## 2 Simulation Framework  
Car-following behavior is the most basic driving behavior, which is prevalent in the traffic system. As one of the cores of traffic flow theory, car-following models can describe the interaction between the successive vehicles in a detailed way, which are the theoretical basis of macro-characteristics of traffic flow and its simulation. [PERSON] et al. [34] believed that drivers would adjust their car-following behavior according to the distance between their vehicle and the front vehicle, and constructed an optimal velocity (OV) model. (All abbreviations, including the ones in the Abstract, and the corresponding full names are as shown in Table A1 in the Appendix A). Calibrating the OV model with trajectory data, [PERSON] et al. [35] found that the model would compute unrealistic acceleration/deceleration. To fix this default, [PERSON] et al. established a generalized force (GF) model with consideration of the negative velocity effect. In the following research, it was found [36] that the GF model could not describe the phenomenon that the object vehicle would not decelerate when the distance between it and its front vehicle was shorter than the safety distance and the front vehicle is much faster than the object vehicle. Based on this, [PERSON] et al. [37] further considered the positive velocity effect and proposed a full velocity difference (FVD) model. The equation of the FVD model is as follows:  
\[\frac{dv_{n}(t)}{dt}=a[V(\Delta x_{n})-v_{n}(t)]+\lambda\Delta v_{n} \tag{1}\]  
where \(a\) is the sensitivity parameter of the driver, \(V(\Delta x_{n})\) is the optimal velocity function, \(\Delta x_{n}=x_{n+1}(t)-x_{n}(t)\) denotes the headway of two successive vehicles and \(\Delta v_{n}=v_{n+1}(t)-v_{n}(t)\) represents their velocity difference. \(x_{n+1}(t)\), \(x_{n}(t)\), \(v_{n+1}(t)\) and \(v_{n}(t)\), respectively, are the position and velocity of the \(n\,\)th vehicle and its front vehicle \(n+1\,\)th where \(t\) represents time. The above models are generally referred to as \"optimal velocity models\", and the core of these models is the optimal velocity function, which is as follows:  
\[V(\Delta x_{n})=\frac{v_{\max}}{2}[\tanh(\Delta x_{n}-h_{c})+\tanh(h_{c})] \tag{2}\]  
\[V(\Delta x_{n})=V_{1}+V_{2}\text{tanh}[C_{1}(\Delta x_{n}-l_{c})-C_{2}] \tag{3}\]  
where \(v_{\max}\) is the maximum velocity, \(h_{c}\) and \(l_{c}\) are the length of the vehicle, \(V_{1}\), \(V_{2}\), \(C_{1}\) and \(C_{2}\) are parameters to be calibrated. The optimal velocity function has properties including monotonically increasing, existing upper bound, existing inflection point at \(\Delta x_{n}=h_{c}\), \(V(\Delta x_{n})\to 0\) when \(\Delta x_{n}\to 0\) and \(V(\Delta x_{n})\to v_{\max}\) when \(\Delta x_{n}\to\infty\), which enable the function to be able to describe characteristics, such as avoiding collisions, following velocity depending on the distance, driving faster when they can, of drivers' car-following behavior from a mathematical standpoint. In subsequent studies, the optimal velocity models, especially the FVD model, showed a high performance in simulating car-following behavior in a vehicles fleet and analyzing the stability of the traffic flow. Many extended models were proposed. However, the optimal velocity models can only reflect the interaction between the object vehicle and its front vehicle, and there are problems existing in directly employing these models to describe drivers' car-following behavior in the V2X environment. Although there are multiple extended models mentioned in Section 1 with consideration of the impacts exerted by the motion state information of an arbitrary number of preceding vehicles in the current lane, there was no research considering the influence caused by preceding vehicles in the adjacent lanes, of which information is available for the driver in the V2X environment.