Vehicle Trajectory Control and Signal Timing Optimization of Isolated Intersection under V2X Environment

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Introduction
In recent years, intelligent transportation and transportation big data have developed rapidly. For a long time to come, the trafc fow on the road will include both traditional manual driving vehicles and connected and autonomous vehicles (CAVs). It will be a big trend to transition from a homogeneous fow composed of one vehicle type to a mixed trafc fow composed of at least two types. At the meanwhile, with the rapid growth of car ownership, the problem of trafc congestion has become increasingly prominent. Road intersections are often the bottleneck of urban road network trafc fow. In addition, the control of trafc lights at intersections makes vehicles at intersections accelerate and decelerate frequently, resulting in low trafc efciency and low fuel economy. Trafc signal coordination is an important way to enhance trafc safety, to improve trafc efciency, and to reduce trafc emissions. Trafc signal coordination is through vehicle-tovehicle (V2V) communication and vehicle-to-infrastructure (V2I) communication to obtain information about the motion status of surrounding vehicles, as well as signal phase and timing (spit) information from signals hundreds of meters away. Trough the obtained information and the trajectory optimization control combined with the signal information, the vehicle fnally realizes the ecological driving of the signal intersection.
Many existing studies have conducted relevant research on the guidance, control, and signal timing of intelligent connected vehicles in the networked intersection environment.
Jiang et al. [1] evaluated the performance of ecological approach control systems at signalized intersections in partially connected and automated vehicle (CAV) environments. Tey tested two diferent networks, including an isolated signalized intersection and a corridor with two signalized intersections. Te results show that the controller generally improves fuel efciency without afecting maneuverability, and its environmental performance is afected by the lowest CAV speed, green ratio, congestion level, and sign penetration rate. Ghiasi et al. [2] proposed a CAV-based trajectory smoothing model to coordinate trafc, which could improve fuel efciency and reduce environmental impact. Tis real-time control algorithm for trafc coordination is applicable to the mixed trafc environment of manual driving vehicles (HDVs), connecting vehicles (CVs), and CAVs. Yao et al. [3] proposed a two-level joint optimization framework for trafc signals and vehicle trajectories to reduce gasoline consumption and transport emissions. Tere are good results under diferent conditions of CAV permeability. Gutesa et al. [4] proposed an intersection management strategy for automated vehicle corridors based on the vehicle trajectory-driven optimization method. Te automated driving trajectory driven optimization model was based on the vehicle position, trafc conditions, and signal status on the corridor to calculate the optimal trajectory for CAV, and reduced vehicle delays along the signal corridor with fxed time signal control. Guo and Ma [5] proposed a signaling corridor management framework based on CAV technology for vehicle layout and trajectory control (SCoPTO). In this framework, when vehicles on the main roads arrived at the downstream intersections in the form of a platoon, the framework could request to extend the green time to reduce unnecessary parking and improve the utilization rate of green time as much as possible and improve the trafc stability. Guo and Ma [6] proposed a real-time learning and control framework for signalized intersection management, including signal optimization and CAV trajectory control. By using efcient trajectory planning algorithms, you can control the vehicle trajectory of CAV, maximize the use of green time, and reduce the startup loss time. Lu et al. [7] proposed an ecological intelligent driver model (EcoSDM) to improve the fuel efciency and trafc fow of vehicles by adjusting the speed of leading vehicles in feets. Yi et al. [8] had established a hybrid equilibrium model for CAV platoon and humandriven vehicle (HDV), taking into account both the positive and negative aspects of CAV platoon. In addition, the study proposes an optimal path layout method that integrates the travel costs of CAV and HDV into its objective function to reduce negative defects. Te numerical results indicate that introducing CAV platoons may increase initial travel costs, and this method can efectively reduce platform disturbance interference, thereby promoting the widespread application of CAV platoons. Hea and Wu [9] proposed an optimal control model that utilizes promising connected vehicle technology and proposes two eco-driving consulting strategies. Te model better solves the problem of reducing the energy consumption of all vehicles when traditional gasoline vehicles (GVs) and electric vehicles (EVs) form a platoon that is considered energy friendly transportation mode. Te results of numerical experiments show that it is important for eco-driving consulting system to consider the energy consumption characteristics of the