Car-following Research Articles

ATAC-Based Car-Following Model for Level 3 Autonomous Driving Considering Driver’s Acceptance

To date, commercial fully autonomous driving is not realized, while level 3 is the next step in the development of autonomous driving. At level 3, the vehicle is driving under the control of the machine, but when feature requests, human driver must take over control. Therefore, autonomous driving control should consider not only efficiency and safety but also human driver’s acceptance. This paper develops a car-following (CF) model as a longitudinal control strategy for level 3 autonomous driving based on the automating entropy adjustment on Tsallis actor-critic (ATAC) algorithm. 1641 pairs of CF trajectories extracted from the Next Generation Simulation (NGSIM) data are applied to train the reinforcement learning (RL) agent. Based on the empirical data distributions, we use time margin, time gap, and jerk to construct the reward function and testify the proposed CF model’s merits. Simulation results show that the proposed model can enable vehicles to drive safely, efficiently, and comfortably. The proposed model has good stability, and the generated driving behaviors are more acceptable for drivers. This work sheds light on developing a better autonomous driving system from the perspective of human factors.

Impact of Variability of Car-Following Parameters on Road Capacity: The Simple Case of Newell’s Model

This paper contributes to the vehicle-level analysis of two macroscopic features of the road traffic: capacity variability and capacity drop. This paper focuses only on car-following (CF) behavior and leaves the part related to lane-change maneuvers for future research. In particular, a simplistic CF model (Newell’s with bounded acceleration) for a single-lane scenario is studied. In this work, by introducing a speed limitation across a zone, a bottleneck with variable nominal capacity has been created. A continuous event-based numerical resolution method is used. Consequently, it is possible to vary the three Newell’s model parameters: maximal acceleration, minimal distance, and reaction time. It has been shown that the variability of those CF parameters (e.g., reaction time, minimal distance, and maximal acceleration) has a strong impact on pre-breakdown capacity variation and also on queue discharge flow. It has been concluded that this parameters variability does affect the drop (provided that the maximal acceleration has a relatively high mean value). Various distribution shapes (uniform, truncated Gaussian, and Gamma) have been explored. It has been realized that this does not have any significant impact on the capacity distribution. Concerning the amplitude of the capacity distribution, it is demonstrated that reaction time is the parameter with the highest impact followed by minimal distance. If all parameters vary with an amplitude of 30%, it is shown that the capacity standard deviation, in this scenario without lane changes, is about half the experimental values reported in the literature.

Congestion-mitigating MPC design for adaptive cruise control based on Newell’s car following model: History outperforms prediction

Currently, model predictive control (MPC) for adaptive cruise control (ACC) systems relies on the prediction of the leader’s motion to plan the follower’s trajectory. However, such predictions must be accurate to guarantee string stability, which represents an ongoing challenge for machine learning approaches. This issue can be circumvented by simply incorporating the leader’s history, which follows from Newell’s car-following (CF) model where a trajectory under congestion corresponds to a temporal–spatial shift of the leader’s past trajectories. By leveraging this insight, this paper develops a family of MPC models based on Newell’s CF model, labeled Newell MPCs, which are safe and can reduce traffic congestion.Specifically, We first present baseline Newell MPCs to replicate the original Newell’s CF model, including the Xbound-Model, which uses the shifted leader trajectory as an upper envelope; and the Xref-Model, which adopts the shifted leader trajectory as a reference to avoid the issue of infeasible solution triggered by hard constraints. To further improve the control performance, we propose the XV-Model which uses the leader speed history as an additional reference to enhance the model robustness and regulate speed over/under-shootings. In addition, we extend the single-leader Newell’s model through incorporating multiple leaders and propose the Xmul-Model, which can achieve driver anticipation, and correspondingly reduce reaction time and improve string stability. Finally, based on the XV-Model, we present two additional extensions: (i) the XVrelax-Model, which incorporates driver relaxation to achieve smooth response to merging traffic; and (ii) the XVss-Model, which achieves strict string stability to further dampen traffic oscillations. The proposed Newell MPCs are tested using both numerical simulations and field studies on a stock 2019 Honda Civic using Openpilot and Comma.ai; the source code is available at https://github.com/HaoZhouGT/openpilot.

