###### Abstract  
A traffic survey using an unmanned aerial vehicle on the Haixia road in Chongqing, China found a significant correlation between the velocity of the vehicle and the distance of the vehicle when moving forward and laterally. To mitigate driving disruptions owing to vehicle intrusion at a desired distance, personal space (PS) is introduced to analyze the car-following behavior of continuous mixed traffic flow formed by human-driven (HD) vehicles and cooperative adaptive cruise control (CACC) vehicles. PS is a virtual boundary that refers to the space where psychological tension is caused by the invasion of others. Further, an intelligent driver model (IDM) was used to establish a mixed traffic car-following PS-IDM. The stability of the disturbance transfer function analytical model in homogeneous and heterogeneous traffic flows was used to calculate the traffic flow stability region under different CACC vehicle permutations. The results show that the PS-IDM-based car-following model effectively improves the stability fitting effect of mixed traffic flow, and the driving comfort is increased by up to 20.7% when compared with that of the single car-following model. In addition, there is a negative correlation between the PS and the unstable velocity range of the traffic flow. Compared with the homogeneous HD traffic flow, the average intrusion rate of homogeneous CACC traffic flow is reduced by 4.6%, and the driving comfort of vehicles is improved by approximately 65%. traffic engineering: personal space; stability region; mixed traffic flow; car-following model; connected and automated +
Footnote †: journal: Applied  
the microscopic model. On this basis, [PERSON] et al. [5] reviewed 70 years of research on the car-following model. An overview of the main car-following model is shown in Table 1.  
The early car-following model considered the velocity difference between the front and rear cars and the safety distance separately. The optimal velocity model had more comprehensive considerations and was more widely used in simulations; however, it did not consider the acceleration of the leading car [6]. The full velocity difference model compensated for this shortcoming [7]. The intelligent driver model (IDM) is a car-following model proposed in the context of autonomous driving based on reasonable assumptions [8]. The model showed controllable stability in the simulation of actual highway data. It can produce real acceleration distribution and reasonable behavior in all single-lane traffic situations. [PERSON] et al. [9] used IDM to analyze heterogeneous traffic flow mixed with CACC vehicles, and the verification analysis showed that the model can better describe the driving behavior in the intelligently networked environment. Subsequently, researchers mainly improved the IDM model from the perspective of traditional driving characteristics [10] and autonomous driving technologies [11]. However, these models assume that vehicles are driving on the centerline of the lane and do not fully consider the effect of lateral spacing [12]. Therefore, this paper introduces the personal space (PS) to improve the applicability of the car-following model. PS is a domain concept that refers to the space where psychological tension is caused by the invasion of others. In society, individuals have their own PS [13]. In transportation, [PERSON] et al. [14] applied PS to personal mobility vehicles and established a PS-based