vehicle as a whole. Gong and Du [10] have developed a coordinated control algorithm of CAV and HDV to ensure the smoothness and stability of system level trafc fow, as well as the mobility and safety of individual vehicles. Long et al. [11] proposed a comprehensive optimization method based on trafc signals and vehicle motion tracks. Wang et al. [12] described a cooperative ecology-driven (CED) system for signal corridors, focusing on how the penetration rate of CAVs afects the energy efciency of transport networks. In addition, they proposed a role switching protocol that lets CAVs switch between the leader and subsequent vehicles in the string. Aiming at traditional vehicles and diferent cabs in the network, a longitudinal control model is developed according to their roles and distance from the intersection. PTV VISSIM simulation results show that with the increase of CAV penetration, the energy consumption and pollutant emissions of the system decrease gradually. When all vehicles in the proposed system are CAVs, energy consumption can be reduced by more than 7 percent and pollutant emissions by more than 59 percent. Pourmehrab et al. [13] compared two state-of-the-art intersection management algorithms (IMAs) for CAVs and conventional vehicles (CNVs), as well as an actuated signal control system (ASCS). Two IMAs are adopted, Intelligent Intersection Control Algorithm (IICA) and Hybrid Autonomous Intersection Management (H-AIM), to improve the efciency of intersections through vehicle automation and connectivity. Berbar et al. [14] proposed a dual agent (DA) intelligent trafc signal module control based on the reinforcement learning (RL) method. Te speed agent (VA) aimed to minimize fuel consumption by controlling the speed of the platoon and single CAVs crossing the signal intersection and efectively reduce trafc delay through signal sequencing and phases. Zhou et al. [15] proposed a vehicle tracking model based on reinforcement learning to obtain appropriate driving behavior and to improve the driving efciency, fuel consumption, and safety of signalized intersections in real time. Yao et al. [16] evaluated the impact of connected and autonomous vehicles on fuel consumption and emissions of mixed trafc fow on highways. Tree following models were used to capture the following behavior in mixed trafc fow. Te efects of connected and autonomous vehicles on fuel consumption and trafc emissions of mixed trafc fow were studied through numerical simulation. Finally, some factors affecting fuel consumption and trafc emissions of mixed trafc fow were discussed. Te simulation results show that networked automated vehicles can signifcantly reduce fuel consumption and transportation emissions. Nie and Farzaneh [17] proposed a real-time dynamic predictive cruise control (PCC) system. In the comprehensive trafc situation of the comprehensive driving scene, the constraints of the previous vehicle and the infuence of trafc lights are considered to improve the driving performance of the vehicle.
It can be seen from the above studies that most of the previous studies focused on controlling the vehicle's trajectory to achieve the minimum fuel consumption, or controlling the vehicle's trajectory to achieve the highest trafc efciency at the signalized intersection, or comprehensively considering the vehicle's energy consumption and trafc efciency at the intersection. However, most of the studies that comprehensively consider the above two objectives are achieved by controlling the signal phase and timing of the signalized intersection or jointly controlling the vehicle trajectory and the timing and phase of the signalized intersection, but the method is relatively simple. Most of them did not consider the impact of diferent types of drivers and the diferences of CAV car-following behavior in diferent situations. Terefore, the goal of this paper is to develop an intersection control optimizer based on the secondary development of SUMO using Python according to diferent driving situations and the uncertainty brought by manual driving vehicles: (1) A mixed trafc fow driving situation (which can be realized in the real world in the near future) is constructed to comprehensively consider the minimization of vehicle delay and vehicle energy consumption, so as to realize the comprehensive optimization applicable to isolated signalized intersections. (2) A two-level model predictive control system for vehicles is proposed to distinguish driving scenarios through switching logic algorithm to realize recognition, classifcation, and control of vehicle driving status. Te vehicle two-level model predictive control system mainly includes two parts: the vehicle trajectory control model based on signal and the vehicle trajectory control model oriented to car-following. (3) Te randomness of Connected Human-Driven Vehicle (CHV) is considered in the SUMO simulation process. (4) Te fuzzy control algorithm is proposed to optimize the signal phase duration. Under the driving situation of mixed trafc fow (which can be realized in the real world in the near future), the minimization of vehicle delay and vehicle energy consumption shall be comprehensively considered to achieve the comprehensive optimization applicable to isolated signal intersections.

