Car-following model and optimization strategy for connected and automated vehicles under mixed traffic environment

PENG Jia-li; SHANGGUAN Wei; CHAI Lin-guo; QIU Wei-zhi

doi:10.19818/j.cnki.1671-1637.2023.03.018

Volume 23 Issue 3

Jun. 2023

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Article Contents

Abstract

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0. introduction

1. 基于多车状态信息指数平滑融合的跟驰模型

2. Analysis of car following model and car following strategy for mixed traffic environment

3. 仿真验证与应用分析

4. 结语

References

Article Navigation > Journal of Traffic and Transportation Engineering > 2023 > 23(3): 232-247

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PENG Jia-li, SHANGGUAN Wei, CHAI Lin-guo, QIU Wei-zhi. Car-following model and optimization strategy for connected and automated vehicles under mixed traffic environment[J]. Journal of Traffic and Transportation Engineering, 2023, 23(3): 232-247. doi: 10.19818/j.cnki.1671-1637.2023.03.018

Citation:

PENG Jia-li, SHANGGUAN Wei, CHAI Lin-guo, QIU Wei-zhi. Car-following model and optimization strategy for connected and automated vehicles under mixed traffic environment[J]. Journal of Traffic and Transportation Engineering, 2023, 23(3): 232-247. doi: 10.19818/j.cnki.1671-1637.2023.03.018

Citation:

PENG Jia-li, SHANGGUAN Wei, CHAI Lin-guo, QIU Wei-zhi. Car-following model and optimization strategy for connected and automated vehicles under mixed traffic environment[J]. Journal of Traffic and Transportation Engineering, 2023, 23(3): 232-247. doi: 10.19818/j.cnki.1671-1637.2023.03.018

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Car-following model and optimization strategy for connected and automated vehicles under mixed traffic environment

doi: 10.19818/j.cnki.1671-1637.2023.03.018

1.
School of Electronic and Information Engineering, Beijing Jiaotong University, Beijing 100044, China
2.
State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing 100044, China

Funds:

National Natural Science Foundation of China 52272328

Joint Fund of the Ministry of Education for Equipment Preresearch 8091B022238

Natural Science Foundation of Beijing L211022

More Information

Author Bio:
PENG Jia-li(1997-), male, doctoral student, jialipeng@bjtu.edu.cn

SHANGGUAN Wei(1979-), male, professor, PhD, wshg@bjtu.edu.cn
Received Date: 2022-11-30
Available Online: 2023-07-07
Publish Date: 2023-06-25

Abstract

Abstract

To improve the driving efficiency and traffic flow stability of vehicles in the mixed traffic environment, the informations such as the velocities and accelerations of multiple vehicles in front were fused, and an exponential smoothing approach was adopted to build a car-following model of connected and automated vehicles (CAVs) based on the backward-looking effect. Then the effects of number of vehicles in front and behind and the completeness of state information on the model stability were studied. The linear stability analysis was carried out and the optimal parameters of the model were determined by combining the Lyapunov's first method and linear harmonic perturbation method. Combined with the characteristics of mixed traffic environments, the car-following strategies of CAVs in different positions and states were proposed in the condition of communication information loss. The numerical simulations were carried out in three typical scenarios with different CAV penetration rates, including vehicle starting, vehicle braking to stop, and circular road. Research results show that in the scenario of vehicle braking to stop, the maximum stopping wave speed of all vehicles increases by 26.1%. In the scenario of vehicle starting, the maximum starting wave speed increases by 15.5%, and the accelerations and speeds of vehicles change more smoothly. In the circular road scenario, when the CAV penetration rate in the mixed traffic flow increases from 40% to 100%, the fluctuation time of average speed of vehicles in the larger disturbance scenario decreases by 44.8%, the wave peak decreases by 5.7%, and the wave trough increases by 19.4%, compared to the low CAV penetration rate scenarios. However, the proposed optimization strategy does not significantly improve the mixed traffic flow at a lower CAV penetration rate. Thus, in the current situation where it is difficult to construct an actual mixed traffic environment and conduct CAV real vehicle tests, the model and strategies can be employed for the car-following simulation and test verification in specific scenarios to effectively guarantee the absorption of traffic flow disturbance and stable driving vehicles in the mixed traffic environment.
- traffic information engineering,
- car-following model,
- numerical simulation,
- mixed traffic environment,
- connected and automated vehicle

