## 5 Simulation Study
### Sensitivity Analysis  
heterogeneous traffic flow stage; when the demand coefficient is equal to 1.5, the traffic demand is in the saturated heterogeneous traffic flow stage; and when the demand coefficient is greater than 1.5, the traffic demand is in the oversaturated heterogeneous traffic flow stage. Control based on VVWL method is used as the basic control group. The CAV percentage is set to 50% during the simulation. Figure 17 depicts the trends between the increase in intersection access demand and the average intersection heterogeneous traffic flow vehicle arrivals for both the VVWL-based and SPDL-based control modes. Figure 17a,b show the uniform arrival of vehicles and Poisson arrival of vehicles, respectively. Based on Figure 17 as a whole, when there is an unbalanced demand for transportation flow (there is no demand coefficient bigger than 1.5), the uniform vehicle arrivals and the demand under control based on both VVWL and SPDL are almost identical, which indicates that the intersection can carry the full demand until the junction is fully utilized. When oversaturated traffic flow (demand factor greater than 1.5) occurs, the average intersection volumes under both VVWL-based control and SPDL-based control begin to deviate from the demand curve, while continuing to go higher. This means that some of the phases appear to be unable to keep up with the demand, and some phases are oversaturated with traffic. However, compared to the VVWL control mode, the average number of vehicles under control based on SPDL deviate more from the demand curve. The demand factor is now rising from 1.5 to 3.5, the average capacity of the intersection continues to increase up to the maximum for both control models, and the two average capacity curves become flat. This is because the capacity under both control models reaches the upper limit and cannot cope with the excessive throughput demand. However, it is still evident that the intersection capacity based on VVWL control is consistently greater than the intersection capacity based on SPDL control. After the two average capacity curves become flat (the demand factor is greater than 3.5), the intersection capacity based on VVWL control increases by 6% compared to the average capacity of the intersection based on SPDL control, and the capacity of the dedicated CAV lane (with a variable virtual waiting zone) and HV lane are 10% and 2% more, respectively. The reasons for these changes are the same as those described in 5.2. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Traffic Demand in pcu/h**} \\ \hline  & \multicolumn{2}{c}{**Left-Turn**} & \multicolumn{2}{c}{**Through**} & \multicolumn{2}{c}{**Right-Turn**} \\ \cline{2-6}  & **CAV** & **HV** & **CAV** & **HV** & \\ \hline Arm 1 & 200 & 200 & 200 & 200 & 100 \\ Arm 2 & 200 & 200 & 200 & 200 & 100 \\ Arm 3 & 200 & 200 & 200 & 200 & 100 \\ Arm 4 & 200 & 200 & 200 & 200 & 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Fundamental traffic demand. Figure 16: CAV intersection speed analysis. The comparison in Figure 18 shows the trend between the increase in intersection access demand and the average intersection heterogeneous traffic flow vehicle delay for both the VVWL-based and SPDL-based control modes. Figure 18a,b shows the uniform arrival of vehicles and Poisson arrival of vehicles, respectively. Figure 18 shows that average vehicle delay across all vehicles under both the VVWL control and the SPDL control increases slightly when there is an unbalanced demand for transportation flow. (There is no demand factor bigger than 1.5.) The typical vehicle delay under VVWS-based control decreases by 13% compared to the average vehicle delay under SPDL-based control, which indicates that the intersection can carry the full demand until the capacity of the intersection is reached, and the vehicle delay is closely related to the intersection control method.