## 5 Simulation Study
### Sensitivity Analysis
#### 5.3.3 Analysis of CAV Share for Left Turns  
In the heterogeneous traffic flow, the CAV percentage is set at 50%. The heterogeneous traffic flow passage delay when the percentage of left-turn CAVs varies from 0% to 100% under different control methods, while considering only straight-ahead and left-turns, is simulated and analysed. Four traffic demands, 1 veh/s, 2 veh/s, 2.5 veh/s and 3.75 veh/s, are used for comparison. The corresponding demand coefficients of the four traffic demands are 1, 2, 2.5, and 3.75. The results in Figure 22 show that the typical vehicle delay under control based on VVWL approach is always less than the typical vehicle delay under control  
Figure 19: CAV and HV delays on average. (**a**) Uniform arrival of vehicles; (**b**) Poisson arrival of vehicles.  
based on VVWL approach, that is, when vehicles are arriving with a uniform distribution for the four different traffic demands. Although the average heterogeneous traffic flow arrival delay under both control methods shows a similar trend with the proportion of left-turning CAVs in the CAV flow rising, that is, it decreases first and then increases, the percentage of left-turning CAVs corresponding to the lowest delay is not the same under both control methods. Under the SPDL-based control approach, the average vehicle delay is minimized only when equal amounts of left-turning and straight-ahead traffic are present, regardless of how the level of traffic has changed. However, the minimum value of the average vehicle delay under VVWL-based control is not fixed at the point where the ratio of through traffic to left-turn traffic is equal, but is slightly greater than 50%. The larger the traffic demand is, the larger the relative value becomes. Taking Figure 22c,d as examples, the left-turn CAV shares corresponding to the minimum average vehicle delay are 55% and 56%, respectively. A further remarkable phenomenon that can be observed is that while travel demand has increased, the lowest point of the typical vehicle delay in the VVWL control mode shifts to the right, while the delay reduction in the control mode based on VVWL becomes increasingly significant compared to the control based on VVWL. The reason for these results is that the overall HV delay is minimized when the ratio of straight-ahead HVs and left-turn HVs is the same. Due to the proposed variable virtual waiting zone, the space resources of the intersection are fully exploited, which makes the CAVs enter the intersection earlier. Given that the size of the left-turn virtual waiting zone is large compared with that of the straight virtual waiting zone, the left-turn CAV running time reduction at the intersection is larger than that of straight CAVs, resulting in a slightly larger number of left-turn CAVs than straight CAVs when the average CAV delay at the intersection is at its minimum, which in turn makes the overall percentage of left-turn CAVs corresponding to the minimum average delay of vehicles slightly larger than 50%. This reflects the advantage of the variable virtual waiting zone in reducing the overall throughput delay and coping with the oversaturated heterogeneous traffic flow. A similar situation is reflected in Figure 23 for the Poisson vehicle arrival distribution.  
Figure 20: Effects of CAV penetration rates on vehicle delay when the distribution of vehicle arrivals is uniform.  
Figure 21: Effects of CAV penetration rates on vehicle delay when the distribution of vehicle arrivals is Poisson.  
Figure 22: Effect of left-turn proportions on vehicle delay when the distribution of vehicle arrivals is uniform.