## 6 Model Validation Analysis
### Simulation Results  
The results of the numerical simulation experiments are listed in Table 4. Taking the \(r\) value of 0.3, the comfort index was calculated, and the results are shown in the tables below.  
It can be noted from Table 4 and Figure 9 that the higher the penetration rate of CACC vehicles, the higher the driving comfort under the same \(T\) value.  
Compared with the homogeneous CACC vehicle traffic flow, the \(CI\) value of the homogeneous HD traffic flow was reduced by 64.67, 66.06, and 72.16% when \(T=1.1\), 1.6, and 2.2 s, respectively. The results showed that an increase in PS improved driving comfort, which was consistent with the analytical results of the longitudinal stability theory.  
Figure 10 shows a comparison chart of the comfort index during the simulation process of the PS-IDM and single IDM models. The solid line is the PS-IDM comfort index fitting curve, and the dashed line is the single IDM comfort index fitting curve. Under the same  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{\(p\)} & \multicolumn{3}{c}{\(CI\)} \\ \cline{2-4}  & \(T=1.1\) s & \(T=1.6\) s & \(T=2.2\) s \\ \hline \multicolumn{4}{c}{PS-IDM} \\ \hline
0 & 0.33466 & 0.27424 & 0.17642 \\
0.2 & 0.17434 & 0.14027 & 0.08766 \\
0.4 & 0.16462 & 0.13556 & 0.07046 \\
0.6 & 0.14485 & 0.13085 & 0.06436 \\
0.8 & 0.12084 & 0.11800 & 0.05064 \\
1 & 0.11846 & 0.09342 & 0.04978 \\ \hline \multicolumn{4}{c}{Single IDM} \\ \hline
0 & 0.34465 & 0.28498 & 0.18776 \\
0.2 & 0.17647 & 0.14648 & 0.09349 \\
0.4 & 0.16894 & 0.14064 & 0.07309 \\
0.6 & 0.14698 & 0.13584 & 0.06618 \\
0.8 & 0.13649 & 0.12986 & 0.06036 \\
1 & 0.34465 & 0.28498 & 0.18776 \\ \hline \hline \end{tabular}
\end{table}
Table 4: PS-IDM and Single IDM comfort index.  
circumstances, the \(CI\) value of a single IDM is greater than the \(CI\) value of the PS-IDM. Compared with a single IDM, the comfort of the PS-IDM can be increased by up to 20.7%.  
The intrusion rate of each vehicle was discrete data, and the simulation experiment was performed using MATLAB. In addition, the average value of the intrusion rate of 50 for the simulated vehicles was taken as the simulation result of the intrusion rate index. Taking \(T=1.1\) s and \(r=0.3\) as an example, the result is shown in Figure 11.  
In Figure 11, when the HD vehicle traffic flow is homogeneous, the average intrusion rate is higher than 24%. As the penetration rate of CACC vehicles increases, the intrusion rate decreases, when the traffic flow of the homogenous HD vehicle changes to the traffic flow of homogenous CACC vehicles. In particular, at the beginning of the transition period (\(p\in(0,0.3)\)), the downward trend is evident. When the mixed traffic flow degenerates into a homogenous CACC vehicle traffic flow (\(p=1\)), the average intrusion rate drops to 19.4%.  
The simulation results show that there is a positive correlation between the intrusion rate index and the comfort index. The smaller the value of the comfort index, the smaller the intrusion rate index value, and the better the driving stability, which is consistent with the analytical results of the lateral stability theory.  
Figure 10: Comparison chart of the index before and after model improvement.  
Figure 9: Scatter plot of PS-IDM comfort index.