## 2 Simulation Framework
Although the above problems can be solved to a certain extent by further subdividing the road sections, this approach can obtain approximately continuous data at the cost of consuming massive computing power, which makes the approach not suitable for the simulation of the large-scale transportation system. To solve these problems, [PERSON] et al. [60; 61; 62; 63; 64; 65] defined the vehicles as cellular instead of road sections and proposed the continuous CA model (as shown in Figure 2) for simulating traffic flow. In the continuous CA model, the vehicles are defined as cellular, and their motion is regarded as the evolution of cellular states, which enables the model to output data \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & \
\begin{tabular}{c} **Generalized Preceding** \\ **Vehicles (GPV) Model** \\ \end{tabular} &
\begin{tabular}{c} **Full Velocity Difference** \\ **(FVD) Model** \\ \end{tabular} \\ \hline \(\alpha\) & 0.767 & 0.852 \\ \(\lambda\) & 0.301 & 0.389 \\ \(p\) & 0.769 & – \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters value in Equation (4) [33]. Figure 1: The discrete cellular automata (CA) model with defining road sections as cellular. Figure 2: The continuous CA model with defining vehicles as cellular. continuous on the time scale. However, the evolution rules in the continuous CA models, which have been applied in simulating traffic flow, are relatively simple and, thus, cannot represent the characteristics of drivers' car-following behavior and directly be used in simulation traffic flow in the V2X environment. Motived by these facts, we define the vehicles as cellular and the velocity as well as position of the vehicles as the cellular state and set the evolution rules based on the car-following model. Based on this, a traffic flow simulation framework (TFSF) for the research on traffic flow characteristics is constructed. The basic structure of the TFSF can be seen in Figure 3.  
In this work, the evolution rules of the cellular state are set based on the GPV model to explore the operating characteristics of traffic flow affected by GPV information in the V2X environment. Rules in the TFSF are set as follows:  
**Initialization Rules of Cellular State**  
In the TFSF, the vehicles are defined as cellular, and the state of each cellular state contains the position and velocity of the corresponding vehicle, i.e., \(S_{n}=[x_{n}(t),v_{n}(t)]\). The initialization rules of the cellular state are as follows:  
(1) Position. At the initial time, there are a total of \(N\) vehicles on the road with a length of \(L\). Assigning the same motion area \(l\) for all vehicles, and the initial position of the \(n\,\mathrm{th}\) (\(n=1,2,\cdots,N\)) vehicle \(x_{n}(0)\), which is defined as the distance between the vehicle head and the starting line of the road, this can be given as  
\[x_{n}(0)\,\sim N\Big{(}nd_{l}+(h_{c}-d_{l})/2,(d_{l}-h_{c})^{2}/36\Big{)} \tag{5}\]  
where \(d_{l}=L/N\) is the length of the motion area \(l\), and \(h_{c}\) is the length of the vehicle. Figure 3: The basic structure of the traffic flow simulation framework (TFSF). According to the properties of normal distribution, it is necessary to set constraints to avoid the \"overlapping\" phenomenon, which means the two successive vehicles overlap in space. The constraints are as follows:  
\[if\ x_{m}(0)>md_{l} \tag{6}\]  
\[then\ x_{m}(0)=md_{l} \tag{7}\]  
\[if\ x_{m}(0)<(m-1)d_{l}+h_{c} \tag{8}\]  
\[then\ x_{m}(0)=(m-1)d_{l}+h_{c} \tag{9}\]  
where \(m=1,2,\ldots,N\). (2) Velocity. According to the NGSIM data, the initial velocity of the vehicle is set as  
Figure 1:0  
where \(r_{1}\) is a random number and \(r_{1}\in(0,1]\), \(v_{\max}\) and \(v_{\min}\) are, respectively, the upper and lower limit of velocity in the simulation, \(v_{d_{n}}\) is the safety limit of velocity to avoid collision, and its value is equal to the headway between the \(n\) th vehicle and its front vehicle, i.e., \(d_{n}(t)=x_{n+1}(t)-x_{n}(t)-h_{c}\).