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0. introduction

With the continuous development and application of the Intelligent Vehicle Infrastructure Cooperation System (I-VICS) in China, as well as the continuous maturity of intelligent networked vehicle communication technology and intelligent decision control related technologies, vehicles can obtain more and more accurate traffic data in real time^[1]Provide information such as the location, speed, acceleration, headway, and situation of surrounding vehicles, and assist in vehicle handling behavior^[2]Correspondingly, the future transportation environment will gradually develop into a mixed traffic environment, that is, a traffic operation scenario that combines human driven vehicles (HDVs) and connected and automated vehicles (CAVs) will gradually become a norm. Therefore, the mechanism analysis and simulation reconstruction of mixed traffic flow play an important role in the stable control of transportation systems and have received widespread attention^[3].

As one of the most fundamental micro behaviors of vehicles, the car following model is an important basic theory for traffic flow simulation. For the study of car following models, scholars at home and abroad have mainly focused on vehicles with different levels of intelligence, combined with their relevant characteristics, to carry out many related research works on car following modeling. For manually driven vehicles, due to the obstruction of visual perception by the preceding vehicle, the motion status of single vehicles in front and behind can usually only be observed. Therefore, most of the car following models in literature only consider a single preceding vehicle. Newell^[4]A HDV car following model based on stimulus response effect was constructed using the distance between car heads; Bando and others^[5]A classic Optimal Velocity (OV) model was proposed by combining the Newell car following model. This model has a simple expression form and can well reproduce many phenomena such as stopping and sudden changes in actual traffic operation. However, the model does not quantify the negative speed difference effect of vehicles; Helbing et al^[6]A generalized force model has been proposed, but it may cause the phenomenon of following vehicles not slowing down, which is not in line with actual driving habits; Jiang et al^[7]The Full Velocity Difference (FVD) model has been proposed, which is closer to the actual vehicle operation data in the traffic network than the optimal speed model and generalized force model. It has shown good stability in both linear and nonlinear analysis. However, when the preceding vehicle suddenly decelerates, a rear end collision may occur due to slow perception response; Sun Dihua and others^[8]On the basis of the full speed difference model, the state information of the following vehicles was added to form the Backward Looking and Velocity Difference (BLVD) model, but the comprehensive effect of the front and rear vehicles on traffic flow stability was not explored; Tang Yi and others^[9]A backward looking and optimal velocity difference (BLOVD) car following model was proposed by combining the FVD model and BLVD model, but the accuracy of this model in characterizing real driving behavior is still not accurate enough.

For connected autonomous vehicles with higher levels of intelligence, Peng et al^[10]The concept of memory factor was proposed, and the FVD model was improved to construct an Optimal Velocity Changes with Memory (OVCM) model. This model can simulate the acceleration and deceleration trends of the preceding vehicle well, but only mining the speed change trends of the preceding and following vehicles is not sufficient for the control of networked autonomous driving vehicles; Ji Yi and others^[11]Explored the impact of multiple preceding vehicle information on model stability, improved the OVCM model with the situational information of five preceding vehicles, and proposed a Multiple Headway Optimal Velocity and Acceleration (MHOVA) following model based on the optimal distance between multiple preceding vehicles. However, this model only considers the information of the five preceding vehicles and does not explore the number of preceding vehicles; Wang et al^[12]A Multiple Vehicles Changes with Memory (MVCM) car following model was proposed with the number of preceding vehicles as the independent variable, and the optimal number of vehicles for obtaining preceding vehicle information was explored; Wu Bing and others^[13]On the basis of considering Vehicle to Vehicle (V2V) communication, a Connected Longitudinal Control Model (C-LCM) is proposed, which takes into account the influence of multiple preceding vehicle speed and acceleration information, as well as a shorter response time. However, this model has low complexity and does not consider the rearview effect of vehicles, making it difficult to accurately describe the driving behavior of CAVs in mixed traffic environments; Zong Fang and others^[14]A Multiple Front and Rear Vehicles Headway Velocity and Acceleration Difference (MFRHVAD) model has been proposed for networked autonomous vehicles, conventional vehicles, and autonomous vehicles. However, this model does not take into account the delay time of driving operations and is difficult to obtain the acceleration and deceleration trends of the front and rear vehicles, making it unable to respond in advance to sudden driving behaviors.

