Coordinated Control Method of Bus Signal Priority and Speed Adjustment Based on Stop-Skipping

Abstract

There is an inherent coupling relationship between the time when buses arrive at the station and the time when they arrive the intersection, and it is essential to study the relationship as a whole to maximize the benefits of company operations and passenger services. In this study, a coordinated control method of signal priority and speed regulation in the stop-skipping mode at peak hours is proposed. First, the decision result of stop-skipping is obtained based on the historical passenger flow data. On this basis, the signal-priority decision is made for each vehicle in combination with the signal period and the arrival time of the intersection, and coordinated control is carried out in combination with the speed adjustment. The result of the genetic algorithm shows that cooperative control and prevention can minimize the passenger delay time and enterprise operation cost. The conclusions obtained in this research lay a theoretical foundation for company operation and signal-priority triggering mechanism.

1. Introduction

With the improvement of living standards and the tendency of the road network to be saturated, traffic accessibility is no longer the main focus for residents’ travel. In order to improve the timeliness and flexibility of bus operation, some scholars have focused on the research of dynamic dispatch on the basis of static dispatch.

Conventional dynamic dispatch strategies include holding, stop-skipping, signal priority, etc. [1,2]. Some scholars have undertaken the following research on the single dynamic dispatch strategy of public transport.

Some scholars put forward a stop-skipping strategy that is robust to travel time in view of the common phenomenon that people and vehicles wait for each other during peak hours [3,4,5]. In order to calibrate the arrival time, some scholars proposed a dynamic holding strategy, which proved that this strategy can significantly improve service efficiency [6,7,8]. Based on bus signal priority systems (BSP), some scholars discussed different types of priority control strategies and evaluated the priority process [9,10,11].

However, a single dynamic bus scheduling strategy is not suitable for dealing with the conventional random disturbance. At this time, the quality of the public transport service cannot be significantly improved, which is counterproductive [12,13]. To deal with this situation, some scholars have studied combined dynamic scheduling strategies based on a single dynamic scheduling strategy.

In order to maintain the stability of the operation interval and reduce the average waiting time of passengers, some scholars proposed a cooperative control strategy of holding and stop-skipping considering the limitation of bus capacity [14,15,16]. On this basis, Zhang et al. [17] developed an optimization scheme for a real-time simulation model of holding and stop-skipping. Milla et al. [18] verified that the combined strategy is better than a single strategy in saving waiting time through global positioning system (GPS) technology and simulation tests.

In order to ensure that buses pass through the intersection, some scholars have proposed an intersection control method combined with speed guidance to provide signal priority for buses. Bie et al. [19] developed a dynamic headway control method for high-frequency routes with bus lanes. The results show that the proposed method can reduce the bus distance bias for all survey periods. Wu et al. [20] proposed a new method to optimize bus stop waiting time and give priority to buses at segregated intersections. Finally, the potential of the proposed method to be applied to the bus priority control system is demonstrated. Seredynski et al. [21] proposed to combine the driver advisory system (DAS) with signal-priority control request, and the results showed that the travel time can be significantly reduced compared with using BSP alone.

In order to solve the problem of delay at intersections and give more road priority, some scholars have proposed a signal-priority control method for dynamic bus lanes [22,23]. On this basis, Levin and Khani [24] proposed a cellular transport model for dynamic bus lanes, which was effectively applied in Austin. Shu et al. [25] proposed a variable bus approach design with a bus guidance and priority control model, which can reduce the delays of through and left-turn buses and provide optimal signal priority for buses.

In addition, some scholars have undertaken the following research combining signal priority and holding. Zimmermann et al. [26] proposed a combination strategy of holding, speed adjustment and signal priority, and verified the effectiveness of the combination strategy in Quebec City, Canada. Koehler et al. [27] proposed a combined control strategy of holding and signal priority to minimize the total delay of passengers, and verified the effectiveness of the proposed strategy in Blumenau, Santa Catarina, Brazil.

To sum up, the research results of the combined dynamic scheduling strategy are rich, but there is still a gap in the combined research of stop-skipping and signal priority in peak hours. At the same time, the signal priority of the intersection is closely related to the bus arrival time, so it is necessary to conduct an overall study of the station and intersection. This study combines speed adjustment and signal priority for coordinated control in the bus stop-skipping mode to fill the gap in this field.

