# Multilane Spatiotemporal Trajectory Optimization Method (MSTTOM) for Connected Vehicles

Authors: Pangwei Wang; Yunfeng Wang; Hui Deng; Mingfang Zhang; Juan Zhang
Journal: Journal of Advanced Transportation
 (2020)

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## Abstract

It is agreed that connected vehicle technologies have broad implications to traffic management systems. In order to alleviate urban congestion and improve road capacity, this paper proposes a multilane spatiotemporal trajectory optimization method (MSTTOM) to reach full potential of connected vehicles by considering vehicular safety, traffic capacity, fuel efficiency, and driver comfort. In this MSTTOM, the dynamic characteristics of connected vehicles, the vehicular state vector, the optimized objective function, and the constraints are formulated. The method for solving the trajectory problem is optimized based on Pontryagin’s maximum principle and reinforcement learning (RL). A typical scenario of intersection with a one-way 4-lane section is measured, and the data within 24 hours are collected for tests. The results demonstrate that the proposed method can optimize the traffic flow by enhancing vehicle fuel efficiency by 32% and reducing pollutants emissions by 17% compared with the advanced glidepath prototype application (GPPA) scheme.


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## Body

## 1. Introduction

The traffic capacity of urban road network is restricted by the time delay, potential safety hazards, and environmental pollution caused by traffic congestion. According to the US Department of Transportation Statistics issued in 2019, 27% of highways in the United States are blocked at the peak of urban traffic and 54% of vehicles are in the state of congestion [1]. Intersections, as important nodes of urban road network, cause 80% of these urban traffic congestions [2]. Therefore, alleviating urban traffic congestion by taking the intersection as the optimization object is a challenging work.The realization of spatiotemporal trajectory optimization mainly includes two parts: (1) realizing the dynamic speed control of multiple vehicles in the longitudinal direction; (2) achieving the cooperative lane-changing control of multiple vehicles in the horizontal direction. In the intelligent traffic system (ITS) strategic plan published by the US Department of Transportation in 2010, dynamic speed coordination based on spatiotemporal trajectory was denoted as one of the important methods for traffic flow optimization of road network [3]. Grumert and Tapani [4] established a variable speed limit (VSL) algorithm based on the traffic occupancy. The results show that VSL can increase traffic flow by 16%. Jo et al. [5] updated a VSL algorithm by detecting vehicles at multiple stations from the perspective of road safety, which solved the guidance delay problem. With the development of cooperative vehicle infrastructure system (CVIS) and connected vehicles (CVs), the problem of discontinuous dynamic speed limit can be solved by continuous dynamic speed control [6]. Considering the random traffic conditions, Zhu and Ukkusuri [7] proposed a method to realize dynamic speed limit control through RL. In this method, a link based dynamic network load model was established in the environment of CVs, which can reduce the total travel time by 18%. Aldana-Muñoz et al. [8] proposed a method by combining environmental driving and speed guidance to optimize the continuous linear spatiotemporal trajectory. The experimental results show that the linear spatiotemporal trajectory optimization can stabilize the change of disturbance on traffic flow. Wang et al. [9] proposed a speed guidance model based on model predictive control (MPC), by which the spatiotemporal trajectory can be constructed in advance. Wei et al. [10] proposed a cooperative optimization method for multivehicle spatiotemporal trajectories, which is established based on the simplified Newell linear car-following model. Considering different road environments and weather conditions, De Mello and Chiodi [11] proposed a fuzzy logic control model of spatiotemporal trajectory, which increases the effectiveness of decision-making process by 13%. Liang et al. [12] presented a method to optimize the common spatiotemporal trajectories for both autonomous vehicles and manual driving vehicles. With the proportion of autonomous vehicles increasing, average delay time is reduced by 25% and average stopping time is reduced by 47%. Wang et al. [13, 14] designed a joint control model for CVs and traffic signal, which aims to optimize vehicular platoon and signal timing to improve traffic efficiency at intersections. The simulation results show that the joint control model can reduce the stopping time by 54%. Mirheli et al. [15] proposed a distributed cooperative control logic based on spatiotemporal trajectory, which can be applied to unsignalized intersections. In this study, vehicles with this logic application scheme can pass through the unsignalized intersection in optimal trajectories without collision. Wang et al. [16] developed a cooperative optimization method of spatiotemporal trajectory with multiple intersection phases. In this method, a lower bound estimator based on dynamic load network was constructed to improve robustness and stability of vehicle dynamic network.Urban roads or expressways with single lane or dual lane were mainly taken in the above studies; however, the multilane spatiotemporal trajectory optimization is still lacked in the research. The main challenge of vehicles in the multilane spatiotemporal trajectory lies in how to solve its complex lane-changing problem. Moreover, accidents caused by lane-changing behaviors make the multiple lanes occupied, which makes the road congestion more serious [17]. Considering the risk of lane-changing produced by vehicle-to-vehicle (V2V) communication delay, Hongil and Jae-Il [18] proposed an oriented bounding box (OBB) method which reduces communication delay by defining the lateral and longitudinal gradient controllers. Li et al. [19] proposed a new lane-changing model based on CVs to evaluate the critical vehicle distance in lane-changing process. The safety potential field theory was integrated, and the vehicle movement state under different speed and acceleration conditions is dynamically presented. Finally, the lane-changing route can be determined through the selection of spatiotemporal trajectory. The majority of studies provide ideas and theoretical support for multivehicle cooperative lane-changing based on spatiotemporal trajectory. However, due to the massive amount of data calculation and high system complexity in multilane spatiotemporal trajectories, the common multilane road section traffic efficiency problem has not been effectively solved and improved through the optimization of multiple single lanes method.To solve the above problems, MSTTOM for connected vehicles is established in this paper. The spatial temporal trajectories are generated and combined with vehicular current state information and the signal timing information. In addition, during the driving process, the trajectories can be optimized by RL. Moreover, the vehicle can change the lane and update its trajectory through the cooperative lane-changing strategy designed in this model. The significant contribution of this research is that vehicles can pass through intersections in optimal spatiotemporal trajectory and further solve the congestion problem in current multilane road section.The rest of this paper is organized as follows: The typical application scenario and the structure of the method are introduced in Section2. The specific content of MSTTOM is described in Section 3, where the trajectory is generated and optimized. The simulation experiment results through SUMO/Python are presented and analyzed in Section 4, and the stability of headway, fuel consumption rate, pollutant emission, and calculation time are also selected as the evaluation indexes. Finally, Section 5 concludes the paper.


## 2. Typical Application Scenario for Connected Vehicles

### 2.1. Application Scenario

The upstream section of the intersection, as the application of multilane scenario, is covered by vehicle-to-everything (V2X) wireless communication and shown in Figure1. The vehicular trajectory from upstream to intersection process will be dynamically calculated based on MSTTOM.Figure 1
The scenario of multilane section based on connected vehicles.


### 2.2. System Structure

The flow chart of MSTTOM is shown in Figure2. The procedure can be described as follows: the traffic signal and vehicular driving information is collected firstly by road-side unit (RSU) and on-board unit (OBU), so that the target lane and arrival time at current intersection can be calculated; secondly, the optimal trajectory is generated through connected vehicular state and constraints, where traffic capacity of current intersection can be optimized online through the cooperative lane-changing strategy; and finally, every connected vehicle can pass through the intersection with least travel time through the optimization result of RL. The spatiotemporal trajectory and the optimized state are clarified in Figure 3.Figure 2
The flow chart of spatiotemporal trajectory optimization process for connected vehicles.Figure 3
The spatiotemporal trajectory with and without optimization.


## 2.1. Application Scenario

The upstream section of the intersection, as the application of multilane scenario, is covered by vehicle-to-everything (V2X) wireless communication and shown in Figure1. The vehicular trajectory from upstream to intersection process will be dynamically calculated based on MSTTOM.Figure 1
The scenario of multilane section based on connected vehicles.