Car following with an inertia-oriented driving technique: A driving simulator experiment

BackgroundFor many decades, car-following (CF) and congestion models have assumed a basic invariance: drivers’ default driving strategy is to keep the safety distance. The present study questions that Driving to keep Distance (DD) is a traffic invariance and, therefore, that the difference between the time required to accelerate versus decelerate must necessarily determine the observed patterns of traffic oscillations. Previous studies have shown that drivers can adopt alternative CF strategies like Driving to keep Inertia (DI) by following basic instructions. The present work aims to test the effectiveness of a DI course that integrates 4 tutorials and 4 practice sessions in a standard PC computer designed to learn more adaptive driving behaviors in dense traffic. Methods. Sixty-eight drivers were invited to follow a leading car that varied its speed on a driving simulator, then they took a DI course on a PC computer, and finally they followed a fluctuating leader again on the driving simulator. The study adopted a pretest-intervention-posttest design with a control group. The experimental group took the full DI course (tutorials and then simulator practice). The control group had access to the DI simulator but not to the tutorials. Results. All participating drivers adopted DD as the default CF mode on the pre-test, yielding very similar results. But after taking the full DI course, the experimental group showed significantly less accelerations, decelerations, and speed variability than the control group, and required greater CF distance, that was dynamically adjusted, spending less fuel in the post-test. A group of 8 virtual cars adopting DD required less space on the road to follow the drivers that took the DI course.

Influence of driving style on traffic flow fuel consumption and emissions based on the field data

Driving style (DS) is an important factor affecting vehicle fuel consumption and emissions (FCE). Here, the relationship between DS and traffic flow FCE under different scenarios has been explored by using open-source field data. DS classification model and two car-following (CF) models for aggressive and cautious DSs were trained by using the field data. Furthermore, we performed numerical simulation experiments, where the speed profiles of the leading vehicles come from the field data. The results indicate that DS has no significant correlation with CO or HC emissions, but has strong correlations with fuel consumption, NOx, and CO2 emissions (FNC). Moreover, the influence of DS on FNC is related to the leader state which can be described by four kinematic parameters: Drive time spent accelerating, Drive time spent decelerating, Average positive acceleration, and Average negative acceleration. Specifically, the penetration rate of aggressive drivers contributes to a 3% absolute change of the FNC, and the position leads to a 1.5% absolute change of the FNC, while the sign of the change is determined by the leading vehicle state. As the intelligent transportation system attracts more and more attention, these findings can give insight for traffic managers and vehicle designers into realizing eco-driving.

Physics-augmented models to simulate commercial adaptive cruise control (ACC) systems

This paper investigates the accuracy and robustness of car-following (CF) and adaptive cruise control (ACC) models in reproducing measured trajectories of commercial ACCs. To this aim, a general modelling framework is proposed, in which ACC and CF models have been incrementally augmented with physics-based extensions: namely, perception delay, linear or nonlinear vehicle dynamics, and acceleration constraints. This framework has been applied to the Intelligent Driver Model (IDM), Gipps’ model, and to three basic ACC algorithms. These are linear controllers which are coupled with a constant time-headway spacing policy, and with two other policies derived from the traffic flow theory: the IDM desired distance function, and Gipps’ equilibrium distance-speed function. The ninety models resulting from the combination of the five base models with the aforementioned extensions, have been assessed and compared through a vast calibration and validation experiment against measured trajectory data of vehicles driven by ACC systems. Overall, the study has shown that physics-based extensions provide limited improvements to the accuracy of existing models. In addition, if an investigation against measured data is not carried out, it is not possible to argue which extension is the most suited for a specific model. The linear controller with Gipps’ spacing policy has resulted the most accurate model, while the IDM the most robust to different input trajectories. Eventually, all models have failed to capture the behaviour of some car brands – just as models fail with some human drivers. Therefore, the choice of the “best” model is independent of the car brand to simulate.