Environment Construction of Mixed Connected Automated Vehicle
Signal-Controlled Intersection. Tis paper designs a bidirectional four-lane cross-intersection scene, as shown in Figure 1. Te two types of vehicles in the scenario are CAV and CHV, both of which have network communication capabilities. CAV is a fully autonomous vehicle with intelligent sensing, decision-making, and control capabilities. CAV also can communicate with other vehicles or trafc lights. CHV can communicate with nearby vehicle V2V. Trafc lights at intersections also have network communication capabilities, which can realize V2I communication with vehicles in the scene. In addition, in order to focus on the problem, this paper makes the following assumptions: (1) Before entering the intersection area, vehicles do not change lanes, reverse, turn around, and other behaviors. Only the straight behaviors of vehicles entering the intersection area are considered and follow the principle of frst-come frst reservation. (2) Te efective communication range of V2I is within 400 m of connected trafc lights (central point of intersection). When vehicles enter the efective communication range of signal lights, CAV shall obey the intersection control and CHV will obey the intersection control with a certain probability. Te network communication is set as real-time and reliable communication, without considering the potential network packet loss, delay, and other unreliable network conditions. (3) Vehicles entering the intersection control range can obtain the position, speed, and other state information of surrounding vehicles by V2V and the phase information of connected trafc lights by V2I.

Construction of Vehicle Double-Layer Model Predictive
Control System. Tis paper aims to develop a real-time predictive control system for vehicles to minimize the energy consumption of vehicles in urban trafc systems and improve the efciency of crossing trafc, taking into account the constraints of preceding vehicles and the infuence of trafc lights. Te method is shown in Figure 1. the distance between the controlled vehicle and the vehicle in front; d TL indicates the relative distance to an upcoming signalized intersection. For vehicles on the road, we divide them into afected CAVs and unafected CAVs according to whether they are afected by the preceding vehicle. Te signal-based vehicle trajectory control model described in 3.1.1 is implemented for the CAV that is not afected by the preceding vehicle, and the trajectory control model based on car-following behavior established in Section (1) is implemented for the afected CAV.
(1) Signal-Based Vehicle Trajectory Control Model. In the context of vehicle-road coordination, CAVs can conduct real-time two-way wireless communication with trafc infrastructure (such as trafc lights) and perceive and obtain relevant information about the surrounding environment. If CAVs detect the presence of vehicles in front of them, CAVs should adjust the vehicle trajectory by the vehicle trajectory control model oriented to real-time trafc signal information optimization at this moment, to cross the upcoming signal intersection at the green light time. Te optimal control command of CAVs is calculated based on real-time trafc signal information, and the optimal control strategy is used to minimize the energy consumption when vehicles pass through the signalized intersection. Te objective function of the signal-based vehicle control algorithm is as follows: wherein E(v host,i , a host,i , T m,i ) represents the energy consumption of the vehicle, v target represents the target vehicle speed optimized based on signal phase information, and ε 1,i and ε 2,i are relaxation variables. φ 1 , φ 2 , and φ 3 are weighting factors, respectively. From this, it can be seen that the vehicle control model based on signal consists of four parts to control diferent targets. Te frst goal is to minimize the energy consumption of vehicles passing through the intersection. However, we consider that if only the frst term exists as our objective function, the vehicle will stop at the intersection, because the frst term forces the vehicle to consume as little energy as possible. When the vehicle stops, the vehicle will consume the least energy. Terefore, in order to avoid this phenomenon, we introduced the second term to punish the diference between the vehicle speed and the reference target vehicle speed, so that the vehicle can be as close as possible to the reference target speed to further minimize the energy consumption. Te third item penalizes ε 1 the slack variable to force the vehicle as close to the stop bar as possible, while stopping appropriately within the red interval. Te fourth item is introduced with relaxation variables ε 2 to minimize the derivative of acceleration to ensure driving comfort.
Te speed of the driving vehicle is calculated through constraint (2), where m eq is the total mass of the vehicle, i g is the single transmission ratio, η e is the total mechanical effciency of the transmissions system, r w is the wheel radius, c r is the rolling resistance coefcient, g is the gravity acceleration, θ is the road slope, ρ a is the air density, A f is the front area of the vehicle, and C D is the air resistance coefcient. Constraint (3) obtains the distance from the signal intersection, and the soft constraint (4) is used to avoid active parking away from the signal intersection. Te vehicle speed is limited in constraint (5).Te vehicle acceleration, deceleration, and motor torque are limited by the technical characteristics of the vehicle itself to constrain (7) to (8).