## 2.2. System Structure

The flow chart of MSTTOM is shown in Figure2. The procedure can be described as follows: the traffic signal and vehicular driving information is collected firstly by road-side unit (RSU) and on-board unit (OBU), so that the target lane and arrival time at current intersection can be calculated; secondly, the optimal trajectory is generated through connected vehicular state and constraints, where traffic capacity of current intersection can be optimized online through the cooperative lane-changing strategy; and finally, every connected vehicle can pass through the intersection with least travel time through the optimization result of RL. The spatiotemporal trajectory and the optimized state are clarified in Figure 3.Figure 2
The flow chart of spatiotemporal trajectory optimization process for connected vehicles.Figure 3
The spatiotemporal trajectory with and without optimization.


## 3. Multilane Spatiotemporal Trajectory Optimization Method (MSTTOM)

Firstly, state vectors defined in this paper contain the information of vehicular driving, such as position, speed, and acceleration, and the information of traffic signal timing. Secondly, the cost function and constraints of vehicular trajectory are formulated. Finally, the optimal vehicular trajectory is dynamically calculated through maximum principle and RL.


### 3.1. State Vector

In the typical scenario of urban intersection, we define the vehicle entering the road section asCmn, where m and n represent the m-th lane of the road section from the right side to the left side (the target vehicle is selected as the reference) and the n-th vehicle from the downstream to the upstream, respectively. Therefore, we define the state vector of vehicle Cmn as xmn (t):(1)xmnt=xmnt,ymnt,vmnt,vmn′tT,where (xmn (t), ymn (t)) is the position of vehicle Cmn at time t, vmn (t) is the driving speed of vehicle Cmn at time t, and v′mn (t) is the lateral speed of vehicle Cmn at time t.The method input is the vehicle accelerationumn (t), which can be expressed as follows:(2)umnt=umnt,umn′tT,where umn (t) is the longitudinal acceleration of vehicle Cmn at time t and u′mn (t) is the current lateral acceleration of vehicle Cmn at time t.Meanwhile, the signal timing information of vehicle target laneφmnt and the traffic flow information Im−1 and Im−1 (t) of adjacent lanes m+1 and m−1 are defined as(3)φmnt=φmnt,tφmnt,Rm,Gm,Im+1t=km+1t,Im−1t=v¯m+1t,km−1t,where φmnt is the target phase state of vehicle Cmn, tφmnt is the remaining time of phase φmnt, Rm is the red light duration of lane m, Gm is the green light duration of lane m, v¯m+1t and v¯m−1t stand for the average traffic flow velocity of left lane m+1 and right lane m-1, and km+1 and km−1 are the average traffic flow density of left lane m+1 and right lane m−1. The average traffic flow speed v¯mt and average traffic flow density km (t) can be expressed as(4)v¯mt=∑N=NmminNmmaxmNNmmax−Nmmin+1,kmt=Nmmax−Nmmin+1L,where N is the total number of vehicles, Nmmax is the maximum number of vehicles in lane m, Nmmin is the minimum number of vehicles in lane m, and L is the length of road section.The system state equation is described as(5)x˙mnt=fxmnt,umnt,φmnt,Im+1t,Im−1t.


### 3.2. Cost Function

In order to ensure that the vehicle can accurately follow the designed trajectory of the system, fixed and variable costs in the process from upstream to downstream are considered and formulated, which can be represented by(6)J=gxmntmnout+∫tmn0tmnouthxmnt,umntdt,where tmnout is the time when vehicle Cmn leaves the road section, tmn0 is the time when the vehicle Cmn enters the road section, gxmntmnout is the fixed cost of the process, and ∫tmn0tmnouthxmnt,umntdt is the variable cost of the process. The fixed cost includes the cost of fixed items (such as the driving distance and expected speed at the intersection) and the travel time of the road section. The process can be described as (7)gxmntmnout=w1tmnout−t¯mnout2+w2xmntmnout−L2+w3vmntmnout−v¯mnout2+w4ymntmnout−dt¯mnoutm¯−122,where t¯mnout is the target time of vehicle Cmn driving out of the road section, v¯mnout is the expected speed of vehicle Cmn at the intersection, m¯ is the target lane of vehicle, and d is the lane width. w1,w2,w3,w4 are the weights of the travel time of the road section, driving length of the road section, expected speed at the intersection, and the target lane at the intersection, respectively. w1,w2,w3,w4 ∈R+.Variable cost involves acceleration and deceleration of the vehicle driving in longitudinal and lateral lanes. Its function can be expressed as(8)hxmnt,umnt=w5umnt2+2umntvmntχumnt+w6umn′t2+2umn′tvmn′t,where w5 and w6 are the weights of energy changes caused by longitudinal and lateral acceleration of the vehicle, receptively. w5, w6 ∈R+. χumnt is the Heaviside function of longitudinal acceleration of networked vehicles and can be used to separate the variable cost induced by acceleration in longitudinal deceleration process:(9)χumnt=0,umnt≤0,1,umnt>0.t¯mnfree denotes the time of vehicles passing through the intersection under the condition of low-density traffic flow, also known as the time for vehicles Cmn leaving the road without restriction. The time consists of four parts: initial time tmn0, time tmnacc at acceleration state, time tmnc.s. at constant speed state, and time tmndec at deceleration state, which can be described as follows:(10)t¯mnfree=tmn0+tmnacc+tmnc.s.+tmndec,where tmnacc, tmnc.s., and tmndec can be expressed as(11)tmnacc=v0lim−vmntmn0umn+max,tmnc.s.=L−v0lim2−vmntmn02/2umn+max−v0lim2−vmlim2/2umn−maxv0lim,tmndec=v0lim−vmlimumn−max,where v0lim is the speed limit of the road section, vmlim is the speed limit at the downstream exit of the lane m, umn+max is the maximum acceleration of vehicle Cmn, and umn−max is the maximum deceleration of vehicle Cmn.However, it is impossible for the urban road section to maintain a low-density state. Therefore, connected vehicles have to pass through current intersection as a temporary platoon. The candidate timet¯mntemp of vehicle Cmn can be calculated as (12)t¯mntemp=maxt¯mn−1out+tmh2h,t¯mnfree,where tmh2h is the minimum headway between two adjacent vehicles in lane m at the downstream exit of the section.In order to improve the traffic capacity of intersections, the target timet¯mnout of vehicle Cmn at current intersection is controlled within the passable green signal, which can be selected according to (13)t¯mnout,=t¯mntemp,t¯mntemp∈ξm,floort¯mntempRm+GmRm+Gm+Rm,t¯mntemp,∉ξm,where ξm is the set of green light periods of lane m, and floor (t) is the function of rounding down.The expected speed of vehicles is defined as the speed limit at the downstream exit to ensure the maximum efficiency of vehicles and can be described as(14)v¯mnout=vmlim.In conclusion, the cost function can be integrated as(15)J=w1tmnout−t¯mnout2+w2xmntmnout−L2+w3vmntmnout−v¯mnout2+w4ymntmnout−dm¯−122+∫tmn0tmnoutw5umnt2+2umntvmntχumnt+w6umn′t2+2umn′tvmn′tdt.


### 3.3. Constraints

In order to minimize the above cost functionJ, seven constraints, namely, initial vehicular state, vehicle spacing, speed, acceleration, jerk, signal timing, and wireless communication, should be satisfied in the optimization problem.


#### 3.3.1. Initial Vehicular State

Suppose that a connected vehicleCmn enters the road section with detectors; when n ≥nmax, the counter will reset. The initial state of vehicle Cmn is defined as (16)xmntmn0=xmntmn0ymntmn0vmntmn0vmn'tmn0=0dm−12vmn0vmn0'.


#### 3.3.2. Vehicle Spacing

The vehicle will inevitably be in the vehicle-following state in the driving process. Therefore, vehicleCmn on the lane m and the front vehicle Cm (n-1) should ensure a certain displacement in space and time. The safety constraint can be formulated as (17)xmnt+τmn≤xmn−1t−dmn,where τmn is the time displacement of vehicle Cmn and the front vehicle Cm (n-1), and dmn is the spatial displacement of vehicle Cmn and the front vehicle Cm (n-1).