1. 基于多车状态信息指数平滑融合的跟驰模型

$\begin{gathered} \frac{\mathrm{d} v_n(t)}{\mathrm{d} t}=a\left\{V\left[\Delta x_n(t)\right]-v_n(t)\right\}+\lambda \Delta v_n(t)+ \\ \gamma\left\{V\left[\Delta x_n(t)\right]-V\left[\Delta x_n(t-\tau)\right]\right\} \end{gathered}$

(1)

$\begin{gathered} V\left[\Delta x_n(t)\right]=v_{\max }\left\{\tanh \left[\Delta x_n(t)-h_{\mathrm{s}}\right]+\right. \\ \left.\tanh \left(h_{\mathrm{s}}\right)\right\} / 2 \end{gathered}$

(2)

According to equation (1), when the following car istThe optimal speed at any given moment is less thant-τWhen the optimal speed is reached, the following car has a tendency to slow down, and vice versa, it has a tendency to accelerate.

This model introduces the memory effect to quantify the acceleration and deceleration trends, but CAV is a vehicle that continuously obtains self and other vehicle motion information on the road through wireless communication, and can achieve autonomous perception, decision-making, and control. Its model can adjust the vehicle's operating status in a timely manner through more accurate traffic information, such as acceleration/deceleration. Therefore, the type, quantity, and degree of influence of information obtained by CAV have become important research topics in modeling.

This article considers a mixed traffic environment consisting of two types of vehicles, namely HDV and CAV. The way, type, and decision control of HDV to obtain information mainly come from the driver. The driver's abilities in vision, reaction, judgment, and driving decision-making determine the vehicle's motion behavior. CAV can not only achieve autonomous driving, but also use communication technologies such as Vehicle to Everything (V2X) to fuse the vehicle's information with road and vehicle situation information, in order to obtain traffic environment information around the main vehicle, calculate the optimal control strategy for individuals or the entire transportation system, and execute it. Although the combination of connected transportation systems and autonomous driving technology has broad application prospects, CAVs cannot fully obtain information from HDVs in mixed traffic environments. Therefore, scholars have begun to study the impact of CAVs on environmental vehicles or mixed traffic flows. In a mixed traffic environment, the position, speed, penetration rate, and other parameters of CAV in the fleet will affect the operational performance of both the vehicle and the surrounding vehicles. Therefore, it is urgent to improve the CAV's car following model and its optimal car following strategy in different states.

$\begin{aligned} V_{\mathrm{F}}\left[\Delta x_n(t)\right]=\alpha_1\left\{\tanh \left[\Delta x_n(t)-h_{\mathrm{s}}\right]+\right. \\ \left.\tanh \left(h_{\mathrm{s}}\right)\right\}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \end{aligned}$

(3)

$\begin{aligned} V_{\mathrm{B}}\left[\Delta x_n(t)\right]=-\alpha_2\left\{\tanh \left[\Delta x_n(t)-h_s\right]+\right. \\ \left.\tanh \left(h_s\right)\right\}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \end{aligned}$

(4)

In the formula:V_F[Δx_n(t）]AndV_B[Δx_n(t）]They are respectivelytTime vehiclesnThe optimal forward and backward velocity function;α₁andα₂All are speed sensitivity coefficients.

Based on the optimal speed function mentioned above, this paper proposes a Multi Vehicle Information Smooth Fusion (MVISF) car following model, whose mathematical equation is

$\begin{gathered} v_n(t+T)=a\left\{p V_{\mathrm{F}}\left[\Delta x_n(t)\right]+(1-p) V_{\mathrm{B}}\left[\Delta x_{n-1}(t)\right]\right\}+ \\ \ \ \ \ \ \ \ \ \lambda_1 T E(n, k)+\lambda_2 T E(n, h)+\omega_1 T a_{n+1}(t)+\omega_2 T a_{n-1}(t)+ \\ \sum\limits_{i=1}^k T \gamma_i\left\{V_{\mathrm{F}}\left[\Delta x_{n+i-1}(t)\right]-V_{\mathrm{F}}\left[\Delta x_{n+i-1}(t-\tau)\right]\right\}+ \\ \sum\limits_{j=1}^h T \gamma_j\left\{V_{\mathrm{B}}\left[\Delta x_{n-j}(t)\right]-V_{\mathrm{B}}\left[\Delta x_{n-j}(t-\tau)\right]\right\}\ \ \ \ \ \ \ \ \ \ \end{gathered}$

(5)

