Vehicle-to-Infrastructure-Based Traffic Signal Optimization for Isolated Intersection

Abstract

Traffic signal control is critical for traffic efficiency optimization but is usually constrained by traffic detection methods. The emerging V2I (Vehicle to Infrastructure) technology is capable of providing rich information for traffic detection, thus becoming promising for traffic signal control. Based on parallel simulation, this paper presents a new traffic signal optimization method in a V2I environment. In the proposed method, a predictive optimization problem is formulated, and a cellular automata model is employed as traffic flow model. By using genetic algorithm, the predictive optimization problem is solved online to implement receding horizon control. Simulation results show that the proposed method can improve traffic efficiency in the sense of reducing average delay and number of stops. Meanwhile, simulation also shows that greater communication range brings better performance for reducing the average number of stops. Simulation results show that the proposed V2I-based signal control method can improve traffic efficiency, especially when the traffic volume is relatively high. The proposed algorithm can be applied to traffic signal control to improve traffic efficiency.

1. Introduction

Traffic congestion is becoming a serious problem all over the world, causing lots of unnecessary time and energy waste and environmental pollution. By the end of 2020, China’s car ownership reached 273.4 million [1], which might cost tens of millions in economic waste one day.

As a direct and effective solution to traffic congestion, traffic signal control has attracted lots of researchers’ attention since the 1960s. Up until now, traffic signal control has gone through three stages: fixed-time traffic signal control (such as the Webster method [2]), actuated traffic signal control (including MOVA [3], LHVORA [4] and SOS [5]) and adaptive traffic signal control (e.g., SCATS [6] and SCOOTS [7]). Fixed-time traffic control uses historical and statistical traffic data to predetermine a signal phase and timing (SPaT) offline; actuated traffic signal control selects signal phase and extends phase duration according to real-time traffic data collected by detectors; adaptive traffic signal control takes traffic system as an uncertain system and measures traffic state for feedback, thus realizing dynamic optimization. Nowadays, many researchers are trying to apply computational intelligence in adaptive traffic signal control for improving its performance [8].

The evolution of traffic signal control depends on traffic detection technologies to a great degree. In fixed-time signal control, no detectors are needed, which makes this control method cheap but not flexible to respond to varying traffic demands. In actuated traffic signal control, traffic detectors such as inductive loop detectors and video detectors are used to provide limited real time measurements such as vehicle arrival information. This makes it possible to respond to traffic demands online in real time. Furthermore, adaptive traffic signal control uses advanced traffic detectors to acquire more information for improving control performance. For example, SCATS [6] counts vehicles at the stop line, and SCOOTS [7] collects data about traffic flow and queue length before vehicles reach the stop line. In this perspective, if more detailed information can be obtained via traffic detectors, the performance of traffic signal control can be further improved.

With newly emerging and prospering V2I technology, new possibilities are brought for traffic signal control. By using V2I communication as a new kind of traffic detection technology, accurate and rich information becomes available for traffic control, thus making it possible to further improve traffic efficiency. Nowadays, based on V2I technology, many studies on traffic signal control [9,10,11,12,13] and intersection efficiency improvement [14,15] have been conducted. When it comes to how to use this rich information from V2I communication, one typical method is model predictive control (MPC). This method solves a finite horizon open-loop optimal control problem in each sampling interval to find the best control input in the sense of optimizing a predefined objective function [16]. In [17], design and implementation issues of model-based traffic control, especially model predictive control for traffic regulation, were discussed in detail. However, for model predictive control, the traffic flow dynamic is often described with different equations, which might not accurately characterize the time-varying stochastic traffic flow dynamics [18]. Conversely, the newly emerging method called parallel transportation management system [19,20] uses artificial system for computational experiment and parallel execution. This method also uses online optimization but applies more detailed and implicit traffic flow model for prediction. This makes it more flexible to represent the characteristics of the transportation system and attracts an increasing attention [21,22]. Mohammad et al. [23] propose a novel ontology design for intelligent control of traffic signals. Therefore, we apply this idea to traffic signal optimization. Shaikh et al. [24] conduct a comprehensive literature review on applications of evolutionary and swarm intelligence algorithms to TSC. Mahyar et al. [25] propose an analytical model to enhance energy efficiency by optimizing macroscopic traffic variables in signal-free networks. Lu et al. [26] investigate the potential benefits of implementing weather-specific signal control plans for uncoordinated intersections as well as coordinated corridors. Wang et al. [27] propose a new multi-input multi-output optimal bilinear signal control method in which a bilinear dynamic model approximation is used to capture the nonlinear dynamics of the urban traffic networks.

