adopted, or green insertion is adopted. The start and end moments of the new TSP the green time are as follows:(8)Gi,j,ks,newN=gi,jeGi,j,ksN-gi,je≤θ1Gi,j,ksNGi,j,ksN-gi,je>θ1,ri,je-Gi,j,ksN>θ2Gi,j,ksNri,je-Gi,j,ksN≤θ2Gi,j,ke,newN=Gi,j,keNGi,j,ksN-gi,je≤θ1Gi,j,keNGi,j,ksN-gi,je>θ1,ri,je-Gi,j,ksN>θ2ri,jeri,je-Gi,j,ksN≤θ2.TSP green time is inserted in the phasej when phase j′ is green duration originally, so phase j′ should be inserted into a red time whose length is equal as TSP green time.(9)Ri,j′s=Gi,j,ks,newNRi,j′e=Gi,j,ke,newN.In order to obtain the optimal signal plan, a mixed-integer linear programming equation based on the minimum total delays of intersection is proposed to get the optimal TSP green time. The objective function is set as(10)Minimize∑mDm·Occm+∑kDk·Occk.The constraint equation is(11)Gi,j,knew≥GminGi,j,knew≤Gmax.


### 4.5.3. Compensation Signal Plan

As shown in Figure3, the adopted mechanism is the way to compensate the green time for the occupied phase in the next cycle if the green time is occupied in the previous cycle. The green time which meets the priority needs of buses with different arrival times is inserted to the previous cycle, which is based on minimizing the total person delay at the intersection. And the compensational green time is inserted to the next cycle after considering the arrival information of the buses of the compensational phase. The length of the green time occupied in the previous cycle is equal to the green time compensated in the next period, which means that the total green times and the total red times of each phase in the two cycles are equal. It also represents that the length of each cycle is the same.For compensating the green time, the time when buses arrive at the intersection in phasej′ and the green time required for priority will be predicted. If there is no bus at the intersection in phase j′ of cycle i+1, then the signal plan of cycle i+1 meets(12)gi,j+Gi,j,knew=gi+1,j-Gi+1,j′,k′final.If there is a bus to the intersection in phasej′ of cycle i+1, then the signal plan of cycle i+1 meets(13)Gi+1,j′,k′s,com=Gi+1,j′,k′s,newGi+1,j′,k′new≤Gi,j,knewGi+1,j′,k′e,new-Gi+1,j′,k′newGi+1,j′,k′new>Gi,j,knewGi+1,j′,k′e,com=Gi+1,j′,k′e,new.After obtaining the compensation signal plan by (12) and (13), the compensational signal plan which owns the minimum total delay will be selected according to (10) and (11).


## 4.5.1. The Green Time Required for Multiple Requests

As shown in Figure4, queue of vehicles should be dissipated before the bus k reaches the end of the queue, so the green time required to serve a single transit priority request is(5)Gi,j,ks=Ti,j,kB-Xi,j,kBV2=XA-Xi,j,kBVk+Ti,j,kA-Xi,j,kBV2Gi,j,ke=Ti,j,kA+XAVkGi,j,k=Xi,j,kBVk+Xi,j,kBV2.Figure 4
Space-time map.Figure 5
Four situations for busK getting to the stop line.
(a)
Busk arrived at the intersection in red time (b)
Busk arrived at the end of the queue in red time (c)
Busk arrived at the intersection in green time (d)
Busk arrived at the end of the queue in green timeOn the basis of calculating the green time required for giving the busk priority, the green time required for the N buses is calculated. The buses in the same phase are reordered as k′,…,kn. And the green time required to provide the requests for N buses headed by the bus k is solved by iterative method.Step  1 ( N = 1 ) (6) G i , j , k s 1 = G i , j , k s G i , j , k e 1 = G i , j , k e G i , j , k 1 = G k .Step  2 ( N = N + 1 ) (7) G i , j , k s N = m i n G i , j , k s N - 1 , G i , j , k N s G i , j , k e N = m a x G i , j , k e N - 1 , G i , j , k N e G i , j , k N = G i , j , k e N - G i , j , k s N .Step  3. If N=n, the iteration ends.


