## 7 Conclusions  
(1) Aiming at the HD-CACC mixed traffic flow, this study establishes a car-following PS-IDM model based on an intelligent driver model by considering personal space. Using theoretical analysis and MATLAB simulation experiments, the stability regions of homogeneous traffic flows under different PS and heterogeneous traffic flows with different CASC vehicle permeabilities were analyzed. The results show that the PS-IDM model can improve the driving comfort by up to 20.7% compared with a single IDM model, and the average PS intrusion rate is reduced by 4.6%, which verifies the effectiveness of the PS-IDM model.  
(2) The analytical results of the traffic flow stability of car-following behavior, considering PS, indicates that the unstable velocity range of homogeneous or heterogeneous traffic flows decreases with an increase in PS. In addition, the unstable velocity range of the CASC vehicle traffic flow has a negative correlation with the acceleration feedback coefficient. The increased penetration rate of CASC vehicles with the acceleration feedback coefficient below 0.2 could not turn an unstable traffic flow into a stable traffic flow; when the acceleration feedback coefficient exceeded 0.2, the increase in CASC vehicle permeability can effectively transform the stability of traffic flow. Regardless of the value of the acceleration feedback coefficient, increasing the time headway can make the traffic flow to a stable state. Therefore, an increase in the longitudinal distance of the vehicle PS is beneficial to the stability of the traffic flow.  
(3) The results of the numerical simulation experiments were consistent with the analytical results of the stability theory. The model and experiment in this study made assumptions regarding the lane conditions. In the future, we will analyze the lateral factors influencing the multi-lane situation and conduct in-depth research on the lateral distance. In addition, because different values of the acceleration feedback coefficient can correspond to HD, multi-level individual intelligent vehicles, and multi-level connected automated vehicles, further analysis and research on the stability of complex heterogeneous traffic flows will be conducted.  
Conceptualization, X.H. and M.Z.; methodology, X.H.; software, M.Z. and B.L; validation, X.H., M.Z. and J.Z.; formal analysis, J.Z. and G.D.; investigation, B.L. and G.D.; resources, B.L. and G.D.; data curation, B.L., M.Z. and J.Z.; writing--original draft preparation, X.H. and M.Z.; writing--review and editing, M.Z. and J.Z.; visualization, X.H., G.D. and J.Z.; supervision, X.H. and B.L.; project administration, X.H.; funding acquisition, X.H. All authors have read and agreed to the published version of the manuscript.  
Figure 11: Fitting curve of average intrusion rate.  
**Funding:** This research was supported in part by the Chongqing Postgraduate Joint Training Base Project (Chongqing Jiaotong University-Chongqing YouLiang Science & Technology Co., Ltd. Joint Training Base for Postgraduates in Transportation), under Grant JDLHYPJ2019007, and in part by the Sichuan Science and Technology Program, under Grant No. 2022 YFG0132.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Due to the nature of this research, participants of this study did not agree for their data to be shared publicly, thus supporting data are not available.  
**Conflicts of Interest:** The authors declare no conflict of interest.