In this work, based on the assumption that all of the vehicles’ information can be obtained through V2I communication, a new traffic signal optimization method is proposed using the parallel simulation idea. In the method, a cellular automata model is used to present the traffic flow characteristics. Then, genetic algorithm is applied to solve an online predictive optimization problem to obtain the optimal control inputs for receding horizon traffic signal control. A simulation is conducted to verify the proposed method.

The rest of this paper is organized as follows. Section 2 gives a standard formulation of the studied problem. Section 3 details the proposed method for traffic signal optimization. The simulation is demonstrated in Section 4, and the conclusion is presented in Section 5.

2. Problem Formulation

In this research, we mainly consider traffic signal timing optimization for a certain road network containing an isolated intersection. The vehicle state and signal state at time $\mathrm{k}$ are denoted as $V\left(k\right)$ and $S\left(k\right)$, respectively. The vehicle state changes according to vehicle dynamics and the signal state, while the signal state changes according to a pre-defined signal evolution function. Therefore, our objective is to minimize a specific performance index in a finite time horizon $\left[0,T\right]$ by determining the time length of each signal phase subject to necessary constraints. This can be abstractly formulated as the following optimization problem:

$$\underset{G_{i,j}}{\mathit{min}}J=w_1{N}_s+w_2{T}_d$$

(1)

Subject to:

$$V\left(0\right)=V_0,S\left(0\right)=S_0$$

(1a)

$$V\left(k+1\right)=f_V\left(V\left(k\right),V_n\left(k\right),S\left(k\right)\right)$$

(1b)

$$S\left(k\right)=f_S\left(G,k\right),G=\left\{G_{1,1},G_{1,2},\dots ,G_{n_p,n_c}\right\}$$

(1c)

$$N_s=f_N\left(V\right),T_d=f_T\left(V\right),V=\left\{V\left(0\right),V\left(1\right),\dots ,V\left(T\right)\right\}$$

(1d)

$${\displaystyle \sum }_j^{n_c-1}{\displaystyle \sum }_i^{n_p}\left(G_{i,j}+G_{int}\right)<T\le {\displaystyle \sum }_j^{n_c}{\displaystyle \sum }_i^{n_p}\left(G_{i,j}+G_{int}\right)$$

(1e)

$$G_{min}\le G_{i,j}\le G_{max},G_{i,j}\in \mathbb{Z},i\in \left\{1,2,\dots ,n_p\right\},j\in \left\{1,2,\dots ,n_c\right\}$$

(1f)

where $n_c$ is the number of signal cycles in the finite time horizon $\left[0,T\right]$; $n_p$ is the number of signal phases in a signal cycle; $G_{i,j}$ is the time length of the i-th signal phase in the j-th signal cycle; $N_s$ is the total number of stops of all the vehicles in the road network; $T_d$ is the total time delay of all the vehicles in the road network; $w_1,w_2$ are the weight coefficients; $V_0, S_0$ are the initial vehicle state and signal state; $V_n\left(k\right)$. is the state of vehicles entering the road network at time $k;$ $f_V(·)$ is the abstract vehicle dynamics; $f_S(·)$ is the abstract signal evolution function; $f_N(·), f_T(·)$ are the abstract function for calculating $N_s$ and $T_d$; $G_{int}$ is the green interval duration, including all-red light and amber light; $G_{min}, G_{max}$ are the minimum and maximum time length limits.

In the optimization problem (1), (1a) is the initial state condition constraint; (1b) is the vehicle dynamics constraint; (1c) is the abstract signal evolution function; (1d) is an abstract function linking vehicle state and the performance index; (1e) is the time horizon constraint; and (1f) is the time length constrains.

