#### Abstract

In this paper, a self-adaptive, two-stage fuzzy controller is established to realize the real-time online optimization of traffic signal timing plan, which takes multimodels of transportation as the research object to analyze the reliability of the control system at the isolated urban intersection. In this system, the first stage calculates traffic urgency degree for all red phases and selects the red phase with maximum traffic urgency degree as the next green phase. The second stage determines whether to extend or terminate the current signal phase. Aiming at the problems of the parameters of membership functions empirical settings and insufficient response to the real-time fluctuation in traffic flow, the controller introduces an improved hybrid genetic algorithm to solve it and enable the controller to self-learn. Finally, a microsimulation platform is constructed based on the VISSIM and Python language to evaluate the efficiency and reliability of the controller under complex actual traffic conditions. Results showed that the average delay time per vehicle is reduced by 14.59%, while the average number of stops per vehicle is reduced by 0.71% compared with the traditional control method. Results indicate that the traffic signal timing plan generated by the controller can efficiently improve the intersection traffic capacity and has good efficiency and reliability under the condition of medium saturation and unsteady flow.

#### 1. Introduction

At present, with the development of shared mobility and traffic detection techniques theories, many scholars in the field of urban traffic engineering are paying more attention to the collaborative optimization of multi-transport models in traffic safety [1–3], traffic operation efficiency and reliability [4, 5], and environmental protection [6–8]. Driven by the rapid development of the mobile Internet and the sharing economy, dockless bike-sharing systems have grown in popularity in China [9]. For example, in Beijing, the total daily average of cycling trips has reached 5.6 million by 2020, up from 4.62 million in 2017, surpassing the trips by bus and subway and becoming the third-largest way of travel after walking and car [10]. In addition, in the face of congested traffic, people are more likely to choose to use dockless bike-sharing to complete short-distance travel [11]. Shared mobility has led to more walking, and cycling trips significantly changed intersections’ traffic flow structure and brought new challenges to the intersection signal timing optimization. Therefore, considering the travel needs of bicycles and pedestrians in the process of signal timing optimization has become an important research content. At the same time, with the emergence of new detection technologies such as microwave radar and high point video, it is possible to analyze the efficiency and reliability of signal timing control systems in the real environment.

In some developing countries, such as China and India, the most signalized intersection’ control mode is fixed-time or actuated control due to complex traffic flow and lack of effective observation data [12]. As the fixed-time control cannot respond to the real-time change of traffic demand, vehicle actuated control is better than fixed-time control. Though it can optimize the timing scheme of signalized intersections according to the real-time traffic demand, the setting of critical parameters relies on urban traffic engineers’ personal experience [13]. In the past few decades, to address these deficiencies, a variety of adaptive signal control systems have been proposed by Gartener [14], Lin and Cooke [15], Kronborg and Davidson [16], and Lin and Vijayakumar [17]. Because of its excellent real-time and robustness, fuzzy control has become one of the most common intelligent control methods.

Fuzzy control was introduced into the traffic control field in 1977 by Pappis and Mamdani [18]. Since then, single-level, two-level, and three-level fuzzy controllers have been proposed one after another [19–22]. However, as the parameters are pre-defined by experts and unable to change, this fuzzy controller is non-responsive to the real-time fluctuation of traffic demand and disability to learn [23]. To solve the problems above, Henry et al. [24], Bingham [25], Rida et al. [26], and Xu et al. [27] introduce heuristic algorithm, such as reinforcement learning, neural network, and ant colony to optimize fuzzy controller parameters according to the historical traffic data. The simulation result indicates this adaptive fuzzy controller is more effective than a traditional fuzzy controller, but the performance of these traffic signal control methods needed large and valid sample sets. Genetic algorithm (GA) has been widely used with the ability of global search and does not depend on experiential knowledge and a large amount of historical traffic flow data [22, 28]. In light of this, Liu and Zuo [29] take a four-phase isolated signalized intersection as a research object and uses a genetic algorithm to optimize fuzzy rules and membership functions of the fuzzy control. Shahsavari et al. [30] take the total length of traffic queue and pedestrian queue in all phase of isolated intersection as optimization goals, construct a fuzzy multi-objective optimization model, and use a genetic algorithm to optimize the cycle time of the traffic light systems. Yu et al. [31] established a multi-objective optimization model with traffic capacity, average parking delay, and exhaust emissions as optimization goals and used genetic algorithms to optimize the signal cycle time and effectively green light time. However, in the above study, the traffic flow distribution is generally assumed to obey a particular traffic arrival distribution, which does not reflect the fluctuation of actual traffic demand. In addition, pedestrians and non-motor vehicles are also almost not taken into account. Except that, the simulation experiment designed in the existing research has the disability to reflect actual vehicle driving behavior and mixed traffic flow characteristics.