This research mainly focuses on the following three aspects:

• Combining the passenger flow of the station at the peak of the line to make the decision of stop-skipping.
• Combining the triggering mechanism of the intersection with the arrival time of the bus at the intersection and the signal period.
• Combining the cooperative control scheme of the intersection with the speed adjustment.

2. Analysis of Scheduling Strategy

2.1. Problem Description

The departure method and time for the intersection signal-priority scheme need to be considered in bus operation. How to deal with these uncertain factors is a difficult point in bus scheduling strategy [28,29]. Therefore, the platform control method was combined with signal priority, and a combined scheduling strategy was proposed to meet the needs of efficient and convenient commuting.

In this study, the bus vehicles were dispatched in a certain order of departure intervals $h$, and the route consisted of several stations and intersections. The intersection contained one bus lane $L_1$ and two social lanes $L_2$. During peak hours, the bus only arrived at the intersection from lane $L_1$, and the traffic flow was not saturated. The intersection signal period was $R$, and the two phases were $r_1$ and $r_2$, respectively, as shown in Figure 1.

2.2. Combined Scheduling Strategy

This study was conducted in three stages:

(1) Make decision to stop-skip based on historical data.

Bus operation has the characteristics of high departure frequency and short arrival interval during the peak period, and the strategy of stop-skipping helps to optimize the bus stops [30,31]. By setting the objective function and constraint conditions, the decision of stop-skipping can be obtained according to the historical average passenger flow.

(2) Make signal-priority decisions at intersections based on online data.

The intersection is the bottleneck of the urban transportation system, and the traffic signal control has a great impact on the public transportation system [32]. Figure 2 shows the signal-priority control system. The decision trigger detects the vehicle information at the previous stop of the intersection, and makes signal-priority decisions according to the time when the bus arrives at the intersection.

(3) Coordinated control combined with speed adjustment.

According to the signal-priority triggering mechanism, the corresponding signal-priority scheme is adopted. Usually the signal-priority methods include extending the duration of the green lights, turning on the green lights in advance and shortening the duration of the red lights [33], combined with speed adjustment for cooperative control for time intervals that are not suitable for signal priority.

3. Model Building

3.1. Parameter Definition

The meaning of each parameter is defined in

Table 1. Notation.

Symbol	Definition and Description
Sets
$I$	The set of buses.
$J$	The set of stations.
$X$	The set of intersections.
Parameters
$i$	$i\in I,i=1,2,3,\dots m$, $m$ represents the maximum number of bus.
$j$	$j\in J,j=1,2,3,\dots ,n$, $n$ represents the maximum number of station.
$x$	$x\in X,x=1,2,3,\dots ,q$, $q$ represents the maximum number of intersection.
$t_0$	The departure moment of the first bus on the line.
$t_{i,j}$	The time when the bus $i$ runs from the first station to the station $j$.
$t_{i,j}^{\prime }$	The departure time of bus $i$ at station $j$ on the line.
$t_{i,x}^{}$	The moment when bus $i$ arrives at intersection $x$.
$\overline{t}$	The average time of picking-up or dropping-off per passenger.
${\tau }_{i,j}$	The stop time of bus $i$ at station $j$ on the line.
$\mu$	The time of bus acceleration and deceleration.
$\eta$	The coefficient of passengers waiting stations.
$h$	The departure interval of buses on the line.
$h_j$	The headway of two adjacent buses at station $j$.
$h_0$	The safe distance between two adjacent buses.
${\phi }_{i,x}$	The delay time of bus $i$ arriving at intersection $x$ is the remaining red-light time.
$r_{i,x}$	The extended or advanced green-light time for bus $i$ to arrive at intersection $x$.
$r_1$	The red-light time for phase 1.
$r_2$	The red-light time for phase 2.
$R$	The signal period of the intersection.
$d_{i,j}$	The distance of bus $i$ from the departure station to station $j$.
$s_{j,x}$	The distance from station $j$ to intersection $x$.
$v$	The average speed of the bus.
$v\prime$	The adjusted speed of the bus.
$L_{i,j}^p$	The number of passengers on bus $i$ when it arrives at station $j$.
$D_{i,j}^P$	The number of people entering bus $i$ when it arrives at station $j$.
$A_{i,j}^p$	The number of people exiting bus $i$ when it arrives at station $j$.
$W_{i,j}$	The number of people waiting for bus $i$ at station $j$.
$\lambda$	The time value factor for cost reduction.
$Q$	The capacity of the bus.
$\Delta C_{}$	The operating cost of bus stops at the station.
Decision variables
$Z_{i,j}$	$Z_{i,j}=1,$ if bus $i$ stops at station $j$, and $Z_{i,j}=0,$ otherwise.
$Y_{i,x}$	$Y_{i,x}=1,$ if bus $i$ stops at intersection $x$, and $Y_{i,x}=0,$ otherwise.