#### 3.3.3. Speed

In order to ensure the safety of the vehicles in the road section, the speed constraint is applied to them. The longitudinal speed constraint embraces the speed information involving speed limit within the section and the minimum speed 0. Thus, we have(18)0≤vmnt≤v0lim.For the lateral speed constraint, the vehicle deflection angle is mainly constrained by vehicle dynamics, which can be expressed as(19)α−max≤αmnt≤αmax,where αmax is the maximum angle through which the front wheel of the vehicle can turn to the left, αmn (t) represents the steering angle of the front wheel of the current vehicle, and αmax represents the maximum angle through which the front wheel of the vehicle can turn to the right.Therefore, the lateral restraint condition of the vehicle is shown as(20)v0limα−max≤vmn′t≤v0limαmax.


#### 3.3.4. Acceleration

In order to guarantee that the engine can provide enough power and the brake pads can provide the vehicle enough power limit, the acceleration or deceleration of the vehicle should be specified as a constraint. The acceleration constraints can be expressed as(21)u−max≤umnt≤umax,u−max′≤umn′t≤umax′,where umax is the acceleration of the maximum longitudinal braking deceleration of the vehicle, umax is the acceleration of the maximum longitudinal acceleration of the vehicle, u′max is the maximum transverse acceleration of the vehicle to the left, and u′max is the maximum acceleration of the vehicle to the right.


#### 3.3.5. Jerk

The jerk constraint is the change rate constraint of vehicle acceleration, also known as the impact constraint or comfort constraint. The purpose of jerk constraint is to eliminate the negative impact of the acceleration change in the driving process. The jerk constraint is shown as(22)j−max≤∂umnt∂t≤jmax,j−max′≤∂umn′t∂t≤jmax′,where jmax represents the maximum longitudinal backward jerk, jmax represents the maximum longitudinal forward jerk, j′max represents the maximum lateral left acceleration, and j′max represents the maximum lateral right acceleration.


#### 3.3.6. Signal Timing

The signal timing constraint of vehicles can ensure that vehicles avoid violations when passing through the intersection, which can be represented as(23)vmntmnout=0,tmnout∉ξm.


#### 3.3.7. Wireless Communication

V2X is a communication system through which a vehicle communicates with any entity that may affect the vehicle. Thus, the essence of V2X technology is wireless communication technology. In the practical application of wireless communication technology, time delay and packet loss are inevitable, which may affect the stability and security of networked vehicles in the system. The relevant parameters of wireless communication are constrained as follows:(24)τ˜mnt<0.1,Plp|mnt<15%,where τ˜mnt and Plp|mnt represent the time delay and the packet loss probability of the vehicle Cmn at time t.


### 3.4. Solution Method Based on Maximum Principle

MSTTOM is solved by Pontryagin’s maximum principle, and the Hamilton function of the problem is established as(25)Hx,u,λ,t=λTfx,u,t+hx,u,t,where λ is defined as the costate vector of vector x, which represents the additional cost of the change of J caused by the small change ∂x of vector x.In the admissible setU, the minimum input u∗ of the cost must satisfy the minimum state of the Hamilton function, which can be expressed as follows:(26)Hx∗,u∗,λ∗,t≤Hx∗,u,λ∗,t,∀u∈U,t∈tmn0,tmnout,∂H∂u=0,∂H∂x=−λ˙,∂H∂λ=x˙.Therefore, the Hamilton function of MSTTOM is shown as(27)Hmn=λ1vmnt+λ2umnt+w5umnt2+2umntvmntχumnt,where the variation of the lateral movement trajectory is optimized in the process of vehicular cooperative lane-changing.In the process of solving the problem, the state vectorλ should meet the condition of the fixed cost, which is shown as (28)λtmnout=∂gxmntmnout∂xmn⇒λ1tmnout=2w2xmntmnout−Lλ2tmnout=2w3vmntmnout−v¯mnout.


### 3.5. Cooperative Lane-Changing Optimization

In order to accurately describe the process of cooperative lane-changing strategy, the request of the vehicular lane-changing is displayed in Figure4. The vehicle Cmn, selected as the subject vehicle, is a red one in the middle of lane m and ready to change lanes from the current lane m to the target lane m+1. Besides, yellow vehicles are defined as the primary threat vehicles of Cmn, orange vehicles are defined as the secondary threat vehicles of Cmn, and blue vehicles are defined as the non-threat vehicles of Cmn.Figure 4
Schematic chart of lane-changing environment for vehiclesCmn.If target lane is not the adjacent lane, it can be decomposed into multiple lane-changing processes. The optimal trajectory is loaded into the traffic environment, and the potential lane-changing conflict safety inspection can be carried out. The flow chart of lane-changing safety inspection is shown in Figure5.Figure 5
The flow chart of lane-changing safety inspection.If two adjacent vehicles receive the same requests concurrently, there is a priority for the vehicle with a higher speed. If adjacent vehicles based on daily driving habits have similar speed, there is a priority for the vehicle in the left lane.Different traffic saturation should be satisfied in the cooperative lane-changing strategy. The higher the saturation involved in the case is, the higher the complexity of the lane-changing strategy will be supposed. Therefore, the case of higher saturation is discussed as follows:(i)
The subject vehicleCmn initiates a lane-changing request to the target vehicle Cm+1n after the target gap selected.(ii)
The target vehicleCm+1n and its rear vehicle Cm+1n+1 adjust their speeds to confirm a safe gap for vehicle Cmn.(iii)
VehicleCmn drives into the target lane m+1.(iv)
The spatiotemporal trajectories of vehicles in the original lane and target lane are updated, which is shown in Figure6.Figure 6
Vehicular spatiotemporal trajectories in lane-changing process.
(a)(b)


### 3.6. Trajectory Optimization Based on RL

In order to improve the efficiency of MSTTOM, this paper designs an optimization algorithm based on the RL paradigm, which can quickly match the optimal trajectory. The optimization algorithm is formulated with the current position and speed of vehicles. The target lane and time period are modeled as inputs, and the sets of vehicle acceleration are formulated as outputs. When the lane-changing request is initiated, the vehicle can be connected to the trajectory of the cooperative lane-changing strategy through the RL matching network. Once the lane-changing is completed, the spatiotemporal trajectory will be matched by the RL to achieve the multilane trajectory optimization.The state vector of MSTTOM satisfies Markov property; that is, the next statest+1 of the system is only related to the current state st, but not directly related to the preceding state. Thus, the state vector can be shown as follows:(29)st=xmnt,φmnt,Im+1t,Im−1t,Pst+1|st=Pst+1|s1,s2,s3,…,st,where P is the probability matrix of transition between state.Through integration, the set of action vectors will be presented in the form of trajectory data. The action vectorat at current state st is shown as (30)at=umnt.Five tuples (S, A, P, R, γ) are defined to describe the process of MSTTOM. Among them, S is the state set, which includes the current state of vehicles and the traffic flow state in the road section; A is the set of executing actions, that is, the set of lateral and longitudinal acceleration output by optimization; R is the reward function of the process, which is negatively linear with the cost function J; and γ is the discount factor when calculating the value function. For a fixed policy π, the value function vπs can be calculated as (31)vπs=Eπ∑k=0∞γkRt+k+1|St=s.An action value functionqπs,a can be calculated by defining the value of each action a, which is described as (32)qπs,a=Eπ∑k=0∞γkRt+k+1|St=s,At=a.Bellman optimal recursive equations of the optimal state value functionv∗s and the optimal action value function q∗s can be calculated by introducing Markov property into (31) and (32), which can be shown as follows:(33)v∗s=maxaRsa+γ∑s′∈Spss′av∗s′,qπs,a=Rsa+γ∑s′∈Spss′amaxaq∗s′,a′,where s′ and a′ are the state and action of the next moment, respectively.The optimal strategy derived by maximizing the above functions can be represented as(34)π∗a|s=1,ifa=argmaxa∈Aq∗s,a,0,else..The function can be calculated by Q-learning algorithm, and the algorithm process is shown in Algorithm1.Algorithm 1:Q-learning algorithm.
Q-learning algorithm(1)
Initializeq (s, a);(2)
While (st=sT)(3)
{Select the initial states0 and action a0 according to the ε-greedy strategy;(4)
While (st=sT)(5)
{Select the actionat the state st according to the ε-greedy strategy, get reward rt and the next state st+1;(6)
qst,at←qst,at+art+1+γmaxaqst+1,a−qst,at;(7)
st=st+1; } }(8)
Get the optimal strategyπs=argmaxaqs,aIn Algorithm1, sT is the termination state in the fifth row. The current value function of the subsequent state estimation is used to update the optimal action function in the seventh row. In order to enhance the diversity of the exploration ability of the algorithm, the specific formula is shown as(35)πa|s=1−ε+εNa,a=argmaxaqs,a,εNa,a≠argmaxaqs,a,where N (a) is the total number of actions, ε-greedy is the optimal action strategy taken based on 1-ε probability, and random action is the policy of ensuring the possibility of being selected for each action according to the probability of ε.


