## 1 Introduction  
With the continuous advancement in information and network technology, connected and automated vehicles (CAVs) have emerged at the request of the times. With the support of advanced communication technology, traffic information can be transmitted in real time between vehicles, roads, and drivers. CAVs can offer great help in improving the efficiency of traffic flow and optimizing users' riding experience. The traffic flow will be mixed up with the gradually popularized CAVs and regular vehicles (RVs, i.e., human-driven vehicles) in the future. Therefore, it is significant to study the MTF composed of intelligent CAVs and RVs. Car-following behavior is the most common behavior in the driving process that describes the interactive mechanism between vehicles traveling along the same lane from a microscopic perspective. Car-following theorization is conducive to higher efficiency and stability of traffic flows. On a theoretical basis, car-following modeling further dealswith the characteristics of car-following behavior. In the late 1950s, [PERSON] et al. [1] put forward a famous multi-vehicle following hypothesis. Later, [PERSON] et al. [2] proposed a car-following model based on the optimized speed function to characterize the effect of headway on the following vehicles. Based on [PERSON]'s model, [PERSON] et al. [3] analyzed the effect of the speed difference and established the optimal vehicle model (OVM). Subsequently, numerous scholars [4; 5] completely extended the OVM model according to the impact of multi-vehicle information on car-following behavior. Taking a different approach, [PERSON] et al. [6] established an intelligent driver model (IDM) with physical significance which was easy to calibrate. The idea of this model is to obtain the following rules of vehicles according to the relationship between the actual speed of the considered vehicle and the speed and position of the front vehicle. The development of the IDM involved two main aspects. First, such factors as time delay were analyzed from the perspective of artificial driving characteristics. For example, focusing on the time delay, measurement error, and time prediction, [PERSON] et al. [7] proposed the human driver model (HDM). [PERSON] et al. [8] established the task difficulty car-following framework on intelligent driver model (TDIDM) by introducing the difficulty of driving tasks as the dynamic interaction between driving task requirements and the driver's capability. Second, the influences of multi-vehicle speed, acceleration, and headway on car-following behavior were explored based on the cooperative vehicle infrastructure system. With consideration of the acceleration information about the front vehicle, [PERSON] et al. [9] improved the extended IDM proposed by [PERSON] et al. [10] with consideration of the expected acceleration of the front vehicle and verified its stability through theoretical analysis. With the advancement of Internet of Vehicles technology, CAV is closer to people's real life, research on the MTF composed of CAV and RV has become more abundant. [PERSON] et al. [11] deduced a basic graph model for MTF at distinct penetration rates of CAVs and analyzed and optimized the stability of MTF to improve the safety of traffic flow. [PERSON] et al. [12] considered the four types of car-truck following combinations and explored the effect of different combinations on the stability by the original [PERSON]'s optimal velocity (OV) model to heterogeneous form. According to the systematic framework for the analysis of mixed-traffic problems, [PERSON] et al. [13] analyzed the stability of MTF and the energy consumption of vehicles in three different modes of intelligent networked vehicle control (ACC, CACC, and CCC), using the infinite norm theory of transfer function. [PERSON] et al. [14] established a car-following model (MFRHVAD) suitable for mixed traffic flow based on the traditional optimal velocity model (OV) and verified that CAV can make the fleet more stable through microscopic numerical simulation.