After solving the above optimization problem in each time step, the specifc control strategy of the vehicle can be obtained. Te vehicle is controlled and SUMO simulated by the control strategy. Ten, the above process is repeated for the next controllable vehicle, namely, CAV, to achieve the real-time update of vehicle status at the whole intersection and achieve the goal of minimizing vehicle energy consumption at the intersection by continuously repeating the signal-based vehicle control algorithm.
(2) A Car-Following Oriented Vehicle Trajectory Control Model. If the presence of the vehicle ahead is detected by CAVs, CAVs should follow the vehicle in front of it, while maintaining a safe distance from the vehicle in front and achieving a higher road resource utilization rate. In this case, a car-following oriented vehicle trajectory control model is adopted, which is developed to manage the trafc scene of the previous vehicle within the detection range of the vehicle sensor.
Te objective function of this control algorithm is as follows: In constraint (9), ε 3 is a relaxation variable; D safe refers to the dynamic safety distance between the CAV and the previous vehicle; d min refers to the minimum distance between two vehicles at rest; and τ 1 , τ 2 , and τ 3 are all constant values greater than zero. A car-following oriented vehicle trajectory control model has similar objectives as the previous problem. During vehicle following, the speed of CAV approaching the reference target speed is not constrained, but another relaxation variable ε 3 is introduced, in order to maintain a safe distance between the CAV and the previous vehicle during following. According to constraint (18), we can calculate the relative speed between two cars, and the dynamic safe distance between two vehicles is calculated by constraint (19). Te real-time relative distance model is calculated by constraint (20). Constraint (21) ensures driving safety and includes a soft constraint that pushes the CAV forward to achieve subsequent functions. Once the distance between them is greater than D safe , the relaxation variable ε 3 is increased to make the CAV drive faster.
Considering driving safety and road utilization, the safe distance between the CAV and the previous vehicle is calculated as follows: where CTH represents the time progression of a constant. Instead of using constant time interval (CTH), a customized variable time interval (VTH) strategy is designed in this paper, which not only considers the speed of the CAV but also the relative speed between the CAV and the previous vehicle, which is expressed as follows: where v rel is the relative speed between CAV and the vehicle in front of it; τ 1 , τ 2 , and τ 3 are constants greater than 0. By replacing CTH with VTH in the above expression, the adaptive safe distance can be obtained: (3) Switching Logic Algorithm. Te core functional module consists of two linear model predictive controllers, namely, the signal-based vehicle trajectory control model and the carfollowing behavior-based vehicle trajectory control model. Both controllers calculate the optimal control instruction u at each time step as the input of the CAV. In the context of vehicle-road coordination, the instantaneous output of the CAV can be obtained, including its speed v host , the distance between vehicles d rel , and the relative distance to the nearest signalized intersection d TL , as well as phase and time information of real-time trafc lights, speed of the vehicle ahead v pre , and the speed limit of certain road sections v limits , and these information are fed into the switch logic algorithm to correctly select one of the two vehicle trajectory control models. Te specifc control process is shown in Figure 2.
Te specifc control logic is as follows: Te detected sensor d rel is compared with a limit value d limit .
If d rel is not greater than d limit , then select the vehicle trajectory control model based on car-following behavior to control the CAV to follow the vehicle in front.
If d rel is not less than d limit , then based on a customized variable time interval strategy, a vehicle trajectory control model based on car-following behavior will be selected to maintain a safe, comfortable, and efcient road resource usage distance between vehicles.
Terefore, the vehicle trajectory control of the CAV in diferent driving states can be realized through the switch logic algorithm, thereby achieving the goal of minimizing energy consumption.
(4) Signal Fuzzy Control Algorithm. Set detection points in each lane of the intersection, place detectors, and transmit the detected vehicle data arriving at the intersection to the control system. Te system controls the timing strategy of each phase and then sends these timing data to the signal lights for timing.
Tis paper studies the trafc signal control of a single intersection. Tere are three directions of trafc fow: left turn, straight ahead, and right turn at the four entrances. Te signal timing diagram represents the signal timing scheme. Tis paper adopts the two-phase signal timing diagram, as shown in Figure 3, and the phase sequence of the signal lights is switched according to the phase sequence in the diagram.
Fuzzy control algorithm is an efective way to solve signal timing optimization at signal intersections, so this paper plans to use the fuzzy control algorithm to optimize intersection signals. Among them, this paper refers to the literature [18] and optimizes the idea of the fuzzy control system as follows: the observation module obtains vehicle queuing information and trafc arrival situation according to various detection equipment, calculates the trafc intensity of the current phase and the next phase, and compares the trafc intensity of the two phases Te trafc intensity is input to the decision-making module, and before the green time of the current green-light phase ends, the decision-making module determines the green-light extension time of the current green-light phase.