## 4.5.2. Signal Timing Plan

Three control strategies are adopted to avoid the green time diffuse, which are green extension, red truncation, and green insertion. WhenG(i,j,k)s(N)-g(i,j)e≤θ1, green extension is adopted; when r(i,j)e-G(i,j,k)s(N)≤θ2, red truncation is adopted, or green insertion is adopted. The start and end moments of the new TSP the green time are as follows:(8)Gi,j,ks,newN=gi,jeGi,j,ksN-gi,je≤θ1Gi,j,ksNGi,j,ksN-gi,je>θ1,ri,je-Gi,j,ksN>θ2Gi,j,ksNri,je-Gi,j,ksN≤θ2Gi,j,ke,newN=Gi,j,keNGi,j,ksN-gi,je≤θ1Gi,j,keNGi,j,ksN-gi,je>θ1,ri,je-Gi,j,ksN>θ2ri,jeri,je-Gi,j,ksN≤θ2.TSP green time is inserted in the phasej when phase j′ is green duration originally, so phase j′ should be inserted into a red time whose length is equal as TSP green time.(9)Ri,j′s=Gi,j,ks,newNRi,j′e=Gi,j,ke,newN.In order to obtain the optimal signal plan, a mixed-integer linear programming equation based on the minimum total delays of intersection is proposed to get the optimal TSP green time. The objective function is set as(10)Minimize∑mDm·Occm+∑kDk·Occk.The constraint equation is(11)Gi,j,knew≥GminGi,j,knew≤Gmax.


## 4.5.3. Compensation Signal Plan

As shown in Figure3, the adopted mechanism is the way to compensate the green time for the occupied phase in the next cycle if the green time is occupied in the previous cycle. The green time which meets the priority needs of buses with different arrival times is inserted to the previous cycle, which is based on minimizing the total person delay at the intersection. And the compensational green time is inserted to the next cycle after considering the arrival information of the buses of the compensational phase. The length of the green time occupied in the previous cycle is equal to the green time compensated in the next period, which means that the total green times and the total red times of each phase in the two cycles are equal. It also represents that the length of each cycle is the same.For compensating the green time, the time when buses arrive at the intersection in phasej′ and the green time required for priority will be predicted. If there is no bus at the intersection in phase j′ of cycle i+1, then the signal plan of cycle i+1 meets(12)gi,j+Gi,j,knew=gi+1,j-Gi+1,j′,k′final.If there is a bus to the intersection in phasej′ of cycle i+1, then the signal plan of cycle i+1 meets(13)Gi+1,j′,k′s,com=Gi+1,j′,k′s,newGi+1,j′,k′new≤Gi,j,knewGi+1,j′,k′e,new-Gi+1,j′,k′newGi+1,j′,k′new>Gi,j,knewGi+1,j′,k′e,com=Gi+1,j′,k′e,new.After obtaining the compensation signal plan by (12) and (13), the compensational signal plan which owns the minimum total delay will be selected according to (10) and (11).


## 5. Simulation Evaluation

### 5.1. Study Site

An intersection in Changchun City, China, is selected to evaluate the performance of the proposed model. The layout of the intersection and the information of signal timing plan are shown in Figure1. Traffic volumes of Nanhu Road and Donglingnan Street were investigated in April 25th, 26, and the traffic volumes are shown in Table 1.Table 1
Traffic volumes at the intersection.
V/C  LT (veh) TH (veh) RT (veh) LT (bus) TH (bus) RT (bus) 0.5 EB 270 1356 124 4 26 10 WB 170 1294 61 NA 26 NA SB 35 525 140 NA 6 4 NB 182 490 196 10 6 NA  0.7 EB 279 2120 100 4 26 10 WB 165 1823 110 NA 26 NA SB 46 593 250 NA 6 4 NB 205 579 194 10 6 NA  0.9 EB 254 2904 699 4 26 10 WB 191 2312 381 NA 26 NA SB 56 672 315 NA 6 4 NB 296 678 487 10 6 NA