Furthermore, for simplicity, some assumptions are also made in this research:

• All of the vehicles are equipped with V2I communication devices, which means that the signal controller can receive vehicles’ information when vehicles are within the communication range (denoted as $\mathrm{D}$);
• All of the vehicles desire to run at the velocity limit $v_{lim}$ if possible.

3. Algorithm Design

Problem (1) is hard to solve completely, because vehicles’ information is not available before they run into the communication range. To continuously take into account the newly coming vehicles, a predictive optimization problem is built and solved as a feasible approach to approximately find the optimal solution to problem (1). The predictive optimization problem uses the real traffic state at time $k,$ i.e., vehicle state $V\left(k\right)$ and signal state $S\left(k\right)$, as inputs. Then, a traffic flow model is used for prediction. By solving the predictive optimization problem with a heuristic algorithm such as genetic algorithm, the first of the optimal solution is used for signal control. The above steps are repeated online to implement receding horizon control.

3.1. Predictive Optimization Problem

In the predictive optimization problem, we use superscript ‘^’ to represent variables in the predictive horizon $[k, k+\widehat{T}]$ with $k$ being the current time and $\widehat{T}$ being the time length of the predictive horizon. In the predictive horizon, the initial traffic state is given by sampling the state of the real traffic; that is, $\widehat{V}\left(k\right)=V\left(k\right)$ and $\widehat{S}\left(k\right)=S\left(k\right)$.

$\widehat{T}$ can be fixed or dynamic and should be far shorter than $T$ to make the predictive problem easier to solve. For simplicity, we assume that no vehicle runs into the road network in the predictive horizon, i.e., ${\widehat{V}}_n\left(k+p\right)=\varnothing , p\in \{0,1,\dots ,\widehat{T}-1\}$. Furthermore, we also assume that the signal is controlled with fixed-time strategy in the predictive horizon, i.e., the time lengths of the same signal phase in different signal cycles are the same ${\widehat{G}}_{i,j}={\widehat{G}}_i$. Then, the new predictive problem is formulated as follows:

$$\underset{{\widehat{G}}_{i,j}}{\mathit{min}}\widehat{J}=w_1{\widehat{N}}_s+w_2{\widehat{T}}_d$$

(2)

Subject to:

$$\widehat{V}\left(k\right)=V\left(k\right),\widehat{S}\left(k\right)=S\left(k\right)$$

(2a)

$$\widehat{V}\left(k+p+1\right)={\widehat{f}}_V\left(\widehat{V}\left(k+p\right),{\widehat{V}}_n\left(k+p\right),\widehat{S}\left(k+p\right)\right),p\in \left\{0,1,\dots ,\widehat{T}-1\right\}$$

(2b)

$$\widehat{S}\left(k+p\right)=f_S\left(\widehat{G},k+p\right),\widehat{G}=\left\{G_{1,1},G_{1,2},\dots ,G_{n_p,{\widehat{n}}_c}\right\}$$

(2c)

$${\widehat{N}}_s=f_N(\widehat{V}),{\widehat{T}}_d=f_T(\widehat{V}),\widehat{V}=\{\widehat{V}(k),\widehat{V}(k+1),\dots ,\widehat{V}(\widehat{T}-1)\}$$

(2d)

$${\displaystyle \sum }_j^{{\widehat{n}}_c-1}{\displaystyle \sum }_i^{n_p}\left({\widehat{G}}_{i,j}+G_{int}\right)<\widehat{T}\le {\displaystyle \sum }_j^{{\widehat{n}}_c}{\displaystyle \sum }_i^{n_p}\left({\widehat{G}}_{i,j}+G_{int}\right)$$

(2e)

$$G_{min}\le {\widehat{G}}_{i,j}\le G_{max},{\widehat{G}}_{i,j}\in \mathbb{Z},i\in \left\{1,2,\dots ,n_p\right\},j\in \left\{1,2,\dots ,{\widehat{n}}_c\right\}$$