Terefore, we take the number of queuing vehicles and vehicle arrival rate as the input of the observation module and take the trafc intensity of the evaluated phase as the output of the module.
Te specifc trafc signal control algorithm is as follows: (1) Step 1: Give the phase that is currently allowed to pass the shortest green light time g min . Step 4: After the green light of the current phase is extended (g max − g duration ) and then switched to the next green light phase, go to step 5. (5) Step 5: Switch to the next green light phase after the yellow light lasts for g yellow , and go to step 1.
Among them, g min indicates the minimum green light time; g max indicates the maximum green light time; g duration indicates the current phase to last the green light time; and g yellow indicates the yellow light time. Its unit is second (s).
Te structure of the fuzzy control system in this paper is shown in Figure 4. Te fuzzy control system includes an observation module and a decision module. Te observation module evaluates the trafc intensity of the current phase and the next phase. Te decision module determines the green light extension time of the current green light phase according to the current green light phase trafc intensity and the next green light phase trafc intensity.   Table 1 for the fuzzy rules. (2) Decision-making module Te decision-making module determines the green light extension time of the current green light phase according to the current phase trafc intensity and the next phase trafc intensity. Tis module has two input variables, which are the current phase trafc intensity and the next phase trafc intensity, and the output variable is the current green light phase extension time. Te fuzzy subset division of the current phase trafc intensity and the next phase trafc intensity is the same as before. Te extended time domain is [0, 30], divided into 5 fuzzy subsets: {very short, short, medium, long, very long}, abbreviated as {NS, S, M, L, PL}; see Table 2 for the fuzzy rules.
(3) Fuzzy reasoning and reconciliation fuzzifcation Fuzzy reasoning is based on the input fuzzy number, controlled by fuzzy rules to complete fuzzy reasoning to solve fuzzy relational equations. Te fuzzy control system designed in this paper adopts the product inference method and center of gravity method to defuzzify. Te exact calculation method of the center of gravity method is shown in the following formula: In the formula, u * is the precise output of the decision result; u i is the central value of the consequent membership function of the i-th fuzzy rule triggered; μ i is the product of the membership degrees of all input variables of the i-th rule being triggered; and I is the number of triggered fuzzy rules.
(5) Energy Consumption Model. Te energy consumption model of a vehicle is usually related to speed or acceleration. And when we control the vehicle, we mainly control the speed and acceleration of the vehicle. Terefore, we choose an energy consumption model related to speed and acceleration to calculate the total energy consumption of vehicles at the intersection. Tis paper plans to adopt the instantaneous gasoline consumption function proposed by Akcelik (1989) because it takes acceleration and velocity into account. Te gasoline consumption rate is calculated based on the instantaneous speed and acceleration of the vehicle.
Te specifc model is as follows: where α is the constant idle gasoline consumption rate (mL/s), β 1 is an efciency parameter related to engine effciency (mL/KJ), β 2 is the positive acceleration (mL/KJ • m/s 2 ) related to gasoline consumption parameters, v is the vehicle speed, and a is the vehicle acceleration. P represents the total power of the vehicle running (KW), (mL/KJ) is the rolling resistance, d 2 is the engine drag coefcient, and d 3 is the air drag coefcient.
Referring to Akcelik (1989) for parameter values,    randomness of the vehicle tracking model we choose, the vehicle's motion trajectory will be diferent in diferent operations. Terefore, the following model can better solve the uncertain behavior of manual driving vehicles and refect the diference of driving behavior of manual driving vehicles [19]. See Table 3 for the meaning of parameters in the above formula.

Evaluation
In order to verify the efectiveness and reliability of the proposed model and system, this paper uses Python to conduct the secondary development of SUMO simulation platform and build a simulation environment. Te built test scenario is shown in Figure 6, and the setting parameters are shown in Table 4.