### 5.2. Simulation Results

#### 5.2.1. Simulation Background

In this paper, the COM interface of VISSIM simulation software was used to simulate connected vehicle environment. A simulation model was set up in VISSIM simulation software according to the actual intersection of Nanhu Road and Donglingnan Avenue. The COM interface can control the experiment process and get real-time data after the simulation starts. The real-time information of vehicles, including the location, speed, direction, passenger capacity, and simulation time, can be predicted at the time when the buses arrive at the intersection. Then the optimal signal timing plan is obtained.The intersection was simulated under three traffic conditions:V/C=0.5, V/C=0.7, and V/C=0.9. The speed limit on the road was 40 mph and each simulation runs 17 cycles. When the VCR was 0.5, 0.7, and 0.9, four signal control strategies were tested, respectively. The first strategy was no priority (NTSP), and the intersection runs the original signal timing plan. The second strategy used the Transit Signal Priority under connected vehicle environment (CVTSP) for each cycle and did not take any compensation during the next cycle. The third strategy (CVTSP-GD) was to serve the requests of buses by CVTSP in the first cycle and distribute the green time in the second cycle based on the signal plan information of the first cycle. The fourth strategy (CVTSP-CC) was to adopt CVTSP in the first cycle, and the green time was compensated in the next cycle by considering the transit arrival time of the competitive direction.


#### 5.2.2. Results Analysis

In this experiment, four kinds of signal control methods were tested under three different traffic conditions: NTSP, CVTSP, CVTSP-GD, and CVTSP-CC. The results are shown in Table2. Per person delay is used to evaluate the effect of four methods. In addition, compared with the original signal control strategy, the improvement in average private vehicle delay, average bus delay, and average per person delay of three other strategies is shown in Table 2.Table 2
The results of four strategies.
V/C Strategy NTSP CVTSP CVTSP-GD CVTSP-CC Percent change CVTSP CVTSP-GD CVTSP-CC 0.5 Private vehicle delay (s) 36.66 38.81 36.41 35.29 5.86% −0.68% −3.74% Bus delay(s) 44.20 27.40 32.74 20.20 −38.01% −25.93% −54.30% Per person delay (s) 38.61 35.81 35.44 31.44 −7.25% −8.21% −18.57%  0.7 Private vehicle delay (s) 46.79 49.28 46.82 43.22 5.32% 0.06% −7.62% Bus delay(s) 46.19 23.71 37.26 18.45 −48.67% −19.33% −60.06% Per person delay (s) 47.33 47.41 46.36 41.70 0.17% −2.05% −11.88%  0.9 Private vehicle delay (s) 56.01 53.43 53.57 48.67 −4.61% −4.36% −13.10% Bus delay(s) 51.50 34.09 44.56 29.64 −33.81% −13.48% −42.44% Per person delay(s) 54.57 48.8 50.97 44.22 −10.57% −6.60% −18.97%It can be seen from Table2 that average private vehicle delay in the CVTSP increases slightly compared with the NTSP when VCR is 0.5. This is because the CVTSP serves priority to buses at the intersection in each cycle, causing additional delay in private vehicle, which is also the reason why the bus delay is significantly lower than before. In contrast to this, private vehicle delay in CVTSP-GD is almost the same as NTSP owing to the reallocation of the green time. Yet the effect of reducing bus delay in CVTSP-GD is worse than that of CVTSP. As can be seen from the results of the CVTSP-CC, the delay of private vehicles is slightly reduced and the bus delay is decreased by 20.20 seconds. This demonstrates that compensation strategy adopted by CVTSP-CC can reduce the bus delay as much as possible without producing the additional delay in private vehicle and the result is reducing per person delay at the whole intersection. The delay with the saturation of 0.7 is similar to that of 0.5, indicating that the proposed method for transit priority control is also applied perfectly. When V/C is 0.9, private vehicle delay of CVTSP, CVTSP-GD, and CVTSP-CC decreased slightly compared with NTSP. The bus delay of CVTSP is reduced to 34.09 seconds, while CVTSP-GD and CVTSP-CC are 44.56 seconds and 29.64 seconds, respectively. The above shows that when the road is congested, the optimization method for Transit Signal Priority considering multirequest under connected vehicle environment still can effectively reduce the average delay of the intersection.From Table2, it is possible to more clearly compare the effects of the above three control strategies on the per passenger delay of private vehicles, per passenger delay of buses and the per person delay of the intersection. CVTSP-CC can provide public transport priority. Compared with the original signal plan, the bus delay of CVTSP-CC is decreased by 54.31%. CVTSP-CC has a significant effect on reducing bus delay compared to 38.00% reduction in CVTSP and 25.92% in CVTSP-GD. It is worth mentioning that because of compensating for the green time in the next cycle, per person delay is decreased by 18.57% in CVTSP-CC, and private vehicle delay is decreased by 3.73% as well. Similarly, when saturation is 0.7, CVTSP-CC improves per private vehicle delay by 7.62%, per bus delay by 42.44%, and per person delay by 11.88%. It illustrates that proposed method is also applicable to the saturation of 0.7. When saturation is higher (i.e., 0.9), these three control strategies reduce private vehicle delay by 4.60%, 4.35%, and 13.10%. At the same time, bus delay is reduced by 33.81%, 13.48%, and 42.44%, respectively, and per person delay is decreased by 10.57%, 6.59%, and 18.96%. To summarize, CVTSP-CC is beneficial for reducing per person delay at the intersection, especially for reducing bus delay. Both CVTSP and CVTSP-CC can reduce the per person delay of bus passengers significantly. However, CVTSP may increase the per person delay of private vehicles slightly. CVTSP-CC reduced the per person delay by 18.57%, 11.88%, and 18.97% under three conditions, respectively, which is much smaller than the other three signal control methods.


