An improved model-based predictive control approach integrating model-based signal control and queue spillover control is proposed in this paper, which includes three modules: model-based signal control, queue spillover identification, and spillover control to deal with the problem of traffic congestion for urban oversaturated signalized intersection. The main steps are as follows. First of all, according to the real-time traffic flow data, the green time splits for all intersections will be solved online by the model-based signal control controller whose optimization model is based on model-predictive control (MPC) strategy. Second, the queue spillover identification module will be used to detect the potential queue spillover. If potential queue spillover is detected, the spillover control module will be activated to prevent vehicles from the upstream link of the link with possible spillover from entering the downstream link to avoid traffic congestion. The experiment is performed on a simulated road network. The results verify that the proposed scheme can significantly decrease the delay which reflects the overall performance of the studied intersection.
With the rapid development of society and economy, the number of vehicles has grown larger and larger. Urban Signalized intersections are under oversaturated traffic conditions during peak hours more and more frequently. Under this circumstance, the urban traffic congestion becomes more and more serious, resulting in excessive delays and increased travel times. The traffic congestion resulting from oversaturated traffic conditions will bring about significant economic losses and social costs. Therefore, it is necessary to develop an effective control method for the control of urban oversaturated signalized intersection to avoid traffic congestion.
Different solutions including traffic signal control [
To solve the problem of traffic signal control for oversaturated intersections, extensive efforts have been made. To the best of our knowledge, traffic demand which represents the traffic arrivals on intersection approaches is too high to be managed effectively when the intersection is oversaturated, which may induce queue spillover [
For online control method which can adjust the timing scheme according to current collected traffic flow, a number of methods have been presented. Lin et al. [
Although the aforementioned methods can limit the queue length to mitigate oversaturation to some extent, these methods cannot predict future traffic condition. A model-based predictive control method which deals with the optimal problem over a finite horizon according to the current traffic flow can address this problem perfectly. Aboudolas et al. [
The details of the contributions in this paper include two aspects which can be listed as follows. (1) We propose an improved model-based predictive control approach integrating model-based signal control and queue spillover control to obtain an optimal green time allocation scheme and to avoid spillover simultaneously under oversaturated traffic conditions. (2) Considering that the objective of this model is complicated when the model is optimized in several cycles, we propose an improved hybrid artificial bee algorithm to address the optimal control problem of the proposed improved model-based predictive control approach as soon as possible.
The rest of the paper is organized as follows. Section
In this paper, we proposed an improved model-based predictive control method which can simultaneously optimize green time splits according to the predicted traffic demand over a finite horizon and manage queue based on different traffic flow conditions. The framework of the proposed method is shown in Figure
Framework of the proposed method. The proposed method mainly includes three modules: model-based signal control, queue spillover identification, and spillover control.
Figure
In order to control the studied intersection, the corresponding traffic data should be collected by some detectors. The information of queue length and the number of vehicles in link
At the beginning of each signal cycle, the model-based signal control method will firstly be applied to obtain an optimal control sequence (green time splits for each phase at all intersections) with the objective of minimizing the total travel time according to the current traffic flow information including the number of vehicles and queue length for each link. Then the queue spillover identification method will be activated to identify the possible queue spillover according to the real-time traffic flow information (the speed and the vehicle count) which is obtained by the detector periodically and the current traffic signal status. The spillover control method will be used to prevent the potential queue spillover if potential queue spillover is identified. When there is no potential queue spillover on the downstream link, the system will further determine whether the current control cycle should be terminated. If yes, the next cycle will be executed; otherwise, the queue spillover identification method will continue to detect the possible spillover.
Suppose that the signal phase and phase sequence is fixed at each intersection. At every control moment, the model-based signal control method will provide the optimal green time splits at each intersection on the basis of the information of current traffic flow. Accordingly, we should choose an appropriate prediction model to predict traffic flow dynamics and an appropriate optimization model to reflect the optimization objective of traffic control. Finally, a novel optimization algorithm is developed for obtaining solutions of the optimization model. We will first introduce the prediction model and optimization model, respectively [
The model-based signal control method will be executed to obtain the optimal green time splits periodically according to the current number of vehicles and queue length for each link. Therefore, it is necessary to configure the corresponding detectors to detect traffic flow data to provide the input for the model-based signal control controller. The detectors can be deployed after the stop bars for all intersections to detect the queue length and the number of vehicles in all links at the start of every traffic signal cycle periodically. As shown in Figure
Detector configuration at intersection 1. Four queue detectors are deployed over the stop bar at the intersection where arrows represent the corresponding turning movement.