Physical Model versus Artificial Neural Network (ANN) Model: A Comparative Study on Modeling Car-Following Behavior at Signalized Intersections

Many studies have simulated traffic behavior at signalized intersections using various Car-Following (CF) models. However, the performance of which CF Model is superior at signalized intersections has not been thoroughly analyzed and evaluated. In this study, two novel Artificial Neural Network (ANN) CF models, the Convolutional Neural Network—Long Short-term Memory (CNN-LSTM) and the Convolution-LSTM (Conv-LSTM)—are first applied to predict CF behaviors at signalized intersections. Both models can extract spatial and temporal information to address the long-term dependency problem more effectively. Based on the filtered NGSIM dataset, we conduct a comparative empirical study of three conventional CF models and five ANN CF models. The dataset is divided into two categories based on the characteristics of CF behavior at signalized intersections: continuous and discontinuous. The experiments demonstrated that ANN CF models outperformed conventional CF models when the output was the velocity in two categories of traffic flow but only failed to do so when the output was acceleration in discontinuous traffic flow. The proposed models were capable of accurately predicting acceleration, but the traffic fluctuations also existed as time passed. Additionally, it was discovered that while the ANN CF model is preferable for traffic flow simulation, the conventional CF model still cannot be ignored for discontinuous traffic flow simulation, particularly when acceleration is required.

A Motion Planning Method for Automated Vehicles in Dynamic Traffic Scenarios

We propose a motion planning method for automated vehicles (AVs) to complete driving tasks in dynamic traffic scenes. The proposed method aims to generate motion trajectories for an AV after obtaining the surrounding dynamic information and making a preliminary driving decision. The method generates a reference line by interpolating the original waypoints and generates optional trajectories with costs in a prediction interval containing three dimensions (lateral distance, time, and velocity) in the Frenet frame, and filters the optimal trajectory by a series of threshold checks. When calculating the feasibility of optional trajectories, the cost of all optional trajectories after removing obstacle interference shows obvious axisymmetric regularity concerning the reference line. Based on this regularity, we apply the constrained Simulated Annealing Algorithm (SAA) to improve the process of searching for the optimal trajectories. Experiments in three different simulated driving scenarios (speed maintaining, lane changing, and car following) show that the proposed method can efficiently generate safe and comfortable motion trajectories for AVs in dynamic environments. Compared with the method of traversing sampling points in discrete space, the improved motion planning method saves 70.23% of the computation time, and overcomes the limitation of the spatial sampling interval.

Inference of HDVs real-time locations in mixed autonomous traffic flow scenario

In the near future, the road traffic flow will consist of both human-driven vehicles (HDVs) and connected autonomous vehicles (CAVs). Since HDVs cannot communicate with CAVs and road side units (RSU), they are unobservable to CAVs if outside the range of sensing. In such case, the advantages of CAVs will be compromised and various high-level tasks in mixed autonomous traffic flow cannot be achieved. This study proposes a model to infer HDVs information using sensing data of CAVs. The rationale is that CAVs react to HDVs based on the car-following (CF) logic. Inversely, real-time locations of HDVs can be reconstructed using the data from CAVs. The Bayesian network is used to reflect the CF logic and develop a real-time vehicle location inference method for both single and multiple CAVs scenarios. Last, the method is tested using real-world dataset. Both time consumption and near-field estimation precision are validated.

Connected and automated vehicle distributed control for on-ramp merging scenario: A virtual rotation approach

This study proposes a rotation-based connected automated vehicle (CAV) distributed cooperative control strategy for an on-ramp merging scenario. By assuming the mainline and ramp line are straight, we firstly design a virtual rotation approach that transfers the merging problem to a virtual car following (CF) problem to reduce the complexity and dimension of the cooperative CAVs merging control. Based on this concept, a multiple-predecessor virtual CF model and a unidirectional multi-leader communication topology are developed to determine the longitudinal behavior of each CAV. Specifically, we exploit a distributed feedback and feedforward longitudinal controller in preparation for actively generating gaps for merging CAVs, reducing the voids caused by merging, and ensuring safety and traffic efficiency during the process. To ensure the disturbance attenuation property of this system, practical string stability is mathematically proved for the virtual CF controllers to prohibit the traffic oscillation amplification through the traffic stream. Moreover, as a provision for extending the virtual CF application scenarios of any curvy ramp geometry, we utilize a curvilinear coordinate to model the two-dimensional merging control, and further design a local lateral controller based on an extended linear-quadratic regulator to regulate the position deviation and angular deviation of the lane centerlines. For the purpose of systematically evaluating the control performance of the proposed methods, numerical simulation experiments are conducted. As the results indicate, the proposed controllers can actively reduce the void and meanwhile guarantee the damping of traffic oscillations in the merging control area.