(2f)

$${\widehat{V}}_n\left(k+p\right)=\varnothing$$

(2g)

$${\widehat{G}}_{i,j}={\widehat{G}}_i$$

(2h)

where the variables ${\widehat{n}}_c, {\widehat{G}}_{i,j}, {\widehat{N}}_s, {\widehat{T}}_d, {\widehat{V}}_n\left(k\right), {\widehat{f}}_V(·)$ and constraints (2a) to (2f) have the same meanings as those given in problem (1) but are extended to predictive horizon. Furthermore, the last three constraints (2g) to (2i) are based on the assumptions above. In particular, according to (2i), the solution to problem (1) is actually an ordered array of ${\widehat{G}}_i,i\in \left\{1,2,\dots ,n_p\right\}$.

3.2. Traffic Flow Model

In problem (2), we use ${\widehat{f}}_V(·)$ to implicitly represent the vehicle dynamics, because the function $f_V(·)$ in problem (1) is not accurately known. Here, we use a traffic flow model, which acts as the implicit function ${\widehat{f}}_V(·)$, to characterize vehicle dynamics for vehicle state prediction.

The traffic flow model used in this research is a single-lane cellular automaton model at signalized intersection. It is derived from the Na-Sch model [28] with discrete state in both time and space. In the model, the road network is discretized into cells with equal size. The cells can be either empty or occupied by vehicles. When a cell is occupied by a vehicle, its state, including the vehicle’s velocity and position, is updated in discrete time based on a fixed update rule given as follows (here, the sampling is set to be 1 s):

3.2.1. Acceleration Step

For a vehicle instance $n$, it tends to run at a high velocity, so it will accelerate by steps:

$$v_n\to min\left(v_n+a_{veh},v_{lim}\right)$$

(3)

where $v_n$ is the velocity of vehicle $n$; $a_{veh}$ is the acceleration of vehicles; and $v_{lim}$ is the maximum permitted velocity of the vehicle.

3.2.2. Deceleration Step

If the signal ahead of vehicle n is red, or if the cells after the stop line of the intersection are occupied by other vehicles,

$$v_n\to min\left(v_n,d_n,s_n\right)$$

(4)

else,

$$v_n\to min\left(v_n,d_n\right)$$

(5)

where $d_n$ is the distance between vehicle $n$ and the vehicle in front of it, and $s_n$ is the distance between vehicle $n$ and the stop line in front of it.

3.2.3. Randomization Step

With a probability $p_d\left(0\le p_d\le 1\right)$, vehicle $n$ will decelerate randomly, which characterizes driver’s distraction:

$$v_n\to max\left(v_n-1,0\right)$$

(6)

3.2.4. Movement Step

Vehicle $n$ will run with the updated velocity $v_n$:

$$x_n\to x_n+v_n$$

(7)

where $x_n$ is the displacement of vehicle $n$.

In the traffic flow model, for simplicity, vehicles’ complex behaviors such as lane changing, turning and overtaking are not considered. Thus, we simply assume that vehicles will keep their lanes and go straight, because we only care about the behavior of vehicles that have not passed the stop line. In other words, we only consider vehicles that are actually “controllable” by traffic signal lights.

3.3. Genetic Algorithm

To solve problem (2), we use the genetic algorithm to find the optimal or suboptimal solution. It contains six steps:

3.3.1. Chromosome Coding

The chromosome is coded as an ordered array consisting of n_p integers, i.e., $\left[g_1,g_2,\dots ,g_{n_p}\right]$. The integers g_i, i∈ {1,2,…, n_p} are the genes of the chromosome.

3.3.2. Initial Population Generation

We denote the number of individuals in a population as $n_{ind}$. Then, the initial population is generated with a random method: for each individual in the population, each gene of its chromosome is generated with a uniform distribution in the interval $\left[G_{min}, G_{max}\right]$.

