## 5 Simulation Experiments and Numerical Results Analysis
### Visualization of Results  
To illustrate these findings graphically, a set of simulation data closely approximating the mean stop counts was selected. Trajectory plots were then generated for differing traffic volumes and penetration rates, depicting the empty paths of each vehicle according to their respective positions over time. This visual representation offers a clear insight into how varying levels of CAV penetration, under consistent traffic conditions, impact vehicle movement patterns and efficiency.  
As can be seen from Figure 12, when the penetration rate of connected autonomous vehicles was 40%, the spatio-temporal chart before and after the guidance was compared with that before the guidance. The trajectory trend after the guidance was relatively gentle, indicating that connected autonomous vehicles slow down in advance when approaching the intersection after being guided, which is most likely to avoid stopping and waiting in front of the signal light. Meanwhile, as for HDVs in the mixed traffic flow, under the influence of CAVs, some HDVs passed the intersection without stopping. Through the longitudinal comparison of the spatio-temporal trajectory diagram of different traffic flows, the position of the trajectory fluctuation before guidance gradually moved forward with the increase in traffic flow, which was due to the continuous increase in its queue length and slow walking length. Meanwhile, the trajectory fluctuation to the horizontal after guidance gradually decreased, which was due to the increasing number of HDVs being indirectly affected by the guided CAVs. Thus, the number of vehicle stops at the entire intersection was reduced. In Figures 12 and 13 Lane \"E0-1\" represent lane 1; Lane \"E0-0\" represent lane 0.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline  & & \multicolumn{6}{c}{**Delay(s)**} \\ \cline{2-9}  & \multicolumn{2}{c}{**20\%**} & \multicolumn{2}{c}{**40\%**} & \multicolumn{2}{c}{**60\%**} & \multicolumn{2}{c}{**80\%**} \\ \hline
**NO.** & **N.** & **G.** & **N.** & **G.** & **N.** & **G.** & **N.** & **  
Figure 12: Before and after guidance under different flow rates.  
Figure 13: Spatial and temporal maps before and after guiding under different permeability.  
As can be seen from Figure 13, when the flow rate was 1800 veh/h, through horizontal comparison of the spatio-temporal graph and trajectory diagram before and after guidance, the trajectory trend after guidance was obviously flat compared with that before guidance, for the same reasons as those shown Figure 10. Through the longitudinal comparison of the spatio-temporal trajectory diagram of different traffic flows, it was found that with the increase in the permeability of connected autonomous vehicles, the trajectory fluctuation to the horizontal before guidance was significantly reduced, while after guidance, the trajectory fluctuation trend was larger and gradually became flat. At this time, connected autonomous vehicles affect almost all HDVs.  
To sum up, after guidance, the CAV slowed down near the intersection in advance to achieve the purpose of passing the intersection without stopping, and this indirectly affected the manual driving vehicles so that some HDVs also passed the intersection without stopping. In addition, with the increase in traffic volume, the number of artificially driven vehicles indirectly affected by connected autonomous vehicles increased, and with the increase in the penetration rate of connected autonomous vehicles, connected autonomous vehicles gradually occupied a dominant position, and the impact caused by connected autonomous vehicles in both cases also gradually increased. Currently, the effect of applying the speed guidance strategy in this study is better.