Comparing the Effect of Age, Gender, and Desired Speed on Car-Following Behavior by Using Driving Simulator

In this study, the effect of age, gender, and desired speed (DS) factors on General Motors car-following (CF) behavior was investigated. DS was defined as the speed selected by the driver in free driving situation. A low-level driving simulator was used to collect data. The CF model for each driver was calibrated by genetic algorithm. Gender and DS were effective in CF behavior, while the age factor was not. The drivers’ sensitivity to the variables of speed and distance in the CF model increased with increasing the DS. The gender factor affected only the magnitude of deceleration which was higher in women. For further investigation, the effect of the desired speed on the time headway in the steady-state CF was also examined. DS factor was effective in steady-state CF behavior. As the DS increased, the time headway decreased. Examining CF threshold demonstrated that women maintained larger distance than men. Finally, it can be said that DS and gender would be more important than age to be considered in CF models.

Factors affecting motorcyclists’ behavior in car-following condition

Car-following (CF) maneuver plays an important role in both traffic flow analysis and road safety assessment. However, many studies on this issue have focused on the drivers’ behaviour, neglecting the different driving behaviour of the motorcycle riders and the vulnerability of this type of user. The aim of the present paper is to analyse the factors affecting the riders’ behaviour in CF condition, by using two surrogate safety indicators, Time Headway (TH) and Time To Collision (TTC). A field experiment was conducted to collect data. Twenty young motorcyclists participated in the study driving their own motorcycles, which were instrumented with a camera and a global positioning system device (GPS). A digital image processing algorithm was used to obtain CF related indicators. The results of the study showed that Time Headway (TH) and Time To Collision (TTC) are independent of each other, extending the result obtained in the literature for the four wheeled vehicles to the motorcycles. TTC and TH were therefore analyzed separately. As for TTC, it was observed that only in few cases (0.8%) the riders were found in risky condition (TTC < 5 s), confirming the role of this parameter for the detection of an impending risk. On the other hand, TH gives information about a potentially risky situation, and 99% of the riders were found in such condition (TH < 2 s). Due to the few cases in TTC risky conditions, only TH was further modelled by using the hazard-based duration analysis. Accelerated Failure Time (AFT) model specification was used, and the Weibull distribution provided the best fit of the data. The model identified four covariates affecting TH and all of them had the effect of reducing TH, increasing the collision risk. The time spent on CF condition, the speed of the motorcycle, the willingness of overtaking and the engine size of the motorcycle were the factors that reduced TH.The findings of this study could be considered in the development of microsimulation models; the factors that were found affecting the motorcyclists’ behavior in car-following condition could be considered for a more realistic simulation of the riders’ choice of Time Headway.

A comprehensive comparison study of four classical car-following models based on the large-scale naturalistic driving experiment

Car-following (CF) is the most basic human driving behavior, which is the vital component of traffic flow theories, traffic simulation, and traffic operation. Over the past decades, numerous CF models have been developed based on different interaction logics between the following vehicle and the leading vehicle. Among these, four categories of CF models are the most widely studied and have been long adopted in different traffic simulation systems. The representative models are the Gazis-Herman-Rothery (GHR) model (stimuli-response category), Gipps model (safety distance category), intelligent driver model (IDM) (desired measures category), Wiedemann model (psycho-physical category). However, there is still a lack of comprehensive comparisons of the four classical CF models, especially their adaptabilities to key influencing factors (driving styles and traffic flow facilities). This study adopted the large-scale naturalistic driving data to conduct a comprehensive comparison of four classical CF models through over 5,000 extracted CF events. The results prove that the IDM performs best in depicting the CF behavior overall, as well as in various driving styles and traffic flow facilities, since the error of the IDM is at least lower than the GHR model, Gipps model, and Wiedemann model 16.16%, 19.51%, and 56.75%, respectively. Then, the best-performed IDM model was further improved with an additional term described by an α-stable distribution, to better reproduce heterogeneity in simulation practice. It has a remarkable performance with only one parameter freedom, decreasing over 59% error than the fixed-parameter IDM. These findings could provide better guidance for the choice and the development of the basic CF model in traffic simulation systems.

