## 5 Simulation Study
### Simulation Results and Analysis  
This study is concerned with the cooperative control problem of oversaturated heterogeneous traffic flow at a single intersection. Therefore, minimizing delay and maximizing throughput are used as metrics to evaluate and analyse the performance advantages and disadvantages between the oversaturated heterogeneous traffic flow signal control model (VVWL) based on the variable virtual waiting zone of the dedicated CAV lane and the SPDL-based control model suggested in this study. As seen in the preceding section, the optimal control objective in this study is the minimum vehicle delay, which is equivalent to the period that separates the moment that a vehicle actually travels from the time that it is free to move. The simulation results are displayed in Figures 14 and 15.  
Figure 14: Vehicle passage. (**a**) Uniform arrival of vehicles; **b**) Poisson arrival of vehicles.  
Figure 13: Two demonstrative trajectories with the same travel time.  
Figure 14 compares the vehicle volumes of heterogeneous traffic flows under control based on both VVWL and SPDL in relation to both uniform and Poisson distributions. As seen in Figure 14a, the VVWL-based control mode increases the total volume of all vehicles, CAVs, and HVs, respectively, by 3%, 4.5%, and 0.9%, as opposed to the control based on SPDL mode, when a uniform distribution of vehicles arrive at the intersection. As seen in Figure 14b, whenever a Poisson distribution of vehicles arrive at the crossroads, the vehicle capacity increases by 2.8%, 4%, and 1.2%, respectively. The proposed variable virtual waiting zone helps to improve the intersection capacity and has a greater impact on the improvement of CAV capacity. The main reason to explain this is that the proposed variable virtual waiting zone allows more CAVs into the intersection at the same time, which increases the capacity of CAVs in the same signal control cycle, and this advantage will be more obvious if the demand for passing vehicles is higher.  
Figure 15 compares the average vehicle passage delay of heterogeneous traffic flow under control based on both VVWL and SPDL from both the uniform and Poisson distribution perspectives. The results in Figure 15a show that when all types of vehicles conform to a uniform distribution, all vehicles' delays are reduced by the control based on VVWL mode, CAVs, and HVs by 11.5%, 23.2%, and 4.3%, respectively, compared to the control mode that is based on SPDL. The results in Figure 15b show that when all types of vehicles conform to a Poisson distribution, the control based on VVWL mode cuts down on all vehicles' delays by 10.7%, 21.3%, and 4.4% for CAVs and HVs, respectively, in contrast to the control mode based on SPDL. Obviously, the proposed variable virtual waiting zone effectively reduces the vehicle delays regardless of the distribution, and the CAV delay reduction is more significant. The main reason is that the variable virtual waiting zone improves the average speed of CAVs passing through the intersection. For the sake of illustration, the complete process of CAVs passing through the intersection is taken as an example, as shown in Figure 16, because the variable virtual waiting zone is inside the intersection. When CAVs are performing trajectory planning, the passing zone and the variable virtual waiting zone are connected, causing the average speed of CAVs in the variable virtual waiting zone to be high relative to the average speed after leaving the variable virtual waiting zone; as a result, CAVs traverse the intersection at a faster average speed and experience less traffic congestion.