## 3.1. State Vector

In the typical scenario of urban intersection, we define the vehicle entering the road section asCmn, where m and n represent the m-th lane of the road section from the right side to the left side (the target vehicle is selected as the reference) and the n-th vehicle from the downstream to the upstream, respectively. Therefore, we define the state vector of vehicle Cmn as xmn (t):(1)xmnt=xmnt,ymnt,vmnt,vmn′tT,where (xmn (t), ymn (t)) is the position of vehicle Cmn at time t, vmn (t) is the driving speed of vehicle Cmn at time t, and v′mn (t) is the lateral speed of vehicle Cmn at time t.The method input is the vehicle accelerationumn (t), which can be expressed as follows:(2)umnt=umnt,umn′tT,where umn (t) is the longitudinal acceleration of vehicle Cmn at time t and u′mn (t) is the current lateral acceleration of vehicle Cmn at time t.Meanwhile, the signal timing information of vehicle target laneφmnt and the traffic flow information Im−1 and Im−1 (t) of adjacent lanes m+1 and m−1 are defined as(3)φmnt=φmnt,tφmnt,Rm,Gm,Im+1t=km+1t,Im−1t=v¯m+1t,km−1t,where φmnt is the target phase state of vehicle Cmn, tφmnt is the remaining time of phase φmnt, Rm is the red light duration of lane m, Gm is the green light duration of lane m, v¯m+1t and v¯m−1t stand for the average traffic flow velocity of left lane m+1 and right lane m-1, and km+1 and km−1 are the average traffic flow density of left lane m+1 and right lane m−1. The average traffic flow speed v¯mt and average traffic flow density km (t) can be expressed as(4)v¯mt=∑N=NmminNmmaxmNNmmax−Nmmin+1,kmt=Nmmax−Nmmin+1L,where N is the total number of vehicles, Nmmax is the maximum number of vehicles in lane m, Nmmin is the minimum number of vehicles in lane m, and L is the length of road section.The system state equation is described as(5)x˙mnt=fxmnt,umnt,φmnt,Im+1t,Im−1t.


## 3.2. Cost Function

In order to ensure that the vehicle can accurately follow the designed trajectory of the system, fixed and variable costs in the process from upstream to downstream are considered and formulated, which can be represented by(6)J=gxmntmnout+∫tmn0tmnouthxmnt,umntdt,where tmnout is the time when vehicle Cmn leaves the road section, tmn0 is the time when the vehicle Cmn enters the road section, gxmntmnout is the fixed cost of the process, and ∫tmn0tmnouthxmnt,umntdt is the variable cost of the process. The fixed cost includes the cost of fixed items (such as the driving distance and expected speed at the intersection) and the travel time of the road section. The process can be described as (7)gxmntmnout=w1tmnout−t¯mnout2+w2xmntmnout−L2+w3vmntmnout−v¯mnout2+w4ymntmnout−dt¯mnoutm¯−122,where t¯mnout is the target time of vehicle Cmn driving out of the road section, v¯mnout is the expected speed of vehicle Cmn at the intersection, m¯ is the target lane of vehicle, and d is the lane width. w1,w2,w3,w4 are the weights of the travel time of the road section, driving length of the road section, expected speed at the intersection, and the target lane at the intersection, respectively. w1,w2,w3,w4 ∈R+.Variable cost involves acceleration and deceleration of the vehicle driving in longitudinal and lateral lanes. Its function can be expressed as(8)hxmnt,umnt=w5umnt2+2umntvmntχumnt+w6umn′t2+2umn′tvmn′t,where w5 and w6 are the weights of energy changes caused by longitudinal and lateral acceleration of the vehicle, receptively. w5, w6 ∈R+. χumnt is the Heaviside function of longitudinal acceleration of networked vehicles and can be used to separate the variable cost induced by acceleration in longitudinal deceleration process:(9)χumnt=0,umnt≤0,1,umnt>0.t¯mnfree denotes the time of vehicles passing through the intersection under the condition of low-density traffic flow, also known as the time for vehicles Cmn leaving the road without restriction. The time consists of four parts: initial time tmn0, time tmnacc at acceleration state, time tmnc.s. at constant speed state, and time tmndec at deceleration state, which can be described as follows:(10)t¯mnfree=tmn0+tmnacc+tmnc.s.+tmndec,where tmnacc, tmnc.s., and tmndec can be expressed as(11)tmnacc=v0lim−vmntmn0umn+max,tmnc.s.=L−v0lim2−vmntmn02/2umn+max−v0lim2−vmlim2/2umn−maxv0lim,tmndec=v0lim−vmlimumn−max,where v0lim is the speed limit of the road section, vmlim is the speed limit at the downstream exit of the lane m, umn+max is the maximum acceleration of vehicle Cmn, and umn−max is the maximum deceleration of vehicle Cmn.However, it is impossible for the urban road section to maintain a low-density state. Therefore, connected vehicles have to pass through current intersection as a temporary platoon. The candidate timet¯mntemp of vehicle Cmn can be calculated as (12)t¯mntemp=maxt¯mn−1out+tmh2h,t¯mnfree,where tmh2h is the minimum headway between two adjacent vehicles in lane m at the downstream exit of the section.In order to improve the traffic capacity of intersections, the target timet¯mnout of vehicle Cmn at current intersection is controlled within the passable green signal, which can be selected according to (13)t¯mnout,=t¯mntemp,t¯mntemp∈ξm,floort¯mntempRm+GmRm+Gm+Rm,t¯mntemp,∉ξm,where ξm is the set of green light periods of lane m, and floor (t) is the function of rounding down.The expected speed of vehicles is defined as the speed limit at the downstream exit to ensure the maximum efficiency of vehicles and can be described as(14)v¯mnout=vmlim.In conclusion, the cost function can be integrated as(15)J=w1tmnout−t¯mnout2+w2xmntmnout−L2+w3vmntmnout−v¯mnout2+w4ymntmnout−dm¯−122+∫tmn0tmnoutw5umnt2+2umntvmntχumnt+w6umn′t2+2umn′tvmn′tdt.


## 3.3. Constraints

In order to minimize the above cost functionJ, seven constraints, namely, initial vehicular state, vehicle spacing, speed, acceleration, jerk, signal timing, and wireless communication, should be satisfied in the optimization problem.


### 3.3.1. Initial Vehicular State

Suppose that a connected vehicleCmn enters the road section with detectors; when n ≥nmax, the counter will reset. The initial state of vehicle Cmn is defined as (16)xmntmn0=xmntmn0ymntmn0vmntmn0vmn'tmn0=0dm−12vmn0vmn0'.


### 3.3.2. Vehicle Spacing

The vehicle will inevitably be in the vehicle-following state in the driving process. Therefore, vehicleCmn on the lane m and the front vehicle Cm (n-1) should ensure a certain displacement in space and time. The safety constraint can be formulated as (17)xmnt+τmn≤xmn−1t−dmn,where τmn is the time displacement of vehicle Cmn and the front vehicle Cm (n-1), and dmn is the spatial displacement of vehicle Cmn and the front vehicle Cm (n-1).