The S model as a simplified macroscopic traffic model initially proposed by Lin [
As shown in Figure
A road network including two intersections. The evolution process of traffic flow at two adjacent intersection is demonstrated.
Suppose that
The queue length of different lanes at time step
The total queue length can be calculated as below:
According to the corresponding
To obtain optimal green time splits according to varied traffic flow, it is essential to select an appropriate optimization model which can balance the computation time and accuracy. The model described in [
We regard formula (
According to the queue length and the number of vehicles in all links at time step
Formula (
Formula (
To obtain the solutions of the above optimization model online, we will propose an appropriate optimization algorithm. It will be illustrated in the following.
The ABC algorithm is proposed to solve optimization problems in many different fields, including unconstrained optimization problems [
Suppose that both the size of employed bees and the onlooker bees are
Although the ABC algorithm is simple enough to obtain optimal solutions of complicated problems, it tends to get trapped in local optima. Therefore, a number of scholars studied ABC algorithm and developed various methods to deal with this deficiency which arises from the reduction of diversity of bee population. Zhu et al. [
In order to obtain better solutions, we propose an IGAABC algorithm to overcome the deficiency of premature convergence and slow convergence rate of the basic ABC algorithm. The preceding few steps of this algorithm are analogous to ABC algorithm except that the fitness function of ABC algorithm is modified. After the operations of the scout bee stage are finished, we will add the steps of crossover, mutation operation to improve the basic algorithm. The flowchart of the improved hybrid artificial bee colony optimization for the optimization of signal timing is shown in Figure
The flowchart of the IGAABC. The operators of crossover and mutation are introduced into the basic ABC algorithm to avoid getting trapped in local optima.
It is well known that Genetic Algorithm (GA) [
First, two parents will be selected from the original population. Secondly, the algorithm will generate the number
(1) Generate a vector y containing D “0 or 1” randomly, where D is equal to the dimension of solutions. Each element of y corresponds to the individual's gene (decimal number).
(2) The position whose value is equal to one in y of these two individuals will be crossed as below:
(3) After these two individuals finish crossing, we transfer to the crossover of the other two individuals.
The mutation operator of our algorithm is similar to GA’s. The flowchart of the IGAABC algorithm is shown in Figure
The selection of the fitness function directly affects the convergence speed and determines whether the optimal solution can be found because the performance of the solution is evaluated on the basis of the fitness function. Therefore, it is important to design an appropriate fitness function to determine whether a solution is good or bad so that an optimal solution can be obtained within a limited number of iterations. So we modified the fitness function of the artificial bee algorithm as follows:
Extensive research on queue length based method, occupancy based method, and velocity based method has been carried out to identify queue spillover accurately and timely. In terms of the method based on queue length, it is important to estimate queue length accurately. The queue length estimation mechanisms are analyzed to estimate the queue length based on different layout strategies [
To identify the spillover for each direction of an intersection, it is necessary to add some detectors to the corresponding link. As shown in Figure
Queue spillover identification based on speed detector. Speed detector is deployed to detect the speed when vehicles pass over it.
According to geometric relationships in Figure
The possible queue spillover will be detected by comparing the information collected by the speed detector with the critical speed at which the spillover will happen. We will introduce the process to obtain the critical value in the following.
If the vehicle count which Link 2 can accommodate is too little to receive the vehicles from the upstream link, the spillover will occur. Assume that
According to relationships
Assume that the vehicles entering from the entrance of link 2 begin to decelerate when passing over the speed detector if the vehicles queue in Link 2. These vehicles must stop within distance
Supposing the deceleration rate is constant which is denoted by
According to the above formula (
Therefore, we define critical speed as below:
In view of that it is difficult to obtain the parameter of
Otherwise, the queue spillover will not occur unless the vehicle speed passing over the speed detector is nonpositive, that is,
Considering the disturbance in vehicle speed in real life, the method to identify the possible queue spillover can be expanded as below.
(1) The speed which is less than the critical speed
(2) The speed of vehicles is decreasing.