$\begin{gathered} E(n, k)=\beta \Delta v_{n+1}(t)+(1-\beta) E(n+1, k)= \\ \ \ \ \ \beta \Delta v_{n+1}(t)+(1-\beta)\left[\beta \Delta v_{n+2}(t)+(1-\beta) \cdot\right. \\ \ \ \ \ E(n+2, k)] \cdots=\beta \sum\limits_{l=0}^{k-2}(1-\beta)^l \Delta v_{n+l+1}(t) \end{gathered}$

(6)

$E(n, h)=\beta \sum\limits_{l=0}^{h-1}(1-\beta)^l \Delta v_{n-l-1}(t)$

(7)

$v_n(t+T)=v_n(t)+T a_n(t)$

(8)

$a_n(t)=\frac{1}{T}\left[v_n(t+T)-v_n(t)\right]$

(9)

$\begin{gathered} \frac{\mathrm{d} v_n(t)}{\mathrm{d} t}=a\left\{p V_{\mathrm{F}}\left[\Delta x_n(t)\right]+(1-p) V_{\mathrm{B}}\left[\Delta x_{n-1}(t)\right]-\right. \\ \ \ \ \ \left.v_n(t)\right\}+\lambda_1 E(n, k)+\lambda_2 E(n, h)+\omega_1 a_{n+1}(t)+ \\ \omega_2 a_{n-1}(t)+\sum\limits_{i=1}^k \gamma_i\left\{V_{\mathrm{F}}\left[\Delta x_{n+i-1}(t)\right]-\right.\ \ \ \ \ \ \\ \ \ \ \ \ \ \left.V_{\mathrm{F}}\left[\Delta x_{n+i-1}(t-\tau)\right]\right\}+\sum\limits_{j=1}^h \gamma_j\left\{V_{\mathrm{B}}\left[\Delta x_{n-j}(t)\right]-\right. \\ \left.V_{\mathrm{B}}\left[\Delta x_{n-j}(t-\tau)\right]\right\}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \end{gathered}$

(10)

Ignore variable Δx_n(t－τ）The nonlinear term of Taylor expansion yields a simplified Δx_n(t－τ）For

$\begin{gathered} \Delta x_n(t-\tau)=\Delta x_n(t)-\tau \frac{\mathrm{d} \Delta x_n(t)}{\mathrm{d} t}= \\ \Delta x_n(t)-\tau \Delta v_n(t) \end{gathered}$

(11)

$\begin{gathered} V\left[\Delta x_n(t-\tau)\right]=V\left[\Delta x_n(t)\right]- \\ \tau \Delta v_n(t) V^{\prime}\left[\Delta x_n(t)\right] \end{gathered}$

(12)

Finally obtained

$\begin{gathered} \frac{\mathrm{d} v_n(t)}{\mathrm{d} t}=a\left\{p V_{\mathrm{F}}\left[\Delta x_n(t)\right]+(1-p) V_{\mathrm{B}}\left[\Delta x_{n-1}(t)\right]-\right. \\ \left.v_n(t)\right\}+\lambda_1 \beta \sum\limits_{j=0}^{k-2}(1-\beta)^j \Delta v_{n+j+1}(t)+ \ \ \ \\ \lambda_2 \beta \sum\limits_{l=0}^{h-1}(1-\beta)^l \Delta v_{n-l-1}(t)+\omega_1 a_{n+1}(t)+ \\ \ \ \ \ \ \ \ \ \ \ \ \ \omega_2 a_{n-1}(t)+\sum\limits_{i=1}^k \gamma_i \tau \Delta v_{n+i-1}(t) V_{\mathrm{F}}^{\prime}\left[\Delta x_{n+i-1}(t)\right]+ \\ \sum\limits_{j=1}^k \gamma_j \tau \Delta v_{n-j}(t) V_{\mathrm{B}}^{\prime}\left[\Delta x_{n-j}(t)\right]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \end{gathered}$

(13)

2. Analysis of car following model and car following strategy for mixed traffic environment

2.1 线性稳定性分析

This section analyzes the stability of the proposed MVISF car following model and explores the critical stability conditions for determining its related parameters. Assuming the initial position of the vehicle is

$\left\{\begin{array}{l} x_n(0)=b n+V(b) \\ b=L / N \end{array}\right.$

(14)

In the formula:NandLThey are the number of vehicles and the length of the road, respectively;x_n(0) is the vehiclenAt the beginning of stable traffic flow（t=0) Position;bFor steady-state headway.