The aim of this paper was to take the travel needs of non-motor vehicles, pedestrians, and motor vehicles into account during the optimization process of signal timing scheme. In addition, this paper introduces a hybrid genetic algorithm to make the signal control strategy have the ability of autonomous learning. At the same time, to verify the efficiency and reliability of this control system, the simulation parameters of the platform are calibrated according to the actual vehicle trajectory data.

#### 2. Research Scope and Model Structure

##### 2.1. Experimental Test Intersection

The plan of the signalized isolated intersection is shown in Figure 1. As the intersection has through-left movement, this paper selects a split-phase to control the intersection. Since there is a dedicated right-turn lane at this intersection, right-turn traffic flow is not considered in the research.

As shown in Figure 1, each approach has one microwave radar and many cameras to detect the vehicles’ status information of each lane, such as cross ID, latitude, and longitude, with an average sampling interval of 80 milliseconds. According to the trajectory data, vehicles’ temporal and spatial distribution characteristics can be obtained [32], making it possible to get the real intersection traffic flow information and analyze the driving characteristics of drivers. The daily file size of high-precision track data used in the research is about 1G, and about 8 million track point records are generated. The primary data attributes are shown in Table 1.

Due to the complexity of the real environment, possible packet loss during data transmission, buffer data overflow and on-board equipment and roadside unit failure, there will be problems in the collection of high-precision track data, such as missing field values, missing track information, and change of track ID. At the same time, roadside parking, bad weather, or temporary traffic control may also cause the obtained high-precision trajectory data to fail to reflect the normal operation state of vehicles at the intersection, so the data need to be preprocessed before use. Data cleaning work has been done in a previous work [33], and hence the details are not included to avoid redundancy.

##### 2.2. Self-Adaptive Two-Stage Fuzzy Control Algorithm

The primary process of the self-adaptive two-stage fuzzy control algorithm is as follows: (1) set a minimum green time to a phase until the remainder of the green time is 1 s; (2) calculates the red urgency and green urgency of different approaches according to the real-time motor vehicle, non-motor vehicle, and pedestrians traffic flow data; (3) select the red phase with greatest phase urgency as the next candidate phase; (4) comparing the selected red phase urgency with green phase urgency, decided whether to extend or terminate the current signal phase; (5) if the length of the green phase exceeds maximum green duration, then terminal the current signal phase, otherwise, continue; (6) according to the evaluation of the scheme, decided whether to optimize the parameters of membership functions; (7) if the simulation time does not reached, skip to (2) and continue.

##### 2.3. Structure of Self-Adaptive Two-Stage Fuzzy Controller

Figure 2 shows the structure of the self-adaptive two-stage fuzzy controller. As we can see from the figure, the controller has two main components: (1) two-stage fuzzy controller, which includes four parts: red urgency judgment module, pedestrian urgency judgment module, green urgency judgment module, and decision module; (2) parameter optimization module based on improved hybrid genetic algorithm.

##### 2.4. Computation of the Queue Lengths

When the phase is red, the queue lengths in the approach direction are expressed aswhere is the queue lengths of an approach direction ; is the number of remaining vehicles when the phase is switched to red phase; is the duration of the red phase of approach direction ; and is the amount of arriving vehicles of approach direction duration interval.

When the phase is green, the queue lengths in the approach direction are expressed aswhere is the number of vehicles through stop-line of approach direction duration interval and is the number of remaining vehicles when switched to the green phase.

#### 3. Design of Self-Adaptive Two-Stage Fuzzy Control

##### 3.1. First Stage

Since the first stage has three fuzzy inputs, theoretically, the number of rules necessary for gathering all the possible input combinations for the three-term fuzzy controller is . In practice, the design of a fuzzy controller with so many fuzzy control rules will occupy a large amount of memory and long processing time [34, 35]. Therefore, this study divided the first stage into three sub-modules modules, namely: red urgency judgment module, pedestrian urgency judgment module, and green urgency judgment module, each with two fuzzy inputs and one output variable.

In these sub-modules, phase urgency on each approach direction is determined by the maximum red/green urgency and pedestrian urgency. For example, if approach direction is in red and its red urgency is 2.3, and pedestrian urgency is 2.2, then would have a phase urgency of 2.3 and is named red urgency. The calculation process of the urgency of each submodule is shown below.