### 3.3.3. Speed

In order to ensure the safety of the vehicles in the road section, the speed constraint is applied to them. The longitudinal speed constraint embraces the speed information involving speed limit within the section and the minimum speed 0. Thus, we have(18)0≤vmnt≤v0lim.For the lateral speed constraint, the vehicle deflection angle is mainly constrained by vehicle dynamics, which can be expressed as(19)α−max≤αmnt≤αmax,where αmax is the maximum angle through which the front wheel of the vehicle can turn to the left, αmn (t) represents the steering angle of the front wheel of the current vehicle, and αmax represents the maximum angle through which the front wheel of the vehicle can turn to the right.Therefore, the lateral restraint condition of the vehicle is shown as(20)v0limα−max≤vmn′t≤v0limαmax.


### 3.3.4. Acceleration

In order to guarantee that the engine can provide enough power and the brake pads can provide the vehicle enough power limit, the acceleration or deceleration of the vehicle should be specified as a constraint. The acceleration constraints can be expressed as(21)u−max≤umnt≤umax,u−max′≤umn′t≤umax′,where umax is the acceleration of the maximum longitudinal braking deceleration of the vehicle, umax is the acceleration of the maximum longitudinal acceleration of the vehicle, u′max is the maximum transverse acceleration of the vehicle to the left, and u′max is the maximum acceleration of the vehicle to the right.


### 3.3.5. Jerk

The jerk constraint is the change rate constraint of vehicle acceleration, also known as the impact constraint or comfort constraint. The purpose of jerk constraint is to eliminate the negative impact of the acceleration change in the driving process. The jerk constraint is shown as(22)j−max≤∂umnt∂t≤jmax,j−max′≤∂umn′t∂t≤jmax′,where jmax represents the maximum longitudinal backward jerk, jmax represents the maximum longitudinal forward jerk, j′max represents the maximum lateral left acceleration, and j′max represents the maximum lateral right acceleration.


### 3.3.6. Signal Timing

The signal timing constraint of vehicles can ensure that vehicles avoid violations when passing through the intersection, which can be represented as(23)vmntmnout=0,tmnout∉ξm.


### 3.3.7. Wireless Communication

V2X is a communication system through which a vehicle communicates with any entity that may affect the vehicle. Thus, the essence of V2X technology is wireless communication technology. In the practical application of wireless communication technology, time delay and packet loss are inevitable, which may affect the stability and security of networked vehicles in the system. The relevant parameters of wireless communication are constrained as follows:(24)τ˜mnt<0.1,Plp|mnt<15%,where τ˜mnt and Plp|mnt represent the time delay and the packet loss probability of the vehicle Cmn at time t.


## 3.3.1. Initial Vehicular State

Suppose that a connected vehicleCmn enters the road section with detectors; when n ≥nmax, the counter will reset. The initial state of vehicle Cmn is defined as (16)xmntmn0=xmntmn0ymntmn0vmntmn0vmn'tmn0=0dm−12vmn0vmn0'.


## 3.3.2. Vehicle Spacing

The vehicle will inevitably be in the vehicle-following state in the driving process. Therefore, vehicleCmn on the lane m and the front vehicle Cm (n-1) should ensure a certain displacement in space and time. The safety constraint can be formulated as (17)xmnt+τmn≤xmn−1t−dmn,where τmn is the time displacement of vehicle Cmn and the front vehicle Cm (n-1), and dmn is the spatial displacement of vehicle Cmn and the front vehicle Cm (n-1).


## 3.3.3. Speed

In order to ensure the safety of the vehicles in the road section, the speed constraint is applied to them. The longitudinal speed constraint embraces the speed information involving speed limit within the section and the minimum speed 0. Thus, we have(18)0≤vmnt≤v0lim.For the lateral speed constraint, the vehicle deflection angle is mainly constrained by vehicle dynamics, which can be expressed as(19)α−max≤αmnt≤αmax,where αmax is the maximum angle through which the front wheel of the vehicle can turn to the left, αmn (t) represents the steering angle of the front wheel of the current vehicle, and αmax represents the maximum angle through which the front wheel of the vehicle can turn to the right.Therefore, the lateral restraint condition of the vehicle is shown as(20)v0limα−max≤vmn′t≤v0limαmax.


## 3.3.4. Acceleration

In order to guarantee that the engine can provide enough power and the brake pads can provide the vehicle enough power limit, the acceleration or deceleration of the vehicle should be specified as a constraint. The acceleration constraints can be expressed as(21)u−max≤umnt≤umax,u−max′≤umn′t≤umax′,where umax is the acceleration of the maximum longitudinal braking deceleration of the vehicle, umax is the acceleration of the maximum longitudinal acceleration of the vehicle, u′max is the maximum transverse acceleration of the vehicle to the left, and u′max is the maximum acceleration of the vehicle to the right.


## 3.3.5. Jerk

The jerk constraint is the change rate constraint of vehicle acceleration, also known as the impact constraint or comfort constraint. The purpose of jerk constraint is to eliminate the negative impact of the acceleration change in the driving process. The jerk constraint is shown as(22)j−max≤∂umnt∂t≤jmax,j−max′≤∂umn′t∂t≤jmax′,where jmax represents the maximum longitudinal backward jerk, jmax represents the maximum longitudinal forward jerk, j′max represents the maximum lateral left acceleration, and j′max represents the maximum lateral right acceleration.


## 3.3.6. Signal Timing

The signal timing constraint of vehicles can ensure that vehicles avoid violations when passing through the intersection, which can be represented as(23)vmntmnout=0,tmnout∉ξm.


## 3.3.7. Wireless Communication

V2X is a communication system through which a vehicle communicates with any entity that may affect the vehicle. Thus, the essence of V2X technology is wireless communication technology. In the practical application of wireless communication technology, time delay and packet loss are inevitable, which may affect the stability and security of networked vehicles in the system. The relevant parameters of wireless communication are constrained as follows:(24)τ˜mnt<0.1,Plp|mnt<15%,where τ˜mnt and Plp|mnt represent the time delay and the packet loss probability of the vehicle Cmn at time t.


## 3.4. Solution Method Based on Maximum Principle

MSTTOM is solved by Pontryagin’s maximum principle, and the Hamilton function of the problem is established as(25)Hx,u,λ,t=λTfx,u,t+hx,u,t,where λ is defined as the costate vector of vector x, which represents the additional cost of the change of J caused by the small change ∂x of vector x.In the admissible setU, the minimum input u∗ of the cost must satisfy the minimum state of the Hamilton function, which can be expressed as follows:(26)Hx∗,u∗,λ∗,t≤Hx∗,u,λ∗,t,∀u∈U,t∈tmn0,tmnout,∂H∂u=0,∂H∂x=−λ˙,∂H∂λ=x˙.Therefore, the Hamilton function of MSTTOM is shown as(27)Hmn=λ1vmnt+λ2umnt+w5umnt2+2umntvmntχumnt,where the variation of the lateral movement trajectory is optimized in the process of vehicular cooperative lane-changing.In the process of solving the problem, the state vectorλ should meet the condition of the fixed cost, which is shown as (28)λtmnout=∂gxmntmnout∂xmn⇒λ1tmnout=2w2xmntmnout−Lλ2tmnout=2w3vmntmnout−v¯mnout.