## 5.1. Study Site

An intersection in Changchun City, China, is selected to evaluate the performance of the proposed model. The layout of the intersection and the information of signal timing plan are shown in Figure1. Traffic volumes of Nanhu Road and Donglingnan Street were investigated in April 25th, 26, and the traffic volumes are shown in Table 1.Table 1
Traffic volumes at the intersection.
V/C  LT (veh) TH (veh) RT (veh) LT (bus) TH (bus) RT (bus) 0.5 EB 270 1356 124 4 26 10 WB 170 1294 61 NA 26 NA SB 35 525 140 NA 6 4 NB 182 490 196 10 6 NA  0.7 EB 279 2120 100 4 26 10 WB 165 1823 110 NA 26 NA SB 46 593 250 NA 6 4 NB 205 579 194 10 6 NA  0.9 EB 254 2904 699 4 26 10 WB 191 2312 381 NA 26 NA SB 56 672 315 NA 6 4 NB 296 678 487 10 6 NA


## 5.2. Simulation Results

### 5.2.1. Simulation Background

In this paper, the COM interface of VISSIM simulation software was used to simulate connected vehicle environment. A simulation model was set up in VISSIM simulation software according to the actual intersection of Nanhu Road and Donglingnan Avenue. The COM interface can control the experiment process and get real-time data after the simulation starts. The real-time information of vehicles, including the location, speed, direction, passenger capacity, and simulation time, can be predicted at the time when the buses arrive at the intersection. Then the optimal signal timing plan is obtained.The intersection was simulated under three traffic conditions:V/C=0.5, V/C=0.7, and V/C=0.9. The speed limit on the road was 40 mph and each simulation runs 17 cycles. When the VCR was 0.5, 0.7, and 0.9, four signal control strategies were tested, respectively. The first strategy was no priority (NTSP), and the intersection runs the original signal timing plan. The second strategy used the Transit Signal Priority under connected vehicle environment (CVTSP) for each cycle and did not take any compensation during the next cycle. The third strategy (CVTSP-GD) was to serve the requests of buses by CVTSP in the first cycle and distribute the green time in the second cycle based on the signal plan information of the first cycle. The fourth strategy (CVTSP-CC) was to adopt CVTSP in the first cycle, and the green time was compensated in the next cycle by considering the transit arrival time of the competitive direction.