Surrounding Vehicles’ Contribution to Car-Following Models: Deep-Learning-Based Analysis

Relatively recent increased computational power and extensive traffic data availability have provided a unique opportunity to re-investigate drivers’ car-following (CF) behavior. Classic CF models assume drivers’ behavior is only influenced by their preceding vehicle. Recent studies have indicated that considering surrounding vehicles’ information (e.g., multiple preceding vehicles) could affect CF models’ performance. An in-depth investigation of surrounding vehicles’ contribution to CF modeling performance has not been reported in the literature. This study uses a deep-learning model with long short-term memory (LSTM) to investigate to what extent considering surrounding vehicles could improve CF models’ performance. This investigation helps to select the right inputs for traffic flow modeling. Five CF models are compared in this study (i.e., classic, multi-anticipative, adjacent-lanes, following-vehicle, and all-surrounding-vehicles CF models). Performance of the CF models is compared in relation to accuracy, stability, and smoothness of traffic flow. The CF models are trained, validated, and tested by a large publicly available dataset. The average mean square errors (MSEs) for the classic, multi-anticipative, adjacent-lanes, following-vehicle, and all-surrounding-vehicles CF models are 1.58 × 10−3, 1.54 × 10−3, 1.56 × 10−3, 1.61 × 10−3, and 1.73 × 10−3, respectively. However, the results show insignificant performance differences between the classic CF model and multi-anticipative model or adjacent-lanes model in relation to accuracy, stability, or smoothness. The following-vehicle CF model shows similar performance to the multi-anticipative model. The all-surrounding-vehicles CF model has underperformed all the other models.

Simulation of mixed traffic with cooperative lane changes

AbstractThis study proposes a mixed traffic simulation framework that integrates vehicle car‐following (CF) and lane‐changing (LC) with connected and automated vehicles (CAVs) of different cooperation behaviors. This framework is centered at a CAV LC model incorporated with CF dynamics in mixed traffic. The model was calibrated and validated using data collected from small‐scale field experiments in a previous study. To demonstrate a large‐scale application of this framework, PTV Vissim was used to implement the framework on a segment of Interstate 75 highway. Sensitivity analyses were conducted to investigate the impacts of key parameters on traffic mobility and stability performance. The results show that traffic performance degraded as the traffic demand and vehicle diverging rate increased. As the CAV penetration rate increased, traffic performance fluctuated when CAVs were more conservative. As the CAV cooperation rate, incentive criterion threshold, and incentive criterion bias increased, mobility and stability performance first improved and then degraded. When CAV platooning was considered, traffic performance was enhanced. These findings shed light on mixed traffic management from the perspectives of both transportation operators (e.g., facilities and policies to promote vehicle cooperation) and automakers (e.g., tuning parameters in their LC models) to achieve the best traffic performance.

On multi-class automated vehicles: Car-following behavior and its implications for traffic dynamics

This paper develops a unifying framework to unveil the physical car-following (CF) behaviors of automated vehicles (AVs) under different control paradigms and parameter settings. The proposed framework adopts the flexible asymmetric behavior (AB) model to reveal the control mechanisms and their manifestation in the physical CF behavior, particularly their response to traffic disturbances. A mapping relationship between the AB model parameters and control parameters is then obtained to understand the range of CF behavior possible. Finally, a predictive modeling approach based on a logistic classifier coupled with a convoluted Multivariate Gaussian Process (MGP) is designed to predict the CF behavior of an AV. Analysis of two well-known controllers, linear state-feedback and Model Predictive Control (MPC), show how the proposed framework can uncover the CF mechanisms and provide insights into traffic-level disturbance evolution. The proposed analysis framework remains scalable and can be applied to a variety of controllers. Ultimately, it can guide AV control design that is not myopic, but considers traffic-level performance.

Driving control based on bilevel optimization and fuzzy logic

Driving control in the car-following (CF) driving behavior has two aspects. First, in what measure an approximation distance is taken as a safe distance guaranteeing the safety of the follower drivers. Second, how to control the follower's vehicle velocities based on the stimulus of the leading vehicle. In this context, to resolve the driving control problem in the CF driving behavior, a bilevel optimization is presented in this paper, based on the behaviors of the follower and leader drivers. Bearing in mind that mathematics has contributed to the imitation of human behaviors, they are now reaching a level of complexity requiring the entry on the scene of a new player, which is artificial intelligence. Thus, in this paper; we used the fuzzy logic theory for modeling a follower driver with a nonnormative behavior. To validate our model, we used a data set from the program of the US Federal Highway Administration. Therefore, according to the experimental results, there is homogeneity between the actual and the simulated travel trajectories in terms of deviation. Besides, the driver's behavior adopted (normative or nonnormative) is reflected in his reactions to the various components of the road.