## 3.5. Cooperative Lane-Changing Optimization

In order to accurately describe the process of cooperative lane-changing strategy, the request of the vehicular lane-changing is displayed in Figure4. The vehicle Cmn, selected as the subject vehicle, is a red one in the middle of lane m and ready to change lanes from the current lane m to the target lane m+1. Besides, yellow vehicles are defined as the primary threat vehicles of Cmn, orange vehicles are defined as the secondary threat vehicles of Cmn, and blue vehicles are defined as the non-threat vehicles of Cmn.Figure 4
Schematic chart of lane-changing environment for vehiclesCmn.If target lane is not the adjacent lane, it can be decomposed into multiple lane-changing processes. The optimal trajectory is loaded into the traffic environment, and the potential lane-changing conflict safety inspection can be carried out. The flow chart of lane-changing safety inspection is shown in Figure5.Figure 5
The flow chart of lane-changing safety inspection.If two adjacent vehicles receive the same requests concurrently, there is a priority for the vehicle with a higher speed. If adjacent vehicles based on daily driving habits have similar speed, there is a priority for the vehicle in the left lane.Different traffic saturation should be satisfied in the cooperative lane-changing strategy. The higher the saturation involved in the case is, the higher the complexity of the lane-changing strategy will be supposed. Therefore, the case of higher saturation is discussed as follows:(i)
The subject vehicleCmn initiates a lane-changing request to the target vehicle Cm+1n after the target gap selected.(ii)
The target vehicleCm+1n and its rear vehicle Cm+1n+1 adjust their speeds to confirm a safe gap for vehicle Cmn.(iii)
VehicleCmn drives into the target lane m+1.(iv)
The spatiotemporal trajectories of vehicles in the original lane and target lane are updated, which is shown in Figure6.Figure 6
Vehicular spatiotemporal trajectories in lane-changing process.
(a)(b)


## 3.6. Trajectory Optimization Based on RL

In order to improve the efficiency of MSTTOM, this paper designs an optimization algorithm based on the RL paradigm, which can quickly match the optimal trajectory. The optimization algorithm is formulated with the current position and speed of vehicles. The target lane and time period are modeled as inputs, and the sets of vehicle acceleration are formulated as outputs. When the lane-changing request is initiated, the vehicle can be connected to the trajectory of the cooperative lane-changing strategy through the RL matching network. Once the lane-changing is completed, the spatiotemporal trajectory will be matched by the RL to achieve the multilane trajectory optimization.The state vector of MSTTOM satisfies Markov property; that is, the next statest+1 of the system is only related to the current state st, but not directly related to the preceding state. Thus, the state vector can be shown as follows:(29)st=xmnt,φmnt,Im+1t,Im−1t,Pst+1|st=Pst+1|s1,s2,s3,…,st,where P is the probability matrix of transition between state.Through integration, the set of action vectors will be presented in the form of trajectory data. The action vectorat at current state st is shown as (30)at=umnt.Five tuples (S, A, P, R, γ) are defined to describe the process of MSTTOM. Among them, S is the state set, which includes the current state of vehicles and the traffic flow state in the road section; A is the set of executing actions, that is, the set of lateral and longitudinal acceleration output by optimization; R is the reward function of the process, which is negatively linear with the cost function J; and γ is the discount factor when calculating the value function. For a fixed policy π, the value function vπs can be calculated as (31)vπs=Eπ∑k=0∞γkRt+k+1|St=s.An action value functionqπs,a can be calculated by defining the value of each action a, which is described as (32)qπs,a=Eπ∑k=0∞γkRt+k+1|St=s,At=a.Bellman optimal recursive equations of the optimal state value functionv∗s and the optimal action value function q∗s can be calculated by introducing Markov property into (31) and (32), which can be shown as follows:(33)v∗s=maxaRsa+γ∑s′∈Spss′av∗s′,qπs,a=Rsa+γ∑s′∈Spss′amaxaq∗s′,a′,where s′ and a′ are the state and action of the next moment, respectively.The optimal strategy derived by maximizing the above functions can be represented as(34)π∗a|s=1,ifa=argmaxa∈Aq∗s,a,0,else..The function can be calculated by Q-learning algorithm, and the algorithm process is shown in Algorithm1.Algorithm 1:Q-learning algorithm.
Q-learning algorithm(1)
Initializeq (s, a);(2)
While (st=sT)(3)
{Select the initial states0 and action a0 according to the ε-greedy strategy;(4)
While (st=sT)(5)
{Select the actionat the state st according to the ε-greedy strategy, get reward rt and the next state st+1;(6)
qst,at←qst,at+art+1+γmaxaqst+1,a−qst,at;(7)
st=st+1; } }(8)
Get the optimal strategyπs=argmaxaqs,aIn Algorithm1, sT is the termination state in the fifth row. The current value function of the subsequent state estimation is used to update the optimal action function in the seventh row. In order to enhance the diversity of the exploration ability of the algorithm, the specific formula is shown as(35)πa|s=1−ε+εNa,a=argmaxaqs,a,εNa,a≠argmaxaqs,a,where N (a) is the total number of actions, ε-greedy is the optimal action strategy taken based on 1-ε probability, and random action is the policy of ensuring the possibility of being selected for each action according to the probability of ε.


## 4. SUMO/Python Simulation and Analysis

In this section, we will simulate and analyze the proposed MSTTOM through the SUMO/Python-based platform to verify the feasibility and effectiveness of the scheme. Meanwhile, the optimal level of mobility at the signal intersection will be guaranteed in the experiment.


### 4.1. Experiment Platform Based on SUMO

SUMO is microscopic traffic simulation software [20]. The simulation of SUMO is discrete in time and continuous in space, and the location of each vehicle is described internally. In SUMO, the vehicle model is collision free, so that the variation caused by incomplete model is not allowed to appear in the simulation. SUMO allocates appropriate routes to vehicles considering different traffic demands through Dijkstra algorithm. The structure of SUMO map is shown in Figure 7.Figure 7
The structure of SUMO map.


### 4.2. Experimental Scheme

In the paper, the Netedit of SUMO is used to carry out the multilane experimental scenario based on Figure1, and the simulation scenario is shown in Figure 8. The intersection is a typical cross intersection, and the traffic light is set as a typical four-phase signal light. Due to the similar spatial characteristics of each section, the 4-lane section from west to east is selected for the experiment.Figure 8
Diagrammatic sketch of simulation scenario.In the simulation process, the benchmark scheme in the software, the glidepath prototype application (GPPA) scheme [21], and the MSTTOM scheme proposed in this paper are used to simulate and compare the performance of traffic flow conditions with various vehicle saturation 0.6, 0.8, and 1.0. Vehicles simulation diagram is shown in Figure 9.Figure 9
Diagrammatic sketch of vehicles simulation.The three schemes compared in this paper are defined as follows:(i)
The benchmark scheme: in this scheme, the traditional human driving vehicle model in SUMO software is adopted, which means that there is no controlled vehicle and no network communication. Therefore, the driving situation of vehicles under the current traditional driving habits can be simulated in this scenario.(ii)
GPPA scheme: GPPA driving optimization scheme developed by the Federal Highway Administration (FHWA) has been tested and verified. In this scheme, all vehicles in the traffic flow are CVs and are controlled by the optimized system of GPPA.(iii)
MSTTOM scheme: all vehicles in this scheme are CVs, and MSTTOM was applied to all vehicles in this paper. Compared with GPPA scheme, there are the advantages of strong stability and fast calculation efficiency in MSTTOM. Meanwhile, this scheme is adaptive in the complex multilane and multivehicle scenario.Simulation conditions and parameter settings for these three schemes are shown in Table1. Meanwhile, car-following state is simulated by Krauss car-following model [22].Table 1
Simulation conditions and parameter settings.
ParametersUnitValueDistance from detector to intersection(m)200Minimum headway at rest(m)2Vehicle length(m)4.5Vehicle width(m)1.8Vehicle height(m)1.5Lane width(m)3.5Signal cycle duration(s)60Green light duration(s)12Red light duration(s)45Yellow light duration(s)3Saturated traffic flow rate(Veh/h/lane)1800Maximum vehicle speed(km/h)60Minimum vehicle speed(km/h)0Maximum vehicle acceleration(m/s^2)2.6Maximum vehicle deceleration(m/s^2)−4Maximum vehicle lateral acceleration(m/s^2)2Maximum vehicle lateral deceleration(m/s^2)−2Maximum vehicle jerk(m/s^3)10Weight coefficientw1—100Weight coefficientw2—50Weight coefficientw3—10Weight coefficientw4—200Weight coefficientw5—1Weight coefficientw6—5In order to eliminate the influence of unrelated factors in the scenario, the simulation settings in SUMO are simplified by considering the following conditions:(i)
In the simulation environment, there are the same model, size, and kinematic characteristics with all vehicles.(ii)
There is no special weather effect in the simulation environment, and the road adhesion coefficient remains constant.(iii)
The roads are straight in the simulation environment. There are no ramps, nonmotorized vehicular lanes, or parking spaces, which lead to vehicles entering or exiting.(iv)
There is no inclination change in the road section, which means that the vehicle will not travel uphill or downhill.(v)
The arrival probability of vehicles in the simulation environment is stochastic and obeys the Poisson distribution.The simulation process based on SUMO is shown in Figure10. It can be seen that the red vehicle from the west to the east attempts to go straight through the intersection within the green duration from the rightmost lane. In this process, the red vehicle completes cooperative lane-changing with vehicles in the left lane through MSTTOM.Figure 10
Part of the simulation process based on SUMO.
(a)(b)(c)(d)