### 5.2.2. Results Analysis

In this experiment, four kinds of signal control methods were tested under three different traffic conditions: NTSP, CVTSP, CVTSP-GD, and CVTSP-CC. The results are shown in Table2. Per person delay is used to evaluate the effect of four methods. In addition, compared with the original signal control strategy, the improvement in average private vehicle delay, average bus delay, and average per person delay of three other strategies is shown in Table 2.Table 2
The results of four strategies.
V/C Strategy NTSP CVTSP CVTSP-GD CVTSP-CC Percent change CVTSP CVTSP-GD CVTSP-CC 0.5 Private vehicle delay (s) 36.66 38.81 36.41 35.29 5.86% −0.68% −3.74% Bus delay(s) 44.20 27.40 32.74 20.20 −38.01% −25.93% −54.30% Per person delay (s) 38.61 35.81 35.44 31.44 −7.25% −8.21% −18.57%  0.7 Private vehicle delay (s) 46.79 49.28 46.82 43.22 5.32% 0.06% −7.62% Bus delay(s) 46.19 23.71 37.26 18.45 −48.67% −19.33% −60.06% Per person delay (s) 47.33 47.41 46.36 41.70 0.17% −2.05% −11.88%  0.9 Private vehicle delay (s) 56.01 53.43 53.57 48.67 −4.61% −4.36% −13.10% Bus delay(s) 51.50 34.09 44.56 29.64 −33.81% −13.48% −42.44% Per person delay(s) 54.57 48.8 50.97 44.22 −10.57% −6.60% −18.97%It can be seen from Table2 that average private vehicle delay in the CVTSP increases slightly compared with the NTSP when VCR is 0.5. This is because the CVTSP serves priority to buses at the intersection in each cycle, causing additional delay in private vehicle, which is also the reason why the bus delay is significantly lower than before. In contrast to this, private vehicle delay in CVTSP-GD is almost the same as NTSP owing to the reallocation of the green time. Yet the effect of reducing bus delay in CVTSP-GD is worse than that of CVTSP. As can be seen from the results of the CVTSP-CC, the delay of private vehicles is slightly reduced and the bus delay is decreased by 20.20 seconds. This demonstrates that compensation strategy adopted by CVTSP-CC can reduce the bus delay as much as possible without producing the additional delay in private vehicle and the result is reducing per person delay at the whole intersection. The delay with the saturation of 0.7 is similar to that of 0.5, indicating that the proposed method for transit priority control is also applied perfectly. When V/C is 0.9, private vehicle delay of CVTSP, CVTSP-GD, and CVTSP-CC decreased slightly compared with NTSP. The bus delay of CVTSP is reduced to 34.09 seconds, while CVTSP-GD and CVTSP-CC are 44.56 seconds and 29.64 seconds, respectively. The above shows that when the road is congested, the optimization method for Transit Signal Priority considering multirequest under connected vehicle environment still can effectively reduce the average delay of the intersection.From Table2, it is possible to more clearly compare the effects of the above three control strategies on the per passenger delay of private vehicles, per passenger delay of buses and the per person delay of the intersection. CVTSP-CC can provide public transport priority. Compared with the original signal plan, the bus delay of CVTSP-CC is decreased by 54.31%. CVTSP-CC has a significant effect on reducing bus delay compared to 38.00% reduction in CVTSP and 25.92% in CVTSP-GD. It is worth mentioning that because of compensating for the green time in the next cycle, per person delay is decreased by 18.57% in CVTSP-CC, and private vehicle delay is decreased by 3.73% as well. Similarly, when saturation is 0.7, CVTSP-CC improves per private vehicle delay by 7.62%, per bus delay by 42.44%, and per person delay by 11.88%. It illustrates that proposed method is also applicable to the saturation of 0.7. When saturation is higher (i.e., 0.9), these three control strategies reduce private vehicle delay by 4.60%, 4.35%, and 13.10%. At the same time, bus delay is reduced by 33.81%, 13.48%, and 42.44%, respectively, and per person delay is decreased by 10.57%, 6.59%, and 18.96%. To summarize, CVTSP-CC is beneficial for reducing per person delay at the intersection, especially for reducing bus delay. Both CVTSP and CVTSP-CC can reduce the per person delay of bus passengers significantly. However, CVTSP may increase the per person delay of private vehicles slightly. CVTSP-CC reduced the per person delay by 18.57%, 11.88%, and 18.97% under three conditions, respectively, which is much smaller than the other three signal control methods.