$\begin{aligned} & \frac{\mathrm{d} v_n(t)}{\mathrm{d} t}=\frac{\mathrm{d}^2 y_n(t)}{\mathrm{d} t^2}=a\left[p V_{\mathrm{F}}^{\prime}(b) \Delta y_n(t)+\right. \\ & \ \ \ \ \ \left.(1-p) V_{\mathrm{B}}^{\prime}(b) \Delta y_{n-1}(t)-\frac{\mathrm{d} y_n(t)}{\mathrm{d} t}\right]+ \\ & \ \ \ \ \ \lambda_1 \beta \sum\limits_{j=0}^{k-2}(1-\beta)^j \frac{\mathrm{d} \Delta y_{n+j+1}(t)}{\mathrm{d} t}+\lambda_2 \beta \sum\limits_{l=0}^{h-1}(1-\beta)^t \cdot \\ & \ \ \ \ \ \frac{\mathrm{d} \Delta y_{n-l-1}(t)}{\mathrm{d} t}+\omega_1 \frac{\mathrm{d}^2 y_{n+1}(t)}{\mathrm{d} t^2}+\omega_2 \frac{\mathrm{d}^2 y_{n-1}(t)}{\mathrm{d} t^2}+ \\ & \ \ \ \ \ \sum\limits_{i=1}^k \gamma_i \tau \frac{\mathrm{d} \Delta y_{n+i-1}(t)}{\mathrm{d} t} V_{\mathrm{F}}^{\prime}(b)+ \\ & \ \ \ \ \ \sum\limits_{j=1}^h \gamma_j \tau \frac{\mathrm{d} \Delta y_{n-j}(t)}{\mathrm{d} t} V_{\mathrm{B}}^{\prime}(b) \end{aligned}$

(15)

$\left\{\begin{array}{l} \frac{\mathrm{d} y_n(t)}{\mathrm{d} t}=A z \mathrm{e}^{\mathrm{\varphi \mathit{n}}+z t} \\ \frac{\mathrm{d}^2 y_n(t)}{\mathrm{d} t^2}=A z^2 \mathrm{e}^{\mathrm{\varphi \mathit{n}}+z t} \\ \Delta y_n(t)=A \mathrm{e}^{\mathrm{\varphi \mathit{n}}+z t}\left(\mathrm{e}^{\varphi}-1\right) \end{array}\right.$

(16)

$\begin{aligned} z^2= & a\left[p V_{\mathrm{F}}^{\prime}(b)\left(\mathrm{e}^{\varphi}-1\right)-(1-p) V_{\mathrm{B}}^{\prime}(b)\left(\mathrm{e}^{-\varphi}-1\right)-z\right]+ \\ & \lambda_1 \beta z \sum\limits_{j=0}^{k-2}(1-\beta)^j \mathrm{e}^{\varphi(j+1)}+\lambda_2 \beta z \sum\limits_{l=0}^{h-1}(1-\beta)^l \mathrm{e}^{-\varphi(l+1)}+ \\ & z^2 \mathrm{e}^{\varphi}\left(\omega_1+\omega_2\right)+z \tau V_{\mathrm{F}}^{\prime}(b) \sum\limits_{i=1}^k \gamma_i\left[\mathrm{e}^{\varphi i}-\mathrm{e}^{\varphi(i-1)}\right]+ \\ & z \tau V_{\mathrm{B}}^{\prime}(b) \sum\limits_{j=1}^h \gamma_j\left[\mathrm{e}^{\varphi(1-j)}-\mathrm{e}^{-\varphi i}\right] \end{aligned}$

(17)

$\left\{\begin{array}{l} \mathrm{e}^{\varphi}=1+\varphi+1 /(2 \varphi)^2 \\ \mathrm{e}^{-\varphi}=1-\varphi+1 /(2 \varphi)^2 \\ z=z_1 \varphi+z_2 \varphi^2 \end{array}\right.$

(18)

$z_1=p V_{\mathrm{F}}^{\prime}(b)+(1-p) V_{\mathrm{B}}^{\prime}(b)$

(19)

$\begin{aligned} z_2= & \frac{1}{2}\left[p V_{\mathrm{F}}^{\prime}(b)-(1-p) V_{\mathrm{B}}^{\prime}(b)\right]+ \\ & \frac{1}{a}\left[\lambda_1 \beta \sum\limits_{j=0}^{k-2}(1-\beta)^j z_1+\lambda_2 \beta \sum\limits_{l=0}^{h-1}(1-\beta)^l z_1+\right. \\ & \left(\omega_1+\omega_2-1\right) z_1^2+\tau V_{\mathrm{F}}^{\prime}(b) \sum\limits_{i=1}^k \gamma_i z_1+ \\ & \left.\tau V_{\mathrm{B}}^{\prime}(b) \sum\limits_{j=1}^h \gamma_j z_1\right] \end{aligned}$