:

3.2. Assumptions

(1)

The environment of the waiting facilities at each station is the same.

(2)

Buses pass on dedicated bus lanes.

(3)

The bus vehicle is not fully loaded, and the bus ride demand will be satisfied as long as it stops at the station.

(4)

Passengers waiting at the station will wait until they enter the bus, and the last bus will not refuse passengers.

(5)

The same station cannot be skipped twice by vehicles passing by.

(6)

The vehicle–road coordination system can detect the running state of the vehicle and provide real-time two-way communication for the bus and the signal controller.

(7)

This study ignores the impact of social vehicles, and there is no bus queue at the intersection.

3.3. Objective Function

This research establishes a model with the lowest passenger time cost and the lowest company stopping cost as the optimization goal. The model is divided into five parts:

(1) The waiting time

The running time between stations is not considered here. The waiting time is mainly the stopping time and the acceleration and deceleration time of the vehicle at the station. Due to the random arrival of passengers at each station, the waiting station coefficient $\eta$ is set here.

$$T_1={\displaystyle \sum _{i=1}^m{\displaystyle \sum _{j=1}^n\left[D_{i,j}^P\cdot \eta \left({\tau }_{i,j}+\mu \right)\cdot Z_{i,j}\right]}}$$

(1)

Among them, the stop time at the station:

$${\tau }_{i,j}=\{\begin{array}{c}0;Z_{i,j}=0\\ \max \left\{D_{i,j}^p\cdot \overline{t},A_{i,j}^p\cdot \overline{t}\right\};Z_{i,j}=1\end{array}$$

(2)

It can be seen that the stop time ${\tau }_{i,j}$ depends on $Z_{i,j}$ and the number of passengers entering and exiting.

(2) The extra waiting time for the sites to be crossed

The extra waiting time is the sum of the headway of the skipping vehicle and the adjacent vehicle at the station:

$$T_2={\displaystyle \sum _{i=1}^m{\displaystyle \sum _{j=1}^n\left[D_{i,j}^p\cdot h_j\cdot \left(1-Z_{i,j}\right)\right]}}$$

(3)

The headway satisfies:

$$h_j=t_{i+1,j}-t_{i,j}$$

(4)

The time $t_{{}_{i,j}}^{}$ for bus $i$ to arrive at station $j$ is:

$$t_{{}_{i,j}}^{}=t_0+(i-1)\cdot h+\frac{d_{i,j}}{v}+{\displaystyle \sum _{j=1}^n\left({\tau }_{i,j-1}+\mu \right)\cdot Z_{i,j-1}+{\displaystyle \sum _{x=1}^q\left({\phi }_{i,x}+\mu /2\right)\cdot Y_{i,x}}}$$

(5)

(3) The stopping time of the stations

The stopping time is the stay time of the passengers on the bus, including entering and exiting the bus, as well as the acceleration and deceleration time:

$$T_3={\displaystyle \sum _{i=1}^m{\displaystyle \sum _{j=1}^n\left[\left(L_{i,j}^p-A_{i,j}^p\right)\cdot \left({\tau }_{i,j}+\mu \right)\cdot Z_{i,j}\right]}}$$

(6)

The number of passengers on the bus is determined by the number of people entering and exiting at the previous stop:

$$L_{i,j}^p=L_{i,j-1}^p+D_{i,j-1}^p-A_{i,j-1}^p$$

(7)

The vehicle is not fully loaded; that is, waiting passengers can enter the bus when the vehicle is parked:

$$L_{i,j}^p\le Q, \mathrm{and} D_{i,j}^p=W_{i,j}^p$$

(8)

(4) The delay time at intersections

$$T_4={\displaystyle \sum _{i=1}^m{\displaystyle \sum _{j=1}^n{\displaystyle \sum _{x=1}^q}\left[\left(L_{i,j}^p+D_{i,j}^P-A_{i,j}^p\right)\cdot \left({\phi }_{i,x}+\mu \right)\cdot Y_{i,x}\right]}}$$

(9)

$$\mathrm{When}\mathrm{bus}i\mathrm{passes}\mathrm{at}\mathrm{intersection}x, Y_{i,x}=0; \mathrm{otherwise}, Y_{i,x}=1.$$