### 4.3. Result Analysis

Through the simulation of SUMO software, the output data of the vehicle can be exported and analyzed. The vehicular spatiotemporal trajectories on the left lane of the test road section are shown in Figure11, where the spatiotemporal trajectory of the vehicle running on the right lane is denoted by the blue dotted line, and the spatiotemporal trajectory of the vehicle running on the left lane is represented by the red solid line. It is worth noting that the lane-changing vehicles can complete lane-changing quickly and safely under the optimized method. Once a vehicle requests the change of its lane, vehicles in the target lane can adjust the vehicle position and reserve the optimal safety gap for the vehicle requesting lane-changing. Under the environment of multilane signalized intersection, there is no sharp speed change when vehicles approach the intersection. Therefore, the efficiency of achieving the expected optimization of vehicular lane-changing can be proved for the vehicular cooperative optimization.Figure 11
Spatiotemporal trajectories of left lane.The headway and lost time at the stop line of intersection in the road network are analyzed in Figure12, where the blue curve is the test statistical result of the left lane in the benchmark scheme, the green curve is the test statistical result of the left lane in GPPA scheme, and the red curve is the test statistical result of the left lane in MSTTOM scheme. The meaningless data of the first vehicle in the green and red phases in the experimental results are not included in the above statistics. The jumping part of the curve is the loss time of the first vehicle at the beginning of the green light or the lost time of the headway of the following vehicles. Through observation, it can be found that the headway of vehicles can be effectively reduced, the number of vehicles passing through the intersection stop line in a unit time is increased, and the saturation flow rate at the intersection is improved in MSTTOM scheme. In the process of GPPA scheme, some vehicles are affected by vehicular lane-changing, which results in a significant increase in the headway and raise in the green light loss time. Under MSTTOM scheme, the headway of vehicles at the intersection is significantly reduced, and the saturated flow rate at the intersection is increased. According to the traffic control characteristics of signalized intersections, the increase of effective green time and saturation flow rate will directly lead to an increase in the number of vehicles passing through the stop line at the intersection, which means that the throughput of the intersection will be improved.Figure 12
Headway variation under different schemes.The vehicle fuel efficiency and corresponding profit of the whole system under MSTTOM are analyzed in Figure13. The results of T-test show that there is a significant statistical difference in the vehicle fuel efficiency data between the MSTTOM scheme and the benchmark scheme. Through observation, it can be seen that the use of MSTTOM can effectively improve the vehicle fuel efficiency and reduce the vehicle fuel consumption.Figure 13
Fuel efficiency under different schemes.After calculation, the vehicle fuel consumption profit is shown in Figure14. In the case of different vehicle saturation, there is a significant fuel efficiency benefit in GPPA scheme and MSTTOM scheme. Comparing GPPA scheme with the scheme of optimization method proposed in this paper, the advantages of MSTTOM scheme in improving traffic mobility, enhancing vehicle fuel efficiency, and reducing pollutants emissions are obvious.Figure 14
Vehicle fuel consumption profit under different schemes.In MSTTOM scheme, the system calculation time analysis under different iteration time steps and optimization time spans is demonstrated in Figure15. The maximum calculation time is up to 0.93 when the optimization time span is 50 seconds, and the iteration time step is 0.2 seconds. In the simulation process, the optimization time spans of all CVs are less than 50 seconds, and each iteration time step is greater than 0.2 seconds. Therefore, the calculation time of the system is less than 1 second; that is, the effective performance of the system time meets the requirements of real-time optimization.Figure 15
System calculation time under different optimization parameters.The objectives of ensuring the optimal mobility of vehicles at signalized intersections, enhancing vehicle fuel efficiency, and reducing pollutants emissions can be achieved in MSTTOM scheme. Compared with the existing GPPA algorithm, the strengths of MSTTOM are as follows:(i)
The function of multilane cooperative lane-changing strategy under the condition of random traffic flow is well realized in MSTTOM scheme.(ii)
Compared with the benchmark scheme, the mobility of vehicles within the road section is improved, the vehicle fuel efficiency is enhanced by 32%, and the emissions of pollutants are reduced by 17% in MSTTOM scheme.(iii)
Compared with the advanced GPPA scheme, there is a 24% reduction in the vehicle fuel consumption in MSTTOM scheme.(iv)
The traffic fluctuation caused by the intersection signal control is smooth and the traffic flow in the road section is more reasonable in MSTTOM scheme.(v)
For the randomness in the traffic process, the MSTTOM scheme shows its superiority in robustness than other existing schemes.(vi)
The calculation time in MSTTOM scheme is less than 1 second, and the distribution is mainly concentrated in 0.3 seconds to 0.7 seconds, which satisfies the requirements of real-time optimization.


## 4.1. Experiment Platform Based on SUMO

SUMO is microscopic traffic simulation software [20]. The simulation of SUMO is discrete in time and continuous in space, and the location of each vehicle is described internally. In SUMO, the vehicle model is collision free, so that the variation caused by incomplete model is not allowed to appear in the simulation. SUMO allocates appropriate routes to vehicles considering different traffic demands through Dijkstra algorithm. The structure of SUMO map is shown in Figure 7.Figure 7
The structure of SUMO map.


## 4.2. Experimental Scheme

In the paper, the Netedit of SUMO is used to carry out the multilane experimental scenario based on Figure1, and the simulation scenario is shown in Figure 8. The intersection is a typical cross intersection, and the traffic light is set as a typical four-phase signal light. Due to the similar spatial characteristics of each section, the 4-lane section from west to east is selected for the experiment.Figure 8
Diagrammatic sketch of simulation scenario.In the simulation process, the benchmark scheme in the software, the glidepath prototype application (GPPA) scheme [21], and the MSTTOM scheme proposed in this paper are used to simulate and compare the performance of traffic flow conditions with various vehicle saturation 0.6, 0.8, and 1.0. Vehicles simulation diagram is shown in Figure 9.Figure 9
Diagrammatic sketch of vehicles simulation.The three schemes compared in this paper are defined as follows:(i)
The benchmark scheme: in this scheme, the traditional human driving vehicle model in SUMO software is adopted, which means that there is no controlled vehicle and no network communication. Therefore, the driving situation of vehicles under the current traditional driving habits can be simulated in this scenario.(ii)
GPPA scheme: GPPA driving optimization scheme developed by the Federal Highway Administration (FHWA) has been tested and verified. In this scheme, all vehicles in the traffic flow are CVs and are controlled by the optimized system of GPPA.(iii)
MSTTOM scheme: all vehicles in this scheme are CVs, and MSTTOM was applied to all vehicles in this paper. Compared with GPPA scheme, there are the advantages of strong stability and fast calculation efficiency in MSTTOM. Meanwhile, this scheme is adaptive in the complex multilane and multivehicle scenario.Simulation conditions and parameter settings for these three schemes are shown in Table1. Meanwhile, car-following state is simulated by Krauss car-following model [22].Table 1
Simulation conditions and parameter settings.
ParametersUnitValueDistance from detector to intersection(m)200Minimum headway at rest(m)2Vehicle length(m)4.5Vehicle width(m)1.8Vehicle height(m)1.5Lane width(m)3.5Signal cycle duration(s)60Green light duration(s)12Red light duration(s)45Yellow light duration(s)3Saturated traffic flow rate(Veh/h/lane)1800Maximum vehicle speed(km/h)60Minimum vehicle speed(km/h)0Maximum vehicle acceleration(m/s^2)2.6Maximum vehicle deceleration(m/s^2)−4Maximum vehicle lateral acceleration(m/s^2)2Maximum vehicle lateral deceleration(m/s^2)−2Maximum vehicle jerk(m/s^3)10Weight coefficientw1—100Weight coefficientw2—50Weight coefficientw3—10Weight coefficientw4—200Weight coefficientw5—1Weight coefficientw6—5In order to eliminate the influence of unrelated factors in the scenario, the simulation settings in SUMO are simplified by considering the following conditions:(i)
In the simulation environment, there are the same model, size, and kinematic characteristics with all vehicles.(ii)
There is no special weather effect in the simulation environment, and the road adhesion coefficient remains constant.(iii)
The roads are straight in the simulation environment. There are no ramps, nonmotorized vehicular lanes, or parking spaces, which lead to vehicles entering or exiting.(iv)
There is no inclination change in the road section, which means that the vehicle will not travel uphill or downhill.(v)
The arrival probability of vehicles in the simulation environment is stochastic and obeys the Poisson distribution.The simulation process based on SUMO is shown in Figure10. It can be seen that the red vehicle from the west to the east attempts to go straight through the intersection within the green duration from the rightmost lane. In this process, the red vehicle completes cooperative lane-changing with vehicles in the left lane through MSTTOM.Figure 10
Part of the simulation process based on SUMO.
(a)(b)(c)(d)