(20)

$\begin{aligned} a> & -2\left[\lambda_1 \beta \sum\limits_{j=0}^{k-2}(1-\beta)^j z_1+\lambda_2 \beta \sum\limits_{l=0}^{h-1}(1-\beta)^l z_1+\left(\omega_1+\right.\right. \\ & \left.\left.\omega_2-1\right) z_1^2+\tau V_{\mathrm{F}}^{\prime}(b) \sum\limits_{i=1}^k \gamma_i z_1+\tau V_{\mathrm{B}}^{\prime}(b) \sum\limits_{j=1}^h \gamma_j z_1\right] / \\ & {\left[p V_{\mathrm{F}}^{\prime}(b)-(1-p) V_{\mathrm{B}}^{\prime}(b)\right] } \end{aligned}$

(21)

Figure 1. Sensitivity coefficient curves

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2.2 comparative analysis

Figure 2. Scenario of comparative experiment

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Table 1Described the vehicle speed distribution of five models, namely BLOVD, OVCM, MHOVA, MVCM, and MVISF, at the 50th sampling intervalV_max、V_ave、V_min、R_upandR_downThey are the maximum speed, average speed, minimum speed, upward speed fluctuation rate, and downward speed fluctuation rate of the vehicle. causeTable 1It can be seen that the MVISF model has an upward fluctuation rate of 3.33% and a downward fluctuation rate of 6.13% in vehicle speed. The fluctuation amplitude in speed control is relatively small, and compared to other models, there is a significant improvement; The MHOVA model considers 5 leading vehicles, the MVCM model considers 3 leading vehicles, and the MVISF model achieves better performance in stability and disturbance rejection than all other car following models after considering the rearview effect and incorporating information from multiple leading and trailing vehicles. Therefore, the MVISF model has certain advantages in vehicle and traffic flow control in mixed traffic environments.

Table 1. Comparison of model stability parameters

模型	V_max/ (m·s^-1)	V_min/ (m·s^-1)	V_ave/ (m·s^-1)	R_up/ %	R_down/ %
BLOVD	0.851 5	0.678 1	0.799 7	6.50	15.18
OVCM	1.080 1	0.892 7	0.999 5	8.05	10.69
MHOVA	1.042 8	0.892 7	0.999 7	4.32	10.69
MVCM	1.036 3	0.895 7	0.999 7	3.67	10.39
MVISF	0.826 2	0.750 5	0.799 6	3.33	6.13

| Show Table

DownLoad: CSV

2.3 混行车辆跟驰策略

In a real mixed traffic environment, HDV does not have automatic control and networking functions. The perception of the environment during the entire driving process relies on human senses to judge the driving speed of the preceding and following vehicles and the surrounding driving environment, thus making driving decisions. It is not sensitive to changes in acceleration of other vehicles, and its safety and efficiency are closely related to the driver's driving experience; CAV continuously obtains self and road motion information through wireless communication and can achieve autonomous perception, decision-making, and control, thereby avoiding possible traffic accidents.

Even if V2X can effectively ensure the transmission of status information between vehicles, there may still be communication delays or packet losses, and the positions of CAV and HDV are completely random. Therefore, in order to better match the actual environment with the MVISF model and optimal parameter values, this section designs a more realistic CAV following strategy for the proposed model. This strategy framework mainly focuses on distributed car following control for CAVs, where each sub vehicle is equipped with a controller to make control decisions based on the information transmitted by other vehicles and its current state. During this process, the impact of communication information loss on control effectiveness is mainly considered, and it is assumed that the HDV state information (speed, acceleration, etc.) loss rate is 5%, and there is no information loss in CAVs. The virtual vehicle to be constructed provides designated vehicle status information, such as speed, acceleration, etc., at the location of the vehicle where information is lost, so that the MVISF model can run normally and efficiently, avoiding the impact of information loss on model performance.