In the process of simulation, we fully considered the infuence of the driving style of the network connected driving vehicles on the simulation efect and divided it into conservative network connected manual driving vehicles, stable network connected manual driving vehicles, and aggressive network connected manual driving vehicles. Since our control scheme is aimed at CAVs, in order to prove the inclusiveness and efectiveness of our two-layer control model under diferent CAV permeabilities and diferent vehicle fows, we used Python to carry out the secondary development of SUMO, output relevant result data, and compare SUMO self-control condition, controlling vehicle tracks, and two-layer model control. Tat is, the trafc effciency and energy consumption of intersections under the three schemes of vehicle trajectory control and signal joint control. Te average waiting time and average energy consumption of vehicles are selected as the evaluation and comparison indicators [20].

Comparative Analysis of Vehicle Energy Consumption
at Intersections. Figure 7 shows the comparison of the average vehicle energy consumption of diferent schemes under diferent CAV permeabilities. Te pros and cons of intersection energy consumption control under diferent control schemes are shown in Figure 7. Compared with the schemes with fx signal timing control and only control   vehicle trajectory, the joint control of vehicle trajectory and signal has a signifcant advantage. As can be depicted from Table 5, when the permeability reaches 10%, the energy consumption saved by the joint control of vehicle trajectory and signal is −5.37% higher than that of controlling vehicle trajectory and 7.90% higher than that of no control scheme at all. At this time, due to the small amount of CAV in the road, the joint control strategy has no obvious efect on reducing the average energy consumption of the vehicle due to the infuence of the randomness of the artifcial vehicle driving. When the penetration rate reaches 60%, the energy consumption saved by the combined control of vehicle trajectory and signal is increased by 21.94% compared with only the control of vehicle trajectory and by 17.56% compared with the scheme of no control at all. At this time, CAVs in the road account for a large proportion. Trough the control and guidance of the trajectory of CAVs, the movement trajectory of other CHVs is restricted, which avoids the phenomenon of large-scale queuing and start-stop of vehicles and thus signifcantly reduces the average energy consumption of vehicles at the intersection.
By analyzing the overall trend of the joint control scheme of vehicle trajectory and signal, it can be concluded that under this scheme, when the CAV penetration rate is between 0% and 30%, the efect of this control scheme on improving the overall energy consumption at the intersection is not very obvious. With the gradual increase of CAV permeability, the   scheme achieved a signifcant improvement in the overall energy consumption at the intersection when the CAV permeability reached 30%-60%. After that, with the increase of CAV market penetration, the signifcance of improvement showed an insignifcant or even slightly increasing trend. Tat is, with the increase of CAV penetration, the average energy consumption of vehicles at intersections under this control scheme did not change much. It is concluded that the control model proposed in this paper can better adapt to intersections with low and medium CAV. Trough a more detailed analysis of the simulation results, it can be concluded that when the permeability of CAV reaches 70%, the average energy consumption of vehicles at the intersection presents a slightly increasing trend. In order to better analyze the causes of this phenomenon, the average energy consumption diagram of CAV and CHVs under diferent CAV permeabilities under the joint control strategy of vehicle trajectory and signal was analyzed, as shown in Figure 8. It can be concluded that the reason for the slight increase in the average vehicle energy consumption at this time may be that the average vehicle energy consumption of CHVs at this time shows a trend of increasing compared with that before. Under this scenario, some CHVs may have more start-stop phenomena, resulting in the increase in the average vehicle energy consumption. Under the infuence of CHV, some CAVs also show more start-stop phenomena. Tus, in this case, the average energy consumption of all vehicles presents a higher phenomenon than before. schemes shows a downward trend, which shows that our control strategy for CAV is efective. Te greater the permeability of CAV, the greater the implementation of our control plan and the more comprehensive the control of intersections.

Comparative
In addition, the average waiting time of vehicles under the joint control of signal and vehicles is signifcantly lower than the average waiting time of vehicles under the out of control and only control of the vehicle. Table 6 shows the decrease percentage of vehicle waiting time at intersections under the vehicle control scheme and the double-layer control model. It can be clearly seen that our control scheme has the best optimization efect under the conditions of medium and low permeability; with a decrease percentage of about 25%, the average waiting time of vehicles decreases greatly. With the increase of the penetration rate, the decreasing range gradually decreases. Tis situation is mainly caused by the following two reasons. On the one hand, it shows the uncontrollability of the manual driving of the Internet connected vehicles. According to the user equilibrium principle, all travelers look for the travel path that minimizes their travel time for their own interests, but the driving scheme determined by themselves is not necessarily the optimal scheme, and its driving track will also afect the efciency of the whole intersection. On the other hand, it also shows that our two-layer control scheme is more suitable for the conditions where the vehicle penetration rate is at a moderate level, that is, under the conditions of mixed trafc fow, and it is highly consistent with our research background.