3.3.3. Fitness Value Calculation

For each individual in the population, we take its ordered genes in its chromosome as the time lengths of different signal phases in a signal cycle in the prediction horizon; that is, $\left[{\widehat{G}}_1,{\widehat{G}}_2,\dots ,{\widehat{G}}_{n_p}\right]=\left[g_1,g_2,\dots ,g_{n_p}\right]$. Then, fixed-time signal control with $\left[{\widehat{G}}_1,{\widehat{G}}_2,\dots ,{\widehat{G}}_{n_p}\right]$ as the signal timing plan is applied to the traffic model for simulation. When the prediction horizon ends, the fitness value of the individual is defined as $1/\widehat{J}$, where $\widehat{J}$ is the performance index of problem (1) with $\left[{\widehat{G}}_1,{\widehat{G}}_2,\dots ,{\widehat{G}}_{n_p}\right]$ being the solution.

3.3.4. Natural Selection

When all of the individuals’ fitness values are calculated, a roulette wheel selection according to the fitness values is operated to choose the parents of the new generation. There are totally $n_{ind}-1$ individuals that are selected with the roulette wheel, while the last one, which is called the elite for owning the biggest fitness value, is directly selected as the individual of the new generation.

3.3.5. Chromosome Crossover

For all the parents of the new generation, their chromosomes are interchanged with each other with a possibility of $p_c$. In detail, for a selected individual with chromosome $\left[g_1^1, g_2^1,\dots ,g_{n_p}^1\right]$, it has a possibility of $p_c$ to exchange some segments of its genes with another selected individual with chromosome $\left[g_1^2, g_2^2,\dots ,g_{n_p}^2\right]$. The target individuals for crossover are selected with equal possibilities from all of the other selected individuals, while the target genes for crossover are also selected with equal possibilities from all the genes in the target individuals’ chromosome. During the crossover operation, firstly, the target genes are coded as binary numbers, which are called gene segments. For example, if $g_2^1=50$, and $g_2^2=10$, they will be coded as $g_2^1=0b110010,g_2^2=0b001010$. Then, each gene segment has a same probability to exchange with the other one on the allelic gene. For example if the first and second segments of $g_2^1$ and $g_2^2$ are exchanged, they will become $g_2^1\prime =0b000010,g_2^2\prime =0b111010$. Finally, the new genes are tuned into the feasible range $\left[G_{min}, G_{max}\right]$; that is, $g_2^1{}^{″}=min\left(max\left(g_2^1{}^{\prime },G_{min}\right),G_{max}\right), g_2^2{}^{″}=min\left(max\left(g_2^2{}^{\prime },G_{min}\right),G_{max}\right)$. Thus, as a result, the chromosomes of the two individuals after crossover operation may be such as $\left[g_1^1, g_2^1{}^{″},g_3^1\dots ,g_{n_p}^1\right]$ and $\left[g_1^2, g_2^2{}^{″},g_3^2\dots ,g_{n_p}^2\right]$. Note that the elite will not take part in the chromosome crossover operation.

3.3.6. Gene Mutation

After chromosome crossover operation, for all the parents of the new generation, their genes will mutate with a possibility of $p_m$. In detail, for an individual with chromosome $\left[g_1, g_2,\dots ,g_{n_p}\right]$, each of its gene has a possibility of $p_m$ to be replaced with a random integer number selected from $\left[G_{min}, G_{max}\right]$ with a uniform distribution. The target genes for mutation are selected with equal possibilities from all the genes in a chromosome. Thus, as a result, for example, the chromosome of the individuals after mutation operation may be such as $\left[g_1, g_2^{\prime },\dots ,g_{n_p}\right]$ if its second gene mutates. Note that the elite will not take part in the gene mutation operation.

After step (6), the new generation is generated. Then, steps (3)–(6) are repeated until the total number of generation reaches the maximum generation limit, which is denoted as $g_{max}$, or the maximum fitness values of different generations consecutively remain the same for a certain number of generations, which is denoted as $g_{remain}$. Then, the optimal or suboptimal solution to problem (1) is given by $[{\widehat{G}}_1{}^{*},{\widehat{G}}_2{}^{*},\dots ,{\widehat{G}}_{n_p}{}^{*}]=[g_1{}^{*},g_2{}^{*},\dots ,g_{n_p}{}^{*}]$, where $[g_1{}^{*},g_2{}^{*},\dots ,g_{n_p}{}^{*}]$ is the chromosome of the elite in the last generation.