When potential queue spillover is detected, the spillover control method will prevent the upstream vehicle from entering the downstream link to avoid the queue spillover until the queue dissipation is detected. Therefore, we will introduce the method to identify the queue dissipation and control the spillover in the following.
When the queue dissipation [
Queue dissipation identification based on speed detector. Speed detector is deployed to detect the speed when vehicles pass over it.
The released capacity
When the vehicles waiting on Link 1 are served by the green time, the number of vehicles that will enter the intersection is more than
We can calculate
Therefore, the speed detector can be deployed near the downstream entrance as possible to detect both queue spillover and dissipation which is consistent with Section
(1) The speed which is larger than zero can be detected by two consecutive samplings.
(2) The speed of vehicles is increasing.
The spillover control method can be activated when the possible queue spillover occurs [
The flowchart of queue spillover control on link
Assume Intersection 1 is the studied intersection as shown in Figure
Road network Layout for the simulation. The adjacent intersection is taken into account to simulate the practical road traffic condition.
The design of phase sequence. P1 and P5 are grouped into signal group 1. P2 and P6 are grouped into signal group 2. The residual phases are grouped into signal group 3.
If we want to identify and control the spillover on
We evaluate the results of the proposed method in the above virtual network as shown in Figure
Intersection 1 is the studied intersection in this paper. The intersection adjacent to Intersection 1 is Intersection 2. All the links of the simulation network have three lanes where lane 1, lane 2, and lane 3 which are numbered from left to right on each road represent left-turn lane, through lane, and through right-turn lane, respectively. The VISSIM4.3 is selected as the simulation tool to simulate traffic movements and provide evaluation results to determine the performance of different traffic signal methods. Python provides the output of control parameter of green time splits based on the traffic flow data collected by the corresponding detectors. The saturation flow rate
In order to obtain the results with different traffic signal control methods, we should provide traffic volume from different entries. Table
Traffic volume for Intersection 1 during the simulation duration.
ENTRY | Left Turn[vehicle/h] | Through[vehicle/h] | Right Turn[vehicle/h] |
---|---|---|---|
NB | 147 | 256 | 166 |
SB | 181 | 221 | 168 |
EB | 166 | 1297 | 215 |
WB | 175 | 963 | 183 |
Table
IGAABC parameters settings.
Parameter | Description | value |
---|---|---|
limit | trials_limit | 100 |
SN | The number of employed bees | 15 |
The number of onlooker bee | ||
| Crossover probability | 0.6 |
| Mutation probability | 0.01 |
nruns | Number of iterations | 49 |
We select the average vehicle delay for each phase at the studied intersection and the maximum queue length on link
In this section, the simulation evaluation data of delay and queue length collected from VISSIM4.3 is provided to evaluate the performance of traffic signal control. The proposed control method will be compared with the methods of model-based predictive control and adaptive signal control. In addition, the proposed control method with our improved ABC algorithm will be compared with the method with ABC algorithm to verify the performance of our algorithm. The detailed descriptions of different traffic signal control methods are introduced as below: Model-based predictive control, whose green time splits for all intersections are optimized according to the measured traffic flow state is showed. Adaptive signal control, which can adaptively adjust the green time according to the real-time traffic condition to prevent the possible queue spillover [ Proposed method (ABC), whose control method is based on the proposed improved model-based predictive control method in this paper and optimization algorithm is based on the basic ABC algorithm. Proposed method (IGAABC), whose control method is based on the proposed improved model-based predictive control method, while the optimization algorithm of this method is based on the improved hybrid artificial bee colony algorithm IGAABC proposed in the paper.
The basic green time splits scheme at different intersections. The green time splits of the three signal groups at Intersection 1 are 35 s, 65 s, and 40 s, respectively, while the green time splits of the three signal groups for Intersection 2 are 45 s, 55 s, and 40 s, respectively.
Table
Total average vehicle delay at intersection 1 with different control schemes.
Signal Control Method | Average Vehicle Delay [s] |
---|---|
Model-based predictive control | 535.1 |
Adaptive signal control | 525.3 |
Proposed method (ABC) | 479.3 |
Proposed method (IGAABC) | 464.6 |
The detailed comparisons of average vehicle delay for each phase at intersection 1 are shown in Figure
Average vehicle delay for each phase with different control schemes. The simulation time is one hour with the first three cycles as warm-up time.