## 4.3. Result Analysis

Through the simulation of SUMO software, the output data of the vehicle can be exported and analyzed. The vehicular spatiotemporal trajectories on the left lane of the test road section are shown in Figure11, where the spatiotemporal trajectory of the vehicle running on the right lane is denoted by the blue dotted line, and the spatiotemporal trajectory of the vehicle running on the left lane is represented by the red solid line. It is worth noting that the lane-changing vehicles can complete lane-changing quickly and safely under the optimized method. Once a vehicle requests the change of its lane, vehicles in the target lane can adjust the vehicle position and reserve the optimal safety gap for the vehicle requesting lane-changing. Under the environment of multilane signalized intersection, there is no sharp speed change when vehicles approach the intersection. Therefore, the efficiency of achieving the expected optimization of vehicular lane-changing can be proved for the vehicular cooperative optimization.Figure 11
Spatiotemporal trajectories of left lane.The headway and lost time at the stop line of intersection in the road network are analyzed in Figure12, where the blue curve is the test statistical result of the left lane in the benchmark scheme, the green curve is the test statistical result of the left lane in GPPA scheme, and the red curve is the test statistical result of the left lane in MSTTOM scheme. The meaningless data of the first vehicle in the green and red phases in the experimental results are not included in the above statistics. The jumping part of the curve is the loss time of the first vehicle at the beginning of the green light or the lost time of the headway of the following vehicles. Through observation, it can be found that the headway of vehicles can be effectively reduced, the number of vehicles passing through the intersection stop line in a unit time is increased, and the saturation flow rate at the intersection is improved in MSTTOM scheme. In the process of GPPA scheme, some vehicles are affected by vehicular lane-changing, which results in a significant increase in the headway and raise in the green light loss time. Under MSTTOM scheme, the headway of vehicles at the intersection is significantly reduced, and the saturated flow rate at the intersection is increased. According to the traffic control characteristics of signalized intersections, the increase of effective green time and saturation flow rate will directly lead to an increase in the number of vehicles passing through the stop line at the intersection, which means that the throughput of the intersection will be improved.Figure 12
Headway variation under different schemes.The vehicle fuel efficiency and corresponding profit of the whole system under MSTTOM are analyzed in Figure13. The results of T-test show that there is a significant statistical difference in the vehicle fuel efficiency data between the MSTTOM scheme and the benchmark scheme. Through observation, it can be seen that the use of MSTTOM can effectively improve the vehicle fuel efficiency and reduce the vehicle fuel consumption.Figure 13
Fuel efficiency under different schemes.After calculation, the vehicle fuel consumption profit is shown in Figure14. In the case of different vehicle saturation, there is a significant fuel efficiency benefit in GPPA scheme and MSTTOM scheme. Comparing GPPA scheme with the scheme of optimization method proposed in this paper, the advantages of MSTTOM scheme in improving traffic mobility, enhancing vehicle fuel efficiency, and reducing pollutants emissions are obvious.Figure 14
Vehicle fuel consumption profit under different schemes.In MSTTOM scheme, the system calculation time analysis under different iteration time steps and optimization time spans is demonstrated in Figure15. The maximum calculation time is up to 0.93 when the optimization time span is 50 seconds, and the iteration time step is 0.2 seconds. In the simulation process, the optimization time spans of all CVs are less than 50 seconds, and each iteration time step is greater than 0.2 seconds. Therefore, the calculation time of the system is less than 1 second; that is, the effective performance of the system time meets the requirements of real-time optimization.Figure 15
System calculation time under different optimization parameters.The objectives of ensuring the optimal mobility of vehicles at signalized intersections, enhancing vehicle fuel efficiency, and reducing pollutants emissions can be achieved in MSTTOM scheme. Compared with the existing GPPA algorithm, the strengths of MSTTOM are as follows:(i)
The function of multilane cooperative lane-changing strategy under the condition of random traffic flow is well realized in MSTTOM scheme.(ii)
Compared with the benchmark scheme, the mobility of vehicles within the road section is improved, the vehicle fuel efficiency is enhanced by 32%, and the emissions of pollutants are reduced by 17% in MSTTOM scheme.(iii)
Compared with the advanced GPPA scheme, there is a 24% reduction in the vehicle fuel consumption in MSTTOM scheme.(iv)
The traffic fluctuation caused by the intersection signal control is smooth and the traffic flow in the road section is more reasonable in MSTTOM scheme.(v)
For the randomness in the traffic process, the MSTTOM scheme shows its superiority in robustness than other existing schemes.(vi)
The calculation time in MSTTOM scheme is less than 1 second, and the distribution is mainly concentrated in 0.3 seconds to 0.7 seconds, which satisfies the requirements of real-time optimization.


## 5. Conclusions

This paper proposes a new scheme, MSTTOM, to ease traffic pressure and reduce traffic congestion in multilane road sections. The problem of low traffic efficiency at the multilane intersections is studied and analyzed in this paper. Four stages of work, namely, literature summary, scenario and structure introduction, method optimization design and experimental validation, and optimization objects determination, are conducted. The research results and innovations are as follows:(i)
A vehicular lane-changing method based on V2X is proposed. Firstly, the lane-changing environment information is analyzed to classify and define the potential threat vehicles in the driving environment. Secondly, the lane-changing behaviors of potential threat vehicles are analyzed, and conflict detection is carried out to determine the priority order in the lane-changing process. Then, lane-changing gap and target cooperative vehicles are determined and declared. Finally, the spatiotemporal trajectories of related vehicles are updated. The vehicular cooperative lane-changing strategy lays a foundation for the reasonable planning of MSTTOM.(ii)
This paper designs a multilane spatiotemporal trajectory optimization method. Based on the optimal control theory, the state control models of CVs driven by Pontryagin’s maximum principle are constructed. The cost function is formulated by continuous functional target completion and optimal profit. The constraints in line with the actual situation of the vehicle are also established. Finally, the trajectories data are optimized by Q-learning algorithm to achieve the real-time optimization.(iii)
SUMO software is used to verify the feasibility and effectiveness of MSTTOM by comparing it with GPPA scheme of FHWA in the United States. The experimental results demonstrate that MSTTOM can effectively optimize the traffic flow, improve the vehicle fuel efficiency, reduce pollutants emissions, and improve the traffic efficiency of vehicles at intersections.



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*Source: 8819911-2020-12-15.xml*