(10)

When $Y_{i,x}=1$, wait for the remaining red-light time (where $n^{\prime }$ refers to the number of signal cycles):

$${\phi }_{i,x}=r_1-\left[(t_{i,x}-t_0)-n^{\prime }C\right]$$

(11)

The time when bus $i$ arrives at intersection $x$:

$$t_{i,x}=t_0+(i-1)\cdot h+\frac{d_{i,j}+s_{j,x}}{v}+{\displaystyle \sum _{j=1}^n\left({\tau }_{i,j}+\mu \right)\cdot Z_{i,j}+{\displaystyle \sum _{x=1}^q\left({\phi }_{i,x-1}+\mu \right)Y_{i,x-1}}}$$

(12)

(5) The stopping costs of company

The stopping costs of company mainly refers to the loss and fuel consumption of vehicles when they are parked.

$$C_5={\displaystyle \sum _{i=1}^m{\displaystyle \sum _{j=1}^n\Delta C\cdot Z_{i,j}+{\displaystyle \sum _{i=1}^m{\displaystyle \sum _{x=1}^q\Delta C\cdot Y_{i,x}}}}}$$

(13)

The lowest total cost:

$$\min F=\min (T_1+T_2+T_3+T_4+\lambda C_5)$$

(14)

s.t.

$${\phi }_{i,x}\le r_1$$

(15)

$$r_1+r_2=R$$

(16)

$$t_{i,j}^{\prime }=t_{i,j}+\left({\tau }_{i,j}+\mu \right)\cdot Z_{i,j}$$

(17)

$$\mathrm{When} A_{i,j}^p>0, Z_{i,j}=1$$

(18)

$$\mathrm{When} D_{i,j}^p>0, Z_{i,j}+Z_{i,j+1}\ge 1$$

(19)

$$Z_1=Z_n=1$$

(20)

$$Z_{i,j}+Z_{i+1,j}\ge 1$$

(21)

$$t_{i+1,j}-t_{i,j}\ge h_0$$

(22)

Among the constraints: Equation (15) indicates the time range of the vehicle waiting for the red light at the intersection; Equation (16) indicates the sum of the two phases as the phase period; Equation (17) indicates the time when the vehicle leaves the station; Equation (18) indicates that the vehicle will stop at the station where passengers need to dismount; Equation (19) indicates that the vehicle should not skip two consecutive stops when there are passengers waiting; Equation (20) indicates that the vehicles stop at both the first and last stations; Equation (21) indicates that the station should not be skipped continuously twice; Equation (22) indicates the minimum safe value of headway.

3.4. Collaborative Control

(1)

Signal-priority method

In order to reduce the interference of buses with other vehicles, the green-light time is generally advanced or extended by no more than 10% of the signal period [34]. According to Equation (16), the intersection signal is composed of two phases and the condition $r_1=r_2$ is set in this study. It can be seen that the length of time allowed for signal priority in a cycle is $\frac{1}{5}{r}_1$. The time when the bus arrives at the intersection is divided into four sections (where $n^{\prime }$ refers to the number of signal cycles) to determine the passing time window of the priority application (see Figure 3). The signal-priority mode adopted in Section i is green extension (GE). The signal-priority mode adopted in Section iii is red truncation (RT). Signal priority is not carried out in Section ii. Section iv indicates that vehicles pass normally.

$$t_{i,x}\in (n^{\prime }C,n^{\prime }C+\frac{1}{5}{r}_1),(n^{\prime }=0,1,2,\dots ); Y_{i,x}=0$$

(23)

$$t_{i,x}\in (n^{\prime }C+\frac{1}{5}{r}_1,n^{\prime }C+\frac{4}{5}{r}_1),(n^{\prime }=0,1,2,\dots ); Y_{i,x}=1$$

(24)

$$t_{i,x}\in (n^{\prime }C+\frac{4}{5}{r}_1,n^{\prime }C+r_1),(n^{\prime }=0,1,2,\dots ); Y_{i,x}=0$$

(25)

$$t_{i,x}\in (n^{\prime }C+r_1,n^{\prime }C+C),(n^{\prime }=0,1,2,\dots ); Y_{i,x}=0$$

(26)

According to the time period when the vehicle arrives at the intersection, there are the following priority methods:

Combining Equation (23), it can be seen that the green-light extension method is adopted (section i). Considering the conversion of the yellow light time, the extension time is:

$$r_{i,x}=(t_{i,x}-t_0)-n^{\prime }C+3;$$

(27)

Combining Equation (24), the vehicle cannot pass preferentially (section ii), and needs to wait for the remaining red-light time:

$${\phi }_{i,x}=r_1-\left[(t_{i,x}-t_0)-n^{\prime }C\right];$$

(28)

According to Equation (25), the early red-light mode is adopted (section iii), and the early red-light interruption time is:

$$r_{i,x}=r_1-\left[(t_{i,x}-t_0)-n^{\prime }C\right];$$

(29)

Vehicles are in the green-light time period and pass normally (section iv).