Due to the ability of CAV vehicle mounted equipment to obtain status information of adjacent front and rear vehicles, when the adjacent front and rear vehicles are HDVs and status information is lost, it will not cause input loss to the MVISF car following model; When the CAV is not located in the leading or trailing vehicle but the number of vehicles in front or behind does not meet the required number of vehicles for the model, a virtual HDV is constructed at a safe distance between the leading or trailing vehicles that meets the model requirements (virtual HDV does not consider information loss), and its state information is consistent with that of the leading or trailing vehicle; When the CAV is aheadk(kWhen HDV status information is lost, due to the k-1st car following the k-th car as the preceding car, in the MVISF modela{pV_F[Δx_n(t)]+(1－p)·V_B[Δx_n－1(t）]}Revealed the trend of front and rear vehicle speed and the significant influence of the distance between the front and rear of the vehicle, and its status information is greatly affected by thekThe limitations and constraints of the vehicle, therefore, can be addressed throughkCopy a virtual vehicle with one vehicle as the main body in thekA car, located bykMeasured by onboard equipment of one vehicle, the status information is consistent with thek-1 vehicle remains consistent; Similarly, it can be inferred that when the CAV is behindh(hWhen the status information of HDV is lost, the following shall apply:h-When one vehicle is used as the main body to replicate a virtual vehicle in the h-th vehicle, but multiple HDV status information are lost in front or behind the CAV, it will be difficult to maintain constraints on speed, acceleration, and other status information when constructing a virtual vehicle. The input information provided by constructing a continuous virtual vehicle for the CAV model will be greatly ineffective. Therefore, if multiple HDV information are lost in front or behind the CAV, the number of vehicles in front and behind the MVISF car following model will be affectedkandhAssign values based on the actual information obtained. The following strategy for mixed vehicles is as followsFigure 3As shown.

Figure 3. Car-following strategies

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3. 仿真验证与应用分析

3.1 混行车辆刹车停止场景

The scenario simulation during the braking process of the vehicle is as follows: assuming that the initial 10 vehicles are traveling at the same speed of 12.8 m · s^-1Moving at a constant speed, the position of each vehicle isx_n0n－1)Δx_n(t）Among themn=1, 2, …, 10，t=At 0:00, the distance between the front of the car is Δx_n(0)=8 m， The remaining parameters are the same as in section 3.1.

$\frac{\mathrm{d} v_n(t)}{\mathrm{d} t}=a\left\{V\left[\Delta x_n(t)\right]-v_n(t)\right\}+k \Delta v_n(t)$

(22)

Table 2. Parameter comparison of braking to stop scenario under different CAV penetration rates

CAV渗透率/%	平均加速度/(m·s^-2)	波速/(m·s^-1)
0	-0.504	10.32
50	-0.532	11.37
100	-0.548	13.01

| Show Table

DownLoad: CSV

Figure 4. Vehicle decelerations under different CAV penetration rates

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From the perspective of the entire fleet, compare the braking and stopping scenarios when CAV penetration rates are 0, 50%, and 100%, respectivelyTable 2It can be seen that CAV can reduce the propagation of speed disturbances caused by braking in mixed traffic environments. When the CAV penetration rate is 50%, the average acceleration decreases by 5.6% compared to full HDV, and the stopping wave speed of the fleet increases by 10.2%. When the CAV penetration rate is 100%, the average acceleration decreases by 8.7% compared to full HDV, and the stopping wave speed of the fleet increases by 26.1%. This indicates that CAV can regulate the overall speed of the fleet, enabling the fleet to complete the braking process in a smoother and faster state.

causeFigure 4It can be seen that the deceleration changes of vehicles 5 and 6 are smoother, with approximate troughs of about 8 m · s^-2Vehicle 7 follows the CAV and has a valley difference of 0.3 m · s relative to Vehicle 4^-2As a result, the deceleration performance of vehicle 8 is also better than that of vehicle 4. Therefore, the speed changes of vehicles 5 and 6 are smoother compared to other vehicles, making the driver's riding experience more comfortable. In addition, vehicles 5 and 6 maintain a smaller distance between the front of the vehicle during position changes, indicating that CAV can better control the vehicle speed until it stops compared to HDV when dealing with braking situations, thus avoiding repeated speed changes of vehicles in the convoy.