3.4. Receding Horizon Control

By using the genetic algorithm, the optimal or suboptimal solution to problem (1) is obtained. Then, the solution is used for traffic control for several steps; that is:

$$S\left(k+p\right)=f_S\left({\widehat{G}}^{*},k+p\right),p\in \left\{1,2,\dots ,T_c\right\}$$

(8)

where ${\widehat{G}}^{*}=[{\widehat{G}}_1{}^{*},{\widehat{G}}_2{}^{*},\dots ,{\widehat{G}}_{n_p}{}^{*}]$ is the optimal or suboptimal solution, and $T_c(T_c\le \widehat{T})$ is the size of control steps. After control steps, a new cycle, consisting of traffic state sampling, online predictive optimization and traffic control, is repeated again, as shown in Figure 1. This is called receding horizon control.

4. Simulation

To test the performance of the proposed signal optimization method, simulation was conducted based on the platform shown in Figure 2. The simulation platform uses VISSIM for traffic simulation and MATLAB for signal optimization, both of which are connected to Visual Basic via component object model (COM) for data transmission.

4.1. Simulation Setup

In the simulation, an isolated intersection model was built as shown in Figure 3. The four arms of the intersection are identical with equal traffic flow inputs. Furthermore, the signal sequence is defined in Figure 4, where right-turn is always admissible in all signal phases.

In the simulation, we compare two kinds of signal control methods: actuated signal control method and the proposed V2I signal control method. In the actuated signal control [29], the minimum and maximum time lengths of green light are denoted as $G_{min}$ and $G_{max}$, respectively, and the unit extension time is denoted as $\Delta G$. We also consider the influence of traffic volume ($V_{traffic}$) and communication range ($R_{com}$) on control performance. The other parameters in the simulation are defined in

Table 1. Parameter definition.

Parameter	Value	Parameter	Value
$n_p$	4	$n_{ind}$	20
$w_1$	100	$p_c$	0.6
$w_2$	1	$p_m$	0.01
$G_{min}\left(\mathrm{s}\right)$	10	$g_{max}$	100
$G_{max}\left(\mathrm{s}\right)$	50	$g_{remain}$	30
$G_{int}\left(\mathrm{s}\right)$	5	$v_{lim}\left(\mathrm{m}/\mathrm{s}\right)$	15
$a_{veh}\left(\mathrm{m}/{\mathrm{s}}^2\right)$	1	$T_c$	5
$p_d$	0.1	$\Delta G\left(\mathrm{s}\right)$	3
$\widehat{T}\left(\mathrm{s}\right)$	120

.

In Table 1, the parameters adopted for genetic algorithm are tuned to obtain a good convergence performance as shown in Figure 5. In Figure 5, the mean, minimum and maximum penalty values refer to the average, minimum and maximum values of $\widehat{J}$ of all the individuals in the population, respectively. The minimum penalty value corresponds to the individuals with the best adaptability, or the elite, while the mean penalty value represents the adaptability of the whole population. Thus, the closer the difference between the mean and the minimum penalty value is, the better the population evolves. It is obvious from Figure 5 that the average penalty value converges to the minimum penalty value with the evolution of population, which guarantees the convergence of the solution.

Figure 6 shows the receding horizon signal control scheme. In the figure, each horizontal line represents a signal timing plan, in which the thick ones are the new generated signal timing plan generated at each sample time, while the thin ones correspond to the control step during which the signal timing plan remains the same. The crosses on the horizontal lines represent the actual signal phase for signal control. For example, at the time $t=145$, a signal timing plan is generated shown as the thick horizontal line aligned at the time $t=145$. Because the control step lasts for 5 s ($T_c=5$), in the following 5 s from now on ($t=145~149$), the traffic signal is controlled according to this signal timing plan, i.e., the signal timing plans at the time $t=146~149$ are the same as at the time $t=145$ shown as the thin horizontal lines in Figure 6. Thus, according to the signal timing plan, at the time $t=145~146$, the signal remains green, while at the time $t=147~149$, the signal switches to amber. At the time $t=150$, a new signal timing plan is generated, and the steps mentioned above are repeated again. Finally, the overall signal timing plan is shown on the left side of the figure in accordance with the signal phases at each time. Note that the overall signal timing plan is not decided ahead of time but in receding horizon.