###### 3.1.1. Red Urgency Judgment Module

In this module, the input variable is the queue length of motor vehicles , the red phase duration time . The output variable is urgency . The domain of is (0, 16), the linguistics are {Very Few Vehicles, Rarely Few Vehicles, Medium Vehicles, Rarely More Vehicles, Very More Vehicles}, short as {VFV, RFV, MV, RMV, VMV}. The domain of is (0, 120), the linguistics are {Very Short Time, Rarely Short Time, Medium Time, Rarely Long Time, Very Long Time}, short as {VST, RST, MT, RLT, VLT}. The domain of is (0, 4), the linguistics are {Very Low, Low, Medium, Height, Very Height}, short as {VL, *L*, M, H, VH}.

With linguistic descriptions of as input, the urgency in red direction, , is determined by the fuzzy rules given in Table 2. For example, if is VSF, and is VFV, then is VL.

###### 3.1.2. Pedestrian Urgency Judgment Module

In this module, the input variable is the traffic flow of non-motor and pedestrian on each approach direction , the phase duration time is , and the output variable is urgency . The domain of is (0, 60), the linguistics are {Very Few Pedestrians, Rarely Few Pedestrians, Medium Pedestrians, Rarely More Pedestrians, Very More Pedestrians}, short as {VFP, RFP, MP, RMP, VMP}. The domain of is (0, 120) and (0, 4), respectively. The linguistic subsets of are same as red urgency judgment module. The rules of these modules are shown in Table 3.

###### 3.1.3. Green Urgency Judgment Module

In this module, the input variable is the number of remaining vehicles , and green extension time . The domain and terms of each variable are shown in Table 2. The domain of is (0, 16), (0, 120), (0, 4), respectively. The linguistic subsets of each variable are the same as the red urgency judgment module. The rules of these modules are shown in Table 4.

The research uses the Gaussian fuzzy membership function to describe all parameters and uses the center of gravity method to de-fuzz output results.where represents the membership function center; denotes the membership function width; and indicates the element; and is the membership function.

##### 3.2. Second Stage

The decision module takes and as an input variable, and the output variable represents whether to extend the green time or deliver the right of way to the selected phase (). The domain of is (0, 1). It is divided into two linguistic subsets {No, Yes}, abbreviated as {N, Y}. The rules of these modules are shown in Table 5.

##### 3.3. Parameter Optimization Module

To enable the two-stage fuzzy controller have autonomous learning ability, this paper uses a hybrid genetic algorithm to optimize the membership function of the fuzzy variable and uses a rolling horizon to set the parameters of these membership functions [28, 36]. The framework of the module is shown in Figure 3. Furthermore, the process of parameter optimization is as follows: (1) Detect real-time traffic flow during the control time horizon, evaluate the scheme, and decide whether to optimize membership functions’ parameters. If so, go to step 2; otherwise, end. (2) Optimize the parameters of in membership function by hybrid genetic algorithm (HGA) based on historical traffic flow data. (3) Update the parameters of the fuzzy controller in time, according to the optimized membership function. (4) Repeat the above process until the simulation time is reached.

As shown in Figure 3, this study uses floating-point coding to encode the chromosome and sets a limited value range for each control parameter to avoid the generation gap phenomenon so that no fuzzy rules are activated after the parameters were input. For example, if the parameters of are the element in the linguistic sets of , as the domain of is (0, 16), so the range of is . The fitness value of , denoted by , is computed bywhere is the average delay time per vehicle obtained by the simulation platform.

The parameters of are calculated bywhere is the number of individuals; is fitness value of individual of ; is select probability; is crossing probability; is the minimum crossing probability, 0.2; is the maximum crossing probability, 0.9; is mutation probability; is the minimum crossing probability, 0.01; is the maximum crossing probability, 0.2; and are the rank index of minimum, average, and maximum fitness, respectively.

#### 4. Efficiency and Reliability Analysis

##### 4.1. Simulation Environment

###### 4.1.1. Structure of the Simulation Platform

The proposed control strategy was verified in a prevailing microscopic traffic simulation environment, VISSIM. The control strategy and optimization algorithm are compiled on the visual studio code platform and transmitted to the VISSIM via the COM interface. At each step, according to the current simulation information, the adaptive two-stage fuzzy controller decided whether to terminate or extend the current green signal phase and judgment whether to optimize the membership function or maintain the status quo. The structure of the VISSIM simulation platform is shown in Figure 4.

###### 4.1.2. VISSIM Parameter Calibration

VISSIM simulation software uses a large number of independent simulation parameters to reflect real vehicle operation, traffic flow characteristics, and driving behavior. However, these parameters are calibrated according to Germany and other western countries’ measured data and may not be suitable for China’s actual situation. As these parameters have an important impact on the simulation results, it is necessary to calibrate the default simulation parameters according to the actual situation of the intersection before the simulation. In this study, the seven parameters that significantly impact the simulation results are calibrated, including desired speed distribution, maximum acceleration/deceleration, expected acceleration/deceleration, average standstill distance, additive part, and multiple parts of safety distance [37–39]. The specific calibration process can refer to the literature [33].