(2)

Speed adjustment method

For the situation where the vehicle arrives at the intersection in Section ii, the method of adjusting the speed at the stop before the intersection is adopted, so that the vehicle can pass directly when it arrives at the intersection. This method involves accelerating or decelerating at a station before the intersection and decelerating or accelerating correspondingly at the intersection, so that the running time between the two stations remains unchanged. The maximum running speed of an urban bus usually does not exceed 60 km/s [35]. (Note: $v_1^{\prime }$, $v_2^{\prime }$ is the change speed before and after the intersection)

$$\frac{s_{j,x}}{v}-\frac{s_{j,x}}{v^{\prime }}\ge \frac{4}{5}{r}_1+3$$

(30)

According to Equation (30), the vehicle accelerates at the speed of $v^{\prime }$ at the stop before the intersection:

$$r_1-{\phi }_{i,x}+3=\frac{s_{j,x}}{v}-\frac{s_{j,x}}{v_1^{\prime }}$$

(31)

In order to ensure that the time to reach the next station remains unchanged, the speed will be reduced after crossing the intersection:

$$r_1-{\phi }_{i,x}+3=\frac{s_{x,j+1}}{v_2^{\prime }}-\frac{s_{x,j+1}}{v_1^{\prime }}$$

(32)

The vehicle decelerates at the speed of $v^{\prime }$ at the stop before the intersection when the distance between the station and the intersection does not meet Equation (30):

$${\phi }_{i,x}=\frac{s_{j,x}}{v_1^{\prime }}-\frac{s_{j,x}}{v}$$

(33)

After passing the intersection, the vehicle speeds up to ensure that the time to reach the next stop remains unchanged:

$${\phi }_{i,x}=\frac{s_{x,j+1}}{v_1^{\prime }}-\frac{s_{x,j+1}}{v_2^{\prime }}$$

(34)

4. Algorithm Choice

Cruz-Chávez et al. [36] applied the simulated annealing algorithm to the flexible shop scheduling problem and obtained good solutions. However, the algorithm has low computational accuracy and poor global search ability. Shakibayifar et al. [37] solved the train rescheduling problem using a variable neighborhood search algorithm, but the algorithm has low convergence. Pecin et al. [38] used the branch cut-price algorithm to improve vehicle path planning with different capacities, but the convergence of the algorithm still needs to be improved when solving multi-objective complexity problems.

In contrast, the genetic algorithm is a method of searching for optimal solutions by simulating the evolutionary process of natural selection and survival of the fittest. It has the following advantages: (1) It adopts random probability to guide its search direction in the solution, which is relatively objective [39]. (2) It has strong global search ability when solving multi-objective optimization problems [40]. (3) Genetic algorithms have strong robustness and high convergence in practical applications [41].

Therefore, the genetic algorithm was used to solve the cooperative control model. The solution process was divided into the following stages. (1) According to the historical passenger flow data, the stop-skipping decision was made (see Figure 4a). (2) According to the online passenger flow data, the signal-priority decision and speed adjustment were made on the basis of the stop-skipping decision (see Figure 4b).

(1)

Coding method

If there are m vehicles and n stations, the encoding length is m × n, which is 0–1 encoding; if there are m vehicles and q intersections, the encoding length is m × q, which is 0–1 encoding.

(2)

Variation and crossover

Gene pairing was performed by single-point mutation and two-point crossover. Two parent chromosomes were randomly generated for pairing, and a certain crossover probability was selected to generate two daughter chromosomes.

(3)

Function calculation

Its objective function value was calculated according to Section 3.3, and the fitness function can be expressed as:

$$F_i=\frac{1}{y_i+P_i}$$

(35)

$$y_i=\min f(x)$$

(36)

where $F_i$ represents the fitness value of chromosome $i$, $y_i$ represents the objective function of chromosome $i$, and $P_i$ represents the penalty value of chromosome $i$.