3.2 Hybrid vehicle acceleration scenario during startup

Figure 5. Changes in vehicle parameters during braking and deceleration

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Figure 6. Vehicle accelerations under different CAV penetration rates

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Table 3. Comparison of parameters of vehicle starting scenario under different CAV penetration rates

CAV渗透率/%	平均加速度/(m·s^-2)	波速/(m·s^-1)
0	1.041	5.67
50	1.663	6.01
100	1.922	6.55

| Show Table

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Figure 7. Changes in vehicle parameters during acceleration

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In summary, the MVISF car following model and optimization control method can complete vehicle start-up to uniform motion in a shorter time, and after CAV participates in mixed traffic flow motion, the overall acceleration will increase and the acceleration fluctuation time will be shortened, thereby reducing the time required for the entire fleet to start and accelerate.

3.3 混行车辆环形道路场景

In order to further test the proposed hybrid car following strategy and MVISF car following model, verify the effectiveness of the car following strategy and the influence of CAV penetration rate on the speed fluctuation of the fleet after disturbance, the simulation test parameters for the circular road in this section are set as follows: total length of the roadL400 meters, number of vehiclesNFor 100, expected vehicle speedV_maxFor 2 m · s^-1Safe headway distanceh_sFor 4 meters, the HDV also uses the FVD model, and the remaining parameters of the CAV model are the same as those set during the vehicle braking and stopping process. The probability of HDV information loss is 5%, and the position of each vehicle isx_n0n－1)Δx_n(t）In the numerical simulation process, all vehicle displacement expressions arex_n(t)=x_n(t-1)+v_n(t-1)τ+0.5a_n(t-1)τ²The speed expressions are allv_n(t)=v_n(t-1)+a_n(t-1)τConduct ablation and comparative experiments on the stability performance of the fleet using mixed driving following strategies with CAV penetration rates of 60% and 80% as different test scenarios. Two test scenarios are set for small and large disturbances, and CAV penetration rates of 0%, 20%, 40%, 60%, 80%, and 100% are set as different test scenario conditions to compare the stability performance of the fleet.

Figure 8. Vehicle speed fluctuations

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in compliance withFigure 9As shown: When communication information is lost in HDV, if the following strategy is not improved, the HDV with information loss will increase the headway of CAVs around the vehicle to varying degrees. When the CAV penetration rate is 80%, there is some improvement, but there is still a serious impact on the headway; When the penetration rate of CAV is 60%, the most affected CAV has an average headway of 4.315 meters. After using the mixed car following strategy, the fluctuation time of headway is shortened to 256 seconds, and the peak of headway decreases from 4.41 meters to 4.04 meters, a decrease of 8.39% compared to not using the following strategy. The trough increases from 3.87 meters to 3.96 meters, an increase of 2.32% compared to not using the following strategy; When the penetration rate of CAV is 80%, the average headway of the most affected CAV is 4.432 m. After using the mixed car following strategy, the fluctuation time of the headway is shortened to 201 seconds, and the peak of the headway decreases from 4.51 m to 4.04 m, a decrease of 10.42% compared to not using the following strategy. The trough increases from 3.92 m to 3.96 m, an increase of 1.02% compared to not using the following strategy.

Figure 9. Vehicle headway fluctuations

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Figure 10. Speeds of mixed traffic flow under slight speed disturbance

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Under significant disturbances, the initial speed of 100 vehicles on the roadv_n0V[Δx_n(0)], then apply a disturbance term to the head vehicle, that is, change the position x₁(1)=Δx_n(1) +2, then observe the operational status of the entire fleet when the CAV penetration rates are 0, 20%, 40%, 60%, 80%, and 100%, respectivelyFigure 11As shown, the average speed fluctuation time of the vehicle has been shortened from 348 s to 192 s, a decrease of 44.8% compared to low CAV penetration rate, and the peak has increased from 0.88 m · s^-1Decreased to 0.83 m · s^-1Compared to the low CAV permeability, the decrease is 5.7%, and the trough is 0.62 m · s^-1Rising to 0.74 m · s^-1Compared to low CAV permeability, it increased by 19.4%.

Figure 11. Speeds of mixed traffic flow under large speed disturbance

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4. 结语

(4) This article only considers the mixed traffic environment composed of HDV and CAV vehicles, and further attention needs to be paid to more diverse and complex heterogeneous traffic subject models in future research. In addition, given the limitations of numerical simulation scenarios and model parameter settings, with the implementation of future CAV real vehicle experiments, the next step will be to use CAV real vehicle operation data to reconstruct the model more accurately, thereby improving the model's ability to reproduce the actual mixed traffic environment operating state.

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Car-following model and optimization strategy for connected and automated vehicles under mixed traffic environment

doi: 10.19818/j.cnki.1671-1637.2023.03.018