###### Abstract
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Type** & **Name** & **Year** & **Main Contribution** \\ \hline \multirow{8}{*}{Stimulus–response models} & General Motor & \multirow{2}{*}{1953} & The model calculated the safe following distance based on the velocity of the preceding and following vehicles. \\ \cline{2-3}  & & & The trajectory of the rear car was only a copy of the trajectory of the preceding car after a certain time interval and distance interval, and the trajectory trend in the front and rear cars was always consistent. \\ \cline{2-3}  & Optimal Velocity & \multirow{2}{*}{1995} & The model gave a functional relationship between head spacing and optimal velocity. \\ \cline{2-3}  & & & The same model was used to describe the driver’s following behavior in the traffic flow state from free driving state to traffic congestion state. \\ \cline{2-3}  & Full Velocity & \multirow{2}{*}{2001} & The model considered the impact on vehicle acceleration when the velocity difference between the front and rear vehicles is positive or negative. \\ \cline{2-3}  & [PERSON] model & \multirow{2}{*}{1959} & The model calculated the safe following distance based on the velocity of the preceding and following vehicles. \\ \cline{2-3}  & Gipps model & \multirow{2}{*}{1981} & The model took into account the safety distance and acceleration constraints of the vehicle. \\ \cline{2-3}  & [PERSON] model & \multirow{2}{*}{2003} & The model takes the time headway into account from the driver’s subjective awareness. \\ \hline \multirow{8}{*}{Psycho-spacing models} & [PERSON] & \multirow{2}{*}{1963} & Psycho-physiological model hypothesis proposed by combining psychology with the car-following model theory for the first time \\ \cline{2-3}  & Wiedemann model & \multirow{2}{*}{1974} & The model took the driver’s psychological threshold as parameters. \\ \cline{1-1} \cline{2-3}  & Driving by Visual & \multirow{2}{*}{2007} & The driver’s visual information was the main factor affecting the acceleration \\ \cline{1-1} \cline{2-3}  & Angle model & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Overview table of the main car-following models. avoidance pedestrian assistance system by quantifying the lateral demand distance and forward demand distance of traffic individuals. However, research on applying PS to the analysis of traffic flow is still lacking. The stability analysis of mixed traffic flow considering PS under the connected and automated environment mainly focuses on two aspects: the improvement of the car-following model, and the analysis of the linear stability of the model. (1) In the HD-CACC mixed traffic flow environment, based on the classical IDM, an IDM model considering PS is established. In the model, it is necessary to specifically consider how the PS is represented in the car-following model, and the difference between the CACC and HD vehicle car-following models. (2) Traffic flow stability is an important indicator for judging traffic systems against disturbances [15]. Based on the above model, the traffic flow following stability under different parameter configurations is analyzed. Compared with the classic IDM, the effectiveness of PS for maintaining stability needs to be verified. This paper introduces PS into the study of the car-following behavior of individuals in traffic and constructs a car-following model by considering PS in the environment of HD-CACC mixed traffic flow. Further, the stability domain of the car-following model is analyzed through the linear control theory method, and the validity of the model is verified by comparing it with the classic IDM. This paper is structured as follows. Section 1 is the literature review and problem statement. Section 2, Section 3, and Section 4 cover the test analysis model construction, and stability analysis, respectively. Section 5 discusses the model, and Section 6 verifies the stability and effectiveness through experimental simulation. Finally, Section 7 concludes this paper.