Development of parametric eco-driving models for fuel savings: A novel parameter calibration approach

The existing conventional traffic flow models aims to simulate human-driven following vehicles in real world. In this era of emerging transport solutions, controlling or intervening traffic flow to achieve high fuel efficiency along with good driving safety and travel efficiency becomes a reality. As such, it is worth exploring the possibility of developing eco-driving models to optimise vehicle movements for fuel consumption minimisation, while maintaining safety and efficiency. In this study, we propose a modified genetic algorithm (GA) based calibration method that enables the calibrated parametric traffic flow (car following) models to simulate or control vehicles in an eco-driving manner. By developing a novel objective function for the GA method based on the widely-used VT-Micro fuel consumption model, the proposed method can calibrate model parameters towards improving fuel efficiency. Besides, by subtly using heavy fuel consumptions as a surrogate index to represent low travel efficiency or dangerous driving strategies, the modified GA method with the novel objective function can guide the calibrated model towards achieving complete eco-driving requirements. Experimental simulation results further indicate that traffic flow models calibrated by the modified GA-based method can also alleviate traffic disturbances and oscillations in a more effective manner.

A data-driven feature learning approach based on Copula-Bayesian Network and its application in comparative investigation on risky lane-changing and car-following maneuvers

The era of ‘Big Data’ provides opportunities for researchers to have deep insights into traffic safety. By taking advantages of ‘Big Data’, this study proposes a data-driven method to develop a Copula-Bayesian Network (Copula-BN) using a large-scale naturalistic driving dataset with multiple features. The Copula-BN is able to explain the causality of a risky driving maneuver. As compared with conventional BNs, the Copula-BN developed in this study has the following advantages: the Copula-BN 1. Has a more rational and explainable structure; 2. Is less likely to be over-fitting and can attain more satisfactory prediction performance; and 3. Can handle not only discrete but also continuous features. In terms of technical innovations, Shapley Additive Explanation (SHAP) is used for feature selection, while Gaussian Copula function is employed to build the dependency structure of the Copula-BN. As for applications, the Copula-BNs are used to investigate the causality of risky lane-changing (LC) and car-following (CF) maneuvers, upon which the comparisons are made between the two essential but risky driving maneuvers. In this study, the Copula-BNs are developed based on the Second Highway Research Program (SHRP2) Naturalistic Driving Study (NDS) database. Upon network evaluation, the Copula-BNs for both risky LC and CF maneuvers demonstrate satisfactory structure performance and promising prediction performance. Feature inferences are conducted based on the Copula-BNs to respectively illustrate the causation of the two risky maneuvers. Several interesting findings related to features’ contribution are discussed in this paper. To a certain extent, the Copula-BN developed using the data-driven method makes a trade-off between prediction and causality within the ‘Big Data’. The comparison between risky LC and CF maneuvers also provides a valuable reference for crash risk evaluation, road safety policy-making, etc. In the future, the achievements of this study could be applied in Advanced Driver-Assistance System (ADAS) and accident diagnosis system to enhance road traffic safety.

MVCM Car-Following Model for Connected Vehicles and Simulation-Based Traffic Analysis in Mixed Traffic Flow

Although there have been assorted car-following (CF) models for connected vehicles (CVs), studying their impacts in mixed traffic flow of human-driven vehicles (HVs) and CVs remains a challenge. Considering the multiple front vehicles’ optimal speed changes with memory, this study proposed a new CF model (MVCM model) implemented through vehicle-to-everything (V2X) technology in CVs environment in terms of OVCM (Optimal Velocity Changes with Driving Memory) model. The stability condition of MVCM model was derived through linear stability analysis. Then, the disturbance propagation of MVCM model was compared with that of both classical FVD (Full Velocity Difference) model and MHOVA (Multiple Headway Optimal Velocity and Acceleration) model. Finally, a case study was conducted in VISSIM to analyze the impact of CV (with MVCM model) rates on traffic characteristics, including the average speed, delay time and travel time. Results show that 1) considering more front vehicles’ optimal speed strengthens the stability of traffic flow and the optimal considered vehicle number is 4; 2) MVCM model shows better resistance to disturbance than FVD model; 3) and obtain the same stability with MHOVA model, but with fewer front vehicles considered (only 3); 4) larger rate of CVs leads to higher average speed, smaller average travel time and the delay time of CVs and HVs; and 5) CVs’ positive effects reaches stable when CV rate approaches 0.6.