(4)

Select

The core idea of genetic algorithm is roulette selection, which means that the probability of an individual being selected is proportional to the value of its fitness function. Assuming that the population size is $n$, the fitness function is expressed as $F_i$, and the probability of being selected and inherited to the next generation is $P_i$:

$$P_i=\frac{F_i}{{\displaystyle \sum _{i=1}^n{F}_i}}$$

(37)

5. Case Analysis

This study took the rush hour (8:00–9:00) of a city as an example. The bus line was 15.9 km long, with a total of 10 stations numbered S₁–S₁₀, respectively. There were three intersections in the middle of the line numbered O₁–O₃, respectively. The first intersection was 3600 m away from S₃, the second intersection was 200 m away from S₆ and the third intersection was 1500 m away from S₉ (see Figure 5).

5.1. Parameter Setting

According to the parameter definition in Section 3.1, the parameters were calibrated, as shown in

Table 2. Constant variables in the calculation example.

Variable Name	Variable
The number of buses $m$	6
The number of stations $n$	10
The number of intersections $q$	3
The departure moment of the first bus on the line $t_0$	Am 8:00
The average time of picking-up or dropping-off per passenger $\overline{t}$/s	2
The time of bus acceleration and deceleration $\mu$/s	30
The coefficient of passengers waiting stations $\eta$	2.3
The departure interval of buses on the line $h$/min	10
The safe distance between two adjacent buses $h_0$/s	120
The red-light time for phase 1 $r_1$/s	30
The red-light time for phase 2 $r_2$/s	30
The signal period of the intersection $R$/s	60
The distance from the third station to the first intersection $s_{3,1}$/m	1715
The distance from the sixth station to the second intersection $s_{6,2}$/m	290
The distance from the ninth station to the third intersection $s_{9,3}$/m	1525
The average speed of the bus $v$/(km·h−1)	36
The time value factor for cost reduction $\lambda$/(s/yuan)	500
The capacity of the bus $Q$/person	60
The operating cost of bus stops at the station $\Delta C_{}$/(yuan/bout)	1

.

There were 10 stations on the line, and the station spacing is shown in

Table 3. The distance matrix between stations (m).

Stations	S1	S2	S3	S4	S5	S6	S7	S8	S9	S10
S1	—	1200	2700	4600	5700	8000	10,000	12,200	13,900	15,900
S2	—	—	1500	3400	4500	6800	8800	11,000	12,700	14,700
S3	—	—	—	1900	3000	5300	7300	9500	11,200	13,200
S4	—	—	—	—	1100	3400	5400	7600	9300	11,300
S5	—	—	—	—	—	2300	4300	6500	8200	10,200
S6	—	—	—	—	—	—	2000	4200	5900	7900
S7	—	—	—	—	—	—	—	2200	3900	5900
S8	—	—	—	—	—	—	—	—	1700	3700
S9	—	—	—	—	—	—	—	—	—	2000
S10	—	—	—	—	—	—	—	—	—	—

:

5.2. Analysis of Results

The genetic algorithm in Section 4 was used to solve the model in Section 3, combined with the scheduling strategy in Section 2.2. It was carried out in three stages, and the logical relationship of the three optimization strategies is shown in Figure 6.

5.2.1. Stage 1—Stop-Skipping Decision

The decision of the stop-skipping was made for each station combined with the historical passenger flow of each station. Among them, the passenger capacity of 6 vehicles was taken as the average daily passenger flow during this period, as shown in

Table 4. Passengers waiting and dismounting at each station.

	Stations	S1	S2	S3	S4	S5	S6	S7	S8	S9	S10
Passengers
waiting (V1)		7	1	10	3	8	2	8	8	1	0
dismounting (V1)		0	0	9	0	10	0	7	5	0	-
waiting (V2)		8	7	2	12	1	5	12	3	8	0
dismounting (V2)		0	5	0	5	0	10	2	0	3	-
waiting (V3)		11	1	12	1	20	5	1	12	2	0
dismounting (V3)		0	0	5	0	7	0	0	6	0	-
waiting (V4)		9	7	1	8	1	15	8	2	10	0
dismounting (V4)		0	5	0	6	0	10	7	0	9	-
waiting (V5)		5	3	7	1	13	3	10	9	1	0
dismounting (V5)		0	0	3	0	5	0	3	6	0	-
waiting (V6)		12	8	15	10	12	7	12	11	9	0
dismounting (V6)		0	5	6	3	9	5	6	7	5	-

. It can be seen from Table 1 that “Y” represents the decision variable of whether the vehicle stops at the intersection. The intersection was considered as a “virtual station” (no pick-up and drop-off), and all vehicles were set to pass through the intersections with priority, which was represented as $Y_{i,x}=0$:

MATLAB was used to run the genetic algorithm to obtain the parking situation of each vehicle at each station, as shown in

Table 5. Stop-skipping decision results.