## 5.2.1. Simulation Background

In this paper, the COM interface of VISSIM simulation software was used to simulate connected vehicle environment. A simulation model was set up in VISSIM simulation software according to the actual intersection of Nanhu Road and Donglingnan Avenue. The COM interface can control the experiment process and get real-time data after the simulation starts. The real-time information of vehicles, including the location, speed, direction, passenger capacity, and simulation time, can be predicted at the time when the buses arrive at the intersection. Then the optimal signal timing plan is obtained.The intersection was simulated under three traffic conditions:V/C=0.5, V/C=0.7, and V/C=0.9. The speed limit on the road was 40 mph and each simulation runs 17 cycles. When the VCR was 0.5, 0.7, and 0.9, four signal control strategies were tested, respectively. The first strategy was no priority (NTSP), and the intersection runs the original signal timing plan. The second strategy used the Transit Signal Priority under connected vehicle environment (CVTSP) for each cycle and did not take any compensation during the next cycle. The third strategy (CVTSP-GD) was to serve the requests of buses by CVTSP in the first cycle and distribute the green time in the second cycle based on the signal plan information of the first cycle. The fourth strategy (CVTSP-CC) was to adopt CVTSP in the first cycle, and the green time was compensated in the next cycle by considering the transit arrival time of the competitive direction.