Index Comparison of Various Schemes under Diferent
Trafc Volumes. In order to explore the trafc fow conditions that our two-level control model can adapt to, we compared and analyzed the operating results of each scheme under diferent trafc fows.

Comparative Analysis of Vehicle Energy Consumption at
Intersections. It can be seen from Figure 10 that with the increase of trafc fow, trafc fow gradually transitions from free fow state to steady fow state, and the energy consumption of vehicles shows an upward trend. However, for the vehicle energy consumption under out-of-control scheme,  since the vehicle is not controlled, the energy consumption under diferent trafc fows has been high, and with the increase of the trafc fow, the increase of energy consumption is not obvious. In contrast, the control of vehicle scheme and the control scheme of the double-layer model have a signifcant efect on the reduction of the average energy consumption of the vehicle, especially compared with the fxed signal timing scheme, the average energy consumption of the whole vehicle is reduced by about 32%. Tis demonstrates the efectiveness of our control scheme. Our proposed two-layer control scheme, with the increase of trafc fow, the average energy consumption of vehicles has no obvious upward trend and has always been at a low level, which also shows that our model has good stability and adaptability. Te control efect is better at low and medium levels of trafc fow.

Comparative Analysis of Average Waiting Time of
Vehicles at Intersections. It can be seen from Figure 11 that with the increase of trafc fow, the average waiting time of the three modes of out of control, control of vehicle, and signal and vehicle joint control all gradually increases. Under any level of trafc fow, vehicle trajectory control and joint control of vehicles trajectory and signal have optimization efects on the average waiting time. Among them, the signal and vehicle joint control mode has the best optimization efect on the average waiting time, and only control vehicle optimization had the second best efect on average waiting time. Let us take the fow rate of 1200 veh/h as an example. When no control is performed, the average waiting time is 10 s. When only vehicle control is performed, the average waiting time is 8.13 s, which is about 18.7% lower. Te average waiting time of signal and vehicle joint control is 6.54 s, which is about 34.6% lower, and the optimization ability of the signal and vehicle joint control in the entire trafc fow range is almost unchanged. Te control ability of controlling the vehicle in the middle and low trafc fow interval is almost unchanged, and the optimization ability in the high trafc fow interval is relatively enhanced. To sum up, our combined signal and vehicle control method can signifcantly reduce the average waiting time and improve the trafc capacity and trafc efciency of the intersection.

Conclusion
To sum up, the two-layer model optimization system proposed in this paper, namely, the model of signal and vehicle joint control, has achieved good results in achieving the binocular goals of minimizing vehicle energy consumption and maximizing trafc efciency at intersections. Experimental simulation data show that the two-layer control model in this paper has good applicability when CAV permeability is 30%-60%, which greatly reduces the average energy consumption and average waiting time of vehicles. Compared with the no-control scheme, the average waiting time of vehicles decreases by about 25%. Under the condition of 60% permeability, the average energy consumption of the vehicle was reduced by 17.56% compared with the uncontrolled scheme and 21.94% compared with the control scheme. For the average energy consumption of vehicles, when the CAV permeability is between 0% and 30%, the scheme has a general improvement efect on the average energy consumption of vehicles. When the permeability is more than 60%, the improvement efect of the scheme has little change with the increase of the permeability, but the average energy consumption of the vehicle is signifcantly improved. For the average waiting time, under diferent permeability conditions, the average waiting time of the joint control scheme of vehicle trajectory and signal shows a downward trend, and the optimization efect is signifcant. Especially, when the CAV permeability is between 0% and 50%, the average waiting time of the vehicle decreases by about 25%, which is a large decrease.
In addition, the two-layer model optimization system in this paper has good applicability when the trafc fow is at a moderate level. Te application of the two-layer model optimization system was able to signifcantly reduce the average vehicle energy consumption and the average vehicle waiting time by nearly 35 percent. Te two-layer control model proposed in this paper provides a benefcial reference scheme for the optimization of temporal and spatial resources at intersections with mixed trafc fow. At the same time, it efectively reduces the vehicle energy consumption at intersections and improves the trafc efciency at intersections, which has strong practical signifcance and application value.

Data Availability
All data used to support the fndings of this study are included within the article.

Conflicts of Interest
Te authors declare that they have no conficts of interest.