	Stations	S1	S2	S3	S4	S5	S6	S7	S8	S9	S10
Vehicles
V1		1	0	1	1	1	0	1	1	0	1
V2		1	1	1	1	0	1	1	1	1	1
V3		1	0	1	0	1	1	0	1	1	1
V4		1	1	0	1	0	1	1	0	1	1
V5		1	1	1	0	1	1	1	1	0	1
V6		1	1	1	1	1	1	1	1	1	1

.

The schematic diagram of the stop-skipping decision is shown in Figure 7a below, where means stop-skipping and means stop. Figure 7b shows the passenger flow trend of the number of passengers dismounting at terminal S10 on the basis of Figure 7a (blue dotted line).

During the actual operation of the bus, passengers can decide whether to take the bus after obtaining the stop-skipping status and timetable information through the APP program in advance [42]. We use a Sankey diagram to show the visual dynamic change in the passenger flow of each vehicle at each station, as shown in Figure 8.

5.2.2. Stage 2—Signal-Priority Decision

According to Figure 6, it can be seen that the second stage and the third stage were merged together and calculated synchronously.

Combined with the decision of stop-skipping (Table 5) and the characteristics of signal cycle, the signal-priority decision was made for vehicles arriving at the intersection. The status of each vehicle arriving at each intersection was determined in four sections, a–d.

(1) The time state of each vehicle arriving at each intersection was calculated by genetic algorithm, as shown in

Table 6. Time period of vehicles arriving at each intersection before optimization.

	Intersection	O1	O2	O3
Vehicles
V1		iv	iv	ii
V2		iii	iv	iv
V3		ii	i	iv
V4		iv	ii	ii
V5		ii	ii	iv
V6		i	iv	iii

:

(2) In accordance with Equations (23)–(26), signal-priority decision-making was carried out on the basis of Table 6, as shown in

Table 7. Signal-priority decision results.

	Intersection	O1	O2	O3
Vehicles
V1		0	0	1
V2		0	0	0
V3		1	0	0
V4		0	1	1
V5		1	1	0
V6		0	0	0

:

5.2.3. Stage 3—Collaborative Control Scheme

The result of the signal-priority decision in Section 5.2.2 was combined with speed adjustment to carry out cooperative control and quantitative analysis.

(1)

Signal-priority scheme (section i, iii):

When the vehicle arrived at the intersection and the time is in the red-light state (Sections i, iii), the bus phase was activated in advance by compressing the non-transit phase to achieve the purpose of bus priority. At this time, the program fed back the passable state of the vehicle at the station before the intersection, and fed it back to the signal device: the green light was extended (GE) when the vehicle arrived at the Section i; the red light was used to truncate (RT) early when the vehicle arrived at Section iii.

According to Equation (23), the vehicles V₃ and V₆ arrive at the intersections O₂ and O₁, respectively, and are located in the Section i. According to Equation (27), it is determined that the extended green-light times of vehicles V₃ and V₆ at intersections O₂ and O₁ are 5.46 s and 4.5 s, respectively, as shown in Figure 9a.

According to Equation (25), the vehicles V₂ and V₆ arrive at the intersections O₁ and O₃, respectively, and are located in Section iii. According to Equation (29), it is determined that the red-light times of vehicles V₂ and V₆ at the intersections O₁ and O₃ are shortened by 4.5 s and 5.4 s, respectively, as shown in Figure 9b.

(2)

Speed-adjustment scheme (section ii)

When the vehicle arrives at the intersection and is in the red-light Section ii, the program feeds back to the vehicle for speed adjustment at the station before the intersection. The vehicle accelerates or decelerates at the station before the intersection by integrating GPS and IMU information [43,44,45], so that the vehicle can pass through the intersection without waiting (see

Table 8. Time period of vehicles arriving at each intersection after optimization.

