## 3 Simulation
### The Simulation of Traffic Flow  
To explore the impacts of GPV information on traffic flow under different levels of drivers' attention to the information, the sensitivity parameter \(p\) is respectively set as 0.9, 0.8, 0.7 and 0.6. The FVD model is employed to represent the unconnected environment for comparison. The calibrated values of the corresponding parameters can be seen in Tables 1 and 2. With the simulation of the traffic flow affected by the GPV information in the V2X environment, a volume-density surface can be obtained as shown in Figure 5.  
As shown in Figure 5, the GPV information in the V2X environment has a significant positive influence on the operation of traffic flow. In the V2X environment, the maximum volumes of the traffic flow affected by the GPV information with a different sensitivity parameter \(p\) are as shown in Table 3. \begin{table}
\begin{tabular}{c c c c} \hline
**Parameter \(p\)** & **Maximum Volume** & **Rate A of the Increase** & **Rate B of the Increase** \\ \hline
0.9 & 3110.40 veh\(\cdot\)h\({}^{-1}\) & 52.40\% & 0\% \\
0.8 & 3477.60 veh\(\cdot\)h\({}^{-1}\) & 70.39\% & 11.80\% \\
0.7 & 3715.21 veh\(\cdot\)h\({}^{-1}\) & 82.03\% & 6.83\% \\
0.6 & 3852.00 veh\(\cdot\)h\({}^{-1}\) & 88.73\% & 3.68\% \\ \hline \end{tabular} \({}^{1}\) The rate A is the increasing rate of the corresponding maximum volume compared with the one in the unconnected environment. \({}^{2}\) The rate B is the increasing rate of the corresponding maximum volume compared with the previous one.  
\end{table} 
Table 3: Maximum volumes of the traffic flow affected by the GPV information. Figure 5: The volume–density surface. From Table 3, one can obtain that the maximal volume of traffic flow affected by the GPV information in the V2X environment is significantly increased, and the rate of the increase can reach up to 88.73% compared with the unconnected environment, in which the maximum volume of the traffic flow is 2040.96 veh\(\cdot\)h\({}^{-1}\) under the same condition. To further explore the positive effect of the GPV information on the traffic flow in the V2X environment, extra simulation is carried out, and the fundamental diagram represented by the volume-density relationship is obtained, which can be seen in Figure 6.  
From Figure 6, one can obtain that compared with the unconnected environment, the traffic flow in the V2X environment can maintain the free-flow state under the condition of a higher density of vehicles. The traffic flow in the V2X environment can operate with a higher value of volume and velocity, which is expressed by the derivative value at the corresponding points, under the same density of vehicles after breaking away from the free-flow state. Besides, the jamming density in the V2X environment is much higher than that in the unconnected environment. To reflect the impacts of the GPV information on the operating velocity of traffic flow, the velocity-density surface and the corresponding velocity-density curves are obtained and can be seen in Figures 7 and 8. As shown in Figures 7 and 8, the traffic flow can only maintain the free-flow state within the density of 18.91 veh/km in the unconnected environment, and the traffic flow affected by the GPV information can maintain the free-flow state within the density up to 35.67 veh/km in the V2X environment. The breaking values of density, which mean the traffic flow cannot maintain a free-flow state when the density is higher than this value under the corresponding condition, affected by the GPV information with different values of sensitivity parameter \(p\) in the V2X environment, are as shown in Table 4.  
Figure 6: The fundamental diagram represented by the volume–density relationship. Figure 8: The velocity–density curves.