4.2. Simulation Results

The simulation results are illustrated in Figure 7.

Figure 7 compares four types of control indexes, including average delay, average number of stops, average queue length and maximum queue length, of the two signal control methods. In the comparison, traffic volume varies from 240 veh/h to 720 veh/h while the communication range is fixed with $R_{com}=250\mathrm{m}$. From the upper two plots, it is obvious that the V2I signal control method can help improve traffic efficiency by reducing the average delay and number of stops. In particular, the improvement is more prominent when the traffic volume is relatively high. However, as for average queue length and maximum queue length, the advantage of the V2I signal control method is not that prominent. Actually, the average queue length and maximum queue length are not improved under low traffic volume conditions. This can be intuitively understandable: these two indexes are not explicitly added in the optimization objective function; thus, the improvement for them is limited.

Figure 8 shows the simulation result of the V2I-based control method under different communication range and traffic volume conditions. It is clearly shown that higher traffic volume often causes larger traffic delay and average number of stops. As far as communication range is concerned, the traffic delay does not seem sensitive to the change of communication range $R_{com}$, while the average number of stops shows a decreasing trend with the increase in $R_{com}$. This is because in the predictive horizon fixed-time, signal timing is used. The determination of the fixed signal timing in predictive horizon is influenced by all the vehicles in communication range. Hence, when the communication range becomes larger, more vehicles far from the intersection will have influence on the fixed signal timing in the predictive horizon. However, it is the vehicles near the intersection that are most influenced by the signal timing, because the signal control is in receding horizon. Therefore, a larger communication range may not always help improve the control performance, as shown in Figure 8. If the signal timing for each cycle in predictive horizon can be various, the consideration of vehicles far from the intersection will have less impact on the near ones. This may bring better control performance but also increase the computation load.

Furthermore, in Figure 8, both of the black spot lines for $V_{traffic}=720\mathrm{veh}/\mathrm{h}$ have a peak at $R_{com}=200\mathrm{m}$. This is because when the traffic volume becomes high, more vehicles may be forced to queue before the stop line. Considering model error on vehicle behavior, large vehicle amount will amplify the error and enlarge the impact on vehicle state prediction accuracy. This may randomly cause the deterioration of control performance with the random traffic inputs. Additionally, the global optimality of the control method is not guaranteed, which may cause the fluctuation of the control performance.

5. Conclusions

In this study, a V2I-based traffic signal optimization method is proposed. The method uses traffic flow model and genetic algorithm for online predictive optimization; thus, receding horizon control is implemented for traffic signal control. Simulation results show that the proposed V2I-based signal control method can improve traffic efficiency, especially when the traffic volume is relatively high. Furthermore, the performance is affected by communication range: results show that the average number of stops shows a decreasing trend with the increase in communication range.

The performance of the proposed method relies on the prediction accuracy to some extent. By calibrating the traffic flow model more carefully, the prediction accuracy can be enhanced; thus, the performance can be improved. However, the more accurate the model is, the more computational cost it may bring, which implies a tradeoff between the performance and the efficiency. Compared with those traffic models expressed as differential equations, the implicit rule-based model used in this method is time consuming. Actually, the traffic flow model used in the method can only predict vehicles’ simple longitudinal behaviors such as acceleration and deceleration. Complex maneuvers such as making a U-turn or routine-decision are hard to predict, which is also unnecessary. Advanced optimization algorithms have been applied as solution methods in many different fields, such as e-learning, scheduling, multi-objective optimization, transportation, data classification and more. The effectiveness of advanced optimization algorithms in the above areas and their potential application in the decision problems solved in this study should be considered. In future studies, the proposed genetic algorithm can actually be compared with advanced optimization algorithms.