	Intersection	O1	O2	O3
Vehicles
V1		iv	iv	iv
V2		iii	iv	iv
V3		iv	i	iv
V4		iv	iv	iv
V5		iv	iv	iv
V6		i	iv	iii

). The vehicle decelerates or accelerates after passing the intersection, so that the time remains unchanged when reaching the next station.

According to Equation (30), the vehicle accelerates at the station before the intersection; otherwise, it decelerates. From the parameters in Section 5.1, it can be seen that the vehicle accelerates at the station S₃ before the intersection O₁, decelerates at the station S₆ before the intersection O₂ and accelerates at the station S₉ before the intersection O₃. The schematic diagram of the speed adjustment of vehicles arriving at intersections O₁–O₃ is shown in Figure 10.

According to Equations (31) and (32), it is determined that the speed of V₃ is 10.65 m/s after the speed increases at the station S₃, and the deceleration speed is 6.38 m/s after crossing the intersection O₁, which ensures that the time for the vehicle to arrive at S₄ remains unchanged. In the same way, the speed of vehicle V₅ before and after the intersection O₁ is adjusted to 11.67 m/s and 4.3 m/s, respectively (see Figure 10a). From Equations (33) and (34), the speed of vehicle V₄ before and after the intersection O₂ is adjusted to 6m/s and 11.54 m/s, respectively; similarly, the speed of vehicle V₅ before and after the intersection O₂ is adjusted to 5.74 m/s and 11.4 m/s, respectively (see Figure 10b). From Equations (31) and (32), it is determined that the speeds of vehicles before and after the intersection O₃ are adjusted to 11.29 m/s and 7.32 m/s, respectively, and V₄ is equivalent to V₁ (see Figure 10c).

5.2.4. Comparative Analysis

After the cooperative control of stop-skipping and signal priority, the objective function value is calculated (see situation II in

Table 9. Comparative analysis before and after optimization.

Situations	The Time Cost of Passengers (s)	Company Stopping Costs (s)	Target Value (s)	Optimization Results (s)
Ⅰ	119,360.26	35,000	154,360.26	—
Ⅱ	116,186.12	27,000	143,186.12	11,174.14
Ⅲ	112,905.4	24,000	136,905.4	17,454.86

), and the iteration is as shown in Figure 11a. After the cooperative control of stop-skipping, signal priority and speed adjustment, the objective function value is calculated (see situation Ⅲ in Table 9), and the iteration is as shown in Figure 11b. Combined with the assumptions in Section 3.2, the collaborative optimization method proposed in this study is calculated and demonstrated.

The total objective function of these three schemes is the lowest total cost (Equation (14)), but the time of vehicles arriving at the station and intersection (Formulas (5) and (12)) in their calculation process will have substantial changes due to different methods. Therefore, the genetic algorithm was used to calculate the solution separately, and three different results were obtained. A comparative analysis of three cases: Ⅰ. Stations all parked and signals not prioritized. Ⅱ. Stop-skipping and signal priority. Ⅲ. Stop-skipping, signal priority and speed adjustment. See Table 9.

It can be seen from the comparative results of Table 9 that the total target value was optimized for 11,174.14 s by using the methods of stop-skipping and signal priority. After adopting the coordinated control of stop-skipping, signal priority and speed adjustment, the total target value was optimized for 17,454.86 s. It can be seen that the methods of signal priority and speed coordinated control in the stop-skipping mode could greatly reduce travel delays and operating costs and improve the efficiency of passenger travel. The comparison of quantitative results shows that the optimization method proposed in this study is feasible.

6. Conclusions

In order to improve the timeliness and flexibility of public transport during peak hours, the coordinated control method of signal priority and speed adjustment on the basis of stop-skipping was studied. The contributions of this research are as follows:

First of all, this study started with the time correlation between vehicle arrival stations and intersections, and made a stop-skipping decision based on the historical passenger flow data.

Secondly, according to the online passenger flow data and signal cycle characteristics, the time when the vehicle arrived at the intersection was divided into four sections, and the signal-priority decision was made.

In addition, static and dynamic cooperative control was carried out in combination with signal priority and speed regulation. From the perspective of passenger delay time cost and enterprise operation cost, the effectiveness of the collaborative optimization method was proved, providing a theoretical foundation for the formulation of the priority trigger mechanism and scheme of the intersection signal.

In short, the proposed combined scheduling strategy can improve practical optimization methods for bus operation during peak hours. The disadvantage is that only two phases were considered, and the influence of social vehicles was ignored. Next, we will further integrate social vehicles and explore the study of four phases.