We further study the delay in a specific cycle whose simulation time ranging from 2300 s to 2440 s, where queue spillover will happen frequently. As shown in Figures
Delay of Phase 2 in a cycle. The delay is evaluated in a specific cycle whose simulation time ranging from 2300 s to 2440 s.
Delay of Phase 7 in a cycle. The delay is evaluated in a specific cycle whose simulation time ranging from 2300 s to 2440 s.
According to the simulation results, the proposed method and the adaptive signal control method can both maintain the queue length less than the length of
Maximum queue length on link
The proposed method will spend some time on solving the optimal solutions of green time splits. Table
The CPU time of the integrated method with different prediction horizons.
Prediction Horizon | Average[s] | Maximum[s] | Minimum[s] |
---|---|---|---|
NP=3 | 39.09 | 40.99 | 37.38 |
NP=5 | 51.45 | 56.59 | 48.56 |
NP=7 | 81.28 | 86.44 | 77.48 |
In a word, the proposed method can significantly improve the overall performance of the studied intersection. The proposed signal control method can not only provide appropriate timing plan according to the changing traffic flow, but also it can avoid the occurrence of queue spillover under oversaturated traffic condition. Therefore this method can benefit these two ideas to reduce the delay and improve the efficiency of traffic control.
There are many factors which may affect the performance of signal optimization. Given different traffic volumes, turning movement changes, and speed limits of the road links, the simulation results which can reflect the performance of signal optimization may be different. Li et al. [
Sensitivity analysis under different traffic volume conditions includes 6 traffic scenarios. We select different factors m which are 0.2, 0.4, 0.6, 0.8, 1.0, and 1.2 of the traffic volume shown in Table
Total delay at Intersection 1 with different traffic scenarios.
Traffic volume factor | Proposed method | Model-based predictive control | Adaptive signal control |
---|---|---|---|
0.2 | 380 | 396.1(+4.1%) | 424.7(+10.5%) |
0.4 | 436.2 | 442.3(+1.38%) | 452.5(+3.6%) |
0.6 | 442.5 | 506.4(+12.62%) | 482.1(+8.2%) |
0.8 | 452.8 | 525.1(+13.77%) | 517.5(+12.5%) |
1 | 469.4 | 535.1(+12.28%) | 525.3(+10.64%) |
1.2 | 492.4 | 656.8(+25.03%) | 642.4(+23.35%) |
Sensitivity analysis under different turning movement changes includes 3 scenarios. We assume that
Total delay at Intersection 1 with different turning movement changes.
| | | |
---|---|---|---|
Proposed method | 514 | 441.8 | 533.7 |
Model-based predictive control | 1009 | 792.5 | 996.3 |
Adaptive signal control | 430.5 | 468.3 | 435.1 |
Sensitivity analysis under different speed limits of the road links is shown in Table
Total delay at Intersection 1 with different speed limits of the road links.
speed limits | 30 | 50 | 70 |
---|---|---|---|
Proposed method | 465.3 | 469.4 | 742.1 |
Model-based predictive control | 569.9 | 535.1 | 1302.9 |
Adaptive signal control | 492.6 | 525.3 | 655.8 |
To summarize, our proposed method can deal with the problem of traffic signal control at intersections when capacity of the system cannot satisfy the demand under oversaturated traffic conditions. We propose an improved model-based predictive control approach which can predict traffic demand over a finite horizon according to the measured traffic flow information to calculate the optimal green time splits plan with the objective of total travel time minimum and avoid queue spillover under oversaturated traffic conditions. Moreover, to solve complicated optimization problems in a short time which contributes to online applications, we propose an improved hybrid artificial bee algorithm to address the optimal control problem of the proposed improved model-based predictive control approach as soon as possible. The simulation results verified that our proposed method can manage queue effectively and balance the traffic flow on different roads simultaneously which can improve the performance of the intersection significantly.
Other subjects will be explored in the future. We can first consider the following aspects including how to optimize traffic control along trunk roads or a huge network under oversaturated condition. Second, we can study the algorithm to solve the optimization model to obtain the solutions as soon as possible. Finally, the proposed method is based on a fixed cycle and phase sequence which limits the application in practical urban traffic condition.
The traffic volume data used to support the findings of this study are included within the article. Table
The authors declare that they have no conflicts of interest.
This work was financially supported by Chinese National Science Foundation (61572165) and Projects of Zhejiang Province (LGF18F030006).