## 2 Simulation Framework
Based on these, we considered the motion state information of GPV, which consists of the preceding vehicle, the non-neighboring preceding vehicle and the left/right preceding vehicle in the adjacent lanes, and proposed an extended model named the GPV model [33]. The equation of this model is as follows:  
\[\frac{dv_{n}(t)}{dt}=p\{a[V(\Delta x_{n})-v_{n}(t)]+\lambda v_{n}(t)\}+(1-p)( \overline{v_{n}}-v_{n}(t)) \tag{4}\]  
where \(a\), \(\lambda\) and \(p\) respectively represent the sensitivity of the driver about optimal velocity difference, velocity difference and the difference between the GPV's average velocity and self-vehicle velocity. \(\overline{v_{n}}\) is the average velocity of GPV and \(\overline{v_{n}}=(v_{n+1}(t)+v_{n+2}(t)+v_{l}(t)+v_{r}(t))/4\), where \(v_{n+1}(t)\), \(v_{n+2}(t)\), \(v_{l}(t)\) and \(v_{r}(t)\) are the velocity of front vehicle, non-neighboring front vehicle, left and right front vehicles in adjacent lanes. In the GPV model, the optimal velocity function in Equation (3) was employed and the parameters in the function are as shown in Table 1.  
Performance of the GPV model in describing drivers' car-following behavior with consideration of the GPV motion state information in the V2X environment has been confirmed, and the parameters of the model has been calibrated (the calibration results are as shown in Table 2) with the NGSIM dataset in our previous research. And the stability criterion was also obtained through the linear stability analysis, which confirmed the stabilization effect of GPV information on traffic flow. This research as well as other research mentioned above have explored the drivers' car-following behavior and the \begin{table}
\begin{tabular}{c c c c c c} \hline
**Parameters** & \(\mathbf{V_{1}}\) & \(\mathbf{V_{2}}\) & \(\mathbf{C_{1}}\) & \(\mathbf{C_{2}}\) & \(l_{c}\) \\ \hline  & 6.75 & 7.91 & 0.13 & 1.57 & 5 \\ \hline \end{tabular}
\end{table} 
Table 1: Parameters value in Equation (3) [35]. stability of traffic flow affected by various information in the V2X environment. However, the quantitative analysis of the traffic flow characteristics is absent in these efforts. The characteristics of traffic flow are essentially the overall expression of the microscopic car-following behavior of individual vehicles in the system. The macroscopic traffic flow models [38; 39; 40; 41; 42; 43], which are also known as continuous medium models, are the commonly used approach to explore the impacts of V2X technology on traffic flow in the previous work. In these continuous medium models, vehicles in the system are regarded as a compressible medium, and fluid dynamics as well as other related theories are used to study the traffic flow at the system level. However, these models show a relatively low performance in expressing the differences in macro characteristics of traffic flow caused by the differences in drivers' micro behavior. Based on this, a simulation framework is combined with the car-following model and the CA for the quantitative analysis of traffic flow characteristics affected by the GPV information in the V2X environment. As a mesh dynamic model, the CA model is suitable for simulating the space-time evolution process of complex systems and has been widely used in the simulation of traffic flow [44; 45; 46; 47; 48; 49; 50; 51; 52; 53; 54; 55; 56; 57; 58; 59]. Ordinary CA models, as shown in Figure 1, employed in the simulation of traffic flow define the discrete road sections as cellular. In these models, the cellular state contains whether there is or is not a vehicle and other information, and updates according to the pre-set evolution rules. Research based on discrete CA models could make reappear the evolution of traffic flow and some macroscopic phenomena during the simulation, but the output data are discrete and stepped. Thus, there are some defaults for the discrete CA models in studying traffic flow, especially in the exploration of continuous operation and evolution on the timescale.