## 5.2.2. Results Analysis

In this experiment, four kinds of signal control methods were tested under three different traffic conditions: NTSP, CVTSP, CVTSP-GD, and CVTSP-CC. The results are shown in Table2. Per person delay is used to evaluate the effect of four methods. In addition, compared with the original signal control strategy, the improvement in average private vehicle delay, average bus delay, and average per person delay of three other strategies is shown in Table 2.Table 2
The results of four strategies.
V/C Strategy NTSP CVTSP CVTSP-GD CVTSP-CC Percent change CVTSP CVTSP-GD CVTSP-CC 0.5 Private vehicle delay (s) 36.66 38.81 36.41 35.29 5.86% −0.68% −3.74% Bus delay(s) 44.20 27.40 32.74 20.20 −38.01% −25.93% −54.30% Per person delay (s) 38.61 35.81 35.44 31.44 −7.25% −8.21% −18.57%  0.7 Private vehicle delay (s) 46.79 49.28 46.82 43.22 5.32% 0.06% −7.62% Bus delay(s) 46.19 23.71 37.26 18.45 −48.67% −19.33% −60.06% Per person delay (s) 47.33 47.41 46.36 41.70 0.17% −2.05% −11.88%  0.9 Private vehicle delay (s) 56.01 53.43 53.57 48.67 −4.61% −4.36% −13.10% Bus delay(s) 51.50 34.09 44.56 29.64 −33.81% −13.48% −42.44% Per person delay(s) 54.57 48.8 50.97 44.22 −10.57% −6.60% −18.97%It can be seen from Table2 that average private vehicle delay in the CVTSP increases slightly compared with the NTSP when VCR is 0.5. This is because the CVTSP serves priority to buses at the intersection in each cycle, causing additional delay in private vehicle, which is also the reason why the bus delay is significantly lower than before. In contrast to this, private vehicle delay in CVTSP-GD is almost the same as NTSP owing to the reallocation of the green time. Yet the effect of reducing bus delay in CVTSP-GD is worse than that of CVTSP. As can be seen from the results of the CVTSP-CC, the delay of private vehicles is slightly reduced and the bus delay is decreased by 20.20 seconds. This demonstrates that compensation strategy adopted by CVTSP-CC can reduce the bus delay as much as possible without producing the additional delay in private vehicle and the result is reducing per person delay at the whole intersection. The delay with the saturation of 0.7 is similar to that of 0.5, indicating that the proposed method for transit priority control is also applied perfectly. When V/C is 0.9, private vehicle delay of CVTSP, CVTSP-GD, and CVTSP-CC decreased slightly compared with NTSP. The bus delay of CVTSP is reduced to 34.09 seconds, while CVTSP-GD and CVTSP-CC are 44.56 seconds and 29.64 seconds, respectively. The above shows that when the road is congested, the optimization method for Transit Signal Priority considering multirequest under connected vehicle environment still can effectively reduce the average delay of the intersection.From Table2, it is possible to more clearly compare the effects of the above three control strategies on the per passenger delay of private vehicles, per passenger delay of buses and the per person delay of the intersection. CVTSP-CC can provide public transport priority. Compared with the original signal plan, the bus delay of CVTSP-CC is decreased by 54.31%. CVTSP-CC has a significant effect on reducing bus delay compared to 38.00% reduction in CVTSP and 25.92% in CVTSP-GD. It is worth mentioning that because of compensating for the green time in the next cycle, per person delay is decreased by 18.57% in CVTSP-CC, and private vehicle delay is decreased by 3.73% as well. Similarly, when saturation is 0.7, CVTSP-CC improves per private vehicle delay by 7.62%, per bus delay by 42.44%, and per person delay by 11.88%. It illustrates that proposed method is also applicable to the saturation of 0.7. When saturation is higher (i.e., 0.9), these three control strategies reduce private vehicle delay by 4.60%, 4.35%, and 13.10%. At the same time, bus delay is reduced by 33.81%, 13.48%, and 42.44%, respectively, and per person delay is decreased by 10.57%, 6.59%, and 18.96%. To summarize, CVTSP-CC is beneficial for reducing per person delay at the intersection, especially for reducing bus delay. Both CVTSP and CVTSP-CC can reduce the per person delay of bus passengers significantly. However, CVTSP may increase the per person delay of private vehicles slightly. CVTSP-CC reduced the per person delay by 18.57%, 11.88%, and 18.97% under three conditions, respectively, which is much smaller than the other three signal control methods.


## 6. Conclusions

An optimization method for Transit Signal Priority (TSP) considering multirequest under connected vehicle environment is presented in this paper. This method devotes to solving the conflicting requests of multidirectional buses with different arrival times and brings out transit priority in the premise of minimizing per person delay at the intersection. The central idea of this method is to gain the optimal TSP signal timing plan to serve buses priority in a mixed-integer linear program. Considering buses arrival information of the competitive direction, the green time is inserted into the appropriate position of the compensational phase in the next cycle. The paper designs a kind of green compensation method which meets the requirement of minimizing per person delay at the intersection. Based on the COM interface of VISSIM simulation platform, this paper simulated and evaluated the proposed method. The result shows that the proposed method can reduce the delay of the intersection more effectively than the other three signal control strategies. In the case of the VCR is 0.5. This proposed method reduced per person delay by 18.57%, with 54.31% reduction in per bus passenger delay and 3.73% reduction in per private vehicle delay. When the VCR on the arterial is 0.7, per person delay, per bus delay, and per private vehicle delay were reduced by 11.88%, 42.44%, and 7.62%, respectively. When the VCR on the arterial is 0.9, per person delay, per bus delay, and per private vehicle delay were reduced by 18.96%, 60.06%, and 13.10%, respectively. CVTSP-CC can reduce per person delay of buses significantly, while taking into account the per person delay of private vehicles.



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*Source: 7498594-2018-06-26.xml*