##### 4.2. Experimental Design

###### 4.2.1. Traffic Flow

The traffic flow data of motor vehicles at the intersection extracted based on high-precision trajectory data are shown in Table 6. Data extraction work has been done in a previous work [33], and hence the details are not included to avoid redundancy.

Since trajectory data cannot obtain the traffic flow data of non-motor vehicles and pedestrians, this study assumes that the arrival rates of non-motor vehicles and pedestrians in each approach direction obey Poisson distribution [40]:where is the probability of non-motor or pedestrian arrival in interval; is the average arrival rate per unit time, 0–0.4; and is phase duration of current approach direction.

###### 4.2.2. Traffic Flow Structure

The traffic flow structure data of motor vehicles at the intersection extracted based on trajectory data is shown in Table 7.

###### 4.2.3. Simulation Parameters Calibration

The simulation parameters are calibrated based on the intersection geometry (Figure 1) and traffic flow characteristics. The parameter calibration results are shown in Table 8.

#### 5. Results and Discussion

Figures 5–7 show the simulation results of fixed-time control (FTC), traditional fuzzy control (TFC), and hybrid genetic algorithm fuzzy control (HGAFC). Compared with FTC, the average delay time per vehicle of HGAFC is reduced by 14.59%, and the average number of stops per vehicle is reduced by 0.71%; the average delay time per vehicle of TFC is reduced by 11.08%, and the average number of stops per vehicle is reduced by 0.33%.

The following inferences can be drawn based on Figures 5–7:(1)In the early morning, the effect of the control algorithm is the same. The reason is that when the traffic flow of each approach of the intersection is low, the vehicle queue length is short. The fuzzy control’s main influence factor is each phase’s red/green light duration, and the fuzzy control is in a fixed-time control state.(2)The control algorithm can effectively reduce the average vehicle delay and queue length during peak hours. The reason is that when the traffic flow at the intersection is large, the queuing vehicles cannot get through the parking line in the shortest green time, and the queuing phenomenon begins to appear. The queuing length begins to affect the decision process of the fuzzy controller, and the entrance lane with long queuing begins to obtain the green light extension time, which fully reflects the flexibility and superiority of fuzzy control over timing control.(3)In the morning rush hour, the optimization effect of fuzzy control on the intersection is weaker than in another period, but it is still better than Fixed-time control. The reason is that when there is more traffic flow at the intersection, the queue length of each approach is longer. In this case, the queue length and phase duration are the main influencing factors of fuzzy control, but the phase duration occupies the dominant position.(4)Figures 5 and 6 show the changes of critical parameters in the fuzzy control system under different real traffic conditions. In the simulation model, there are 2911 phases in 54000 time steps, i.e., about 727 cycles. The average cycle length of each cycle is 74 seconds, of which 152 cycles change, accounting for 20.91% of the total cycles. It can be seen from the simulation results that the larger the traffic volume at the intersection, the more significant the signal cycle change, which shows that the signal control strategy generated by the algorithm can effectively adapt to the real-time evolution of intersection traffic flow. Among the 727 cycles, the maximum cycle length is about 100 seconds, and the minimum is 72 seconds. Each phase’s maximum green light time is also within a reasonable range, and there are no extreme cases, indicating that the genetic fuzzy control algorithm has good reliability.

#### 6. Conclusion

In this study, a self-adaptive two-stage fuzzy controller is proposed, which considers multiple modes of transportation: motor, non-motor, and pedestrian. In order to simulate the driving behavior characteristics and real-time traffic flow fluctuation characteristics of vehicles in the real environment, the simulation parameters of the VISSIM simulation platform are calibrated through the intersection vehicle high-precision trajectory data, and the vehicle traffic information extracted based on the trajectory data is used as the input of the simulation platform. Then, its control efficiency and reliability are evaluated based on the micro-simulation platform. Results showed that the average delay time per vehicle is reduced by 14.59%, while the average number of stops per vehicle is reduced by 0.71% compared with the traditional control method. In addition, by analyzing the effectiveness of signal control strategy under different traffic conditions, it is found that the fuzzy controller can only achieve a good control effect under medium saturation or unbalanced traffic flow but has a poor control effect under low or high saturation. This paper researched the optimization question of traffic signal timing in natural traffic conditions, but the optimization module’s timeliness was not, so it is best to introduce the traffic flow prediction module in future research.

#### Data Availability

Data used to support the findings of this study are available from the corresponding author upon request.

#### Conflicts of Interest

The authors declare that there are no conflicts of interest regarding the publication of this study.

#### Acknowledgments

This study was supported by project National Key R&D Program of China (No. 2019YFF0301403).