## 5 Simulation Study  
### Simulation Settings  
To systematically analyse the properties of the recommended model, a single classic four-way intersection with a left-centre-right direction of travel is used, as shown in Figure 2, where there are no traffic lights to manage right-turning vehicles. The passing zone is 500 m long, and the variable virtual waiting zone length is 20 m for the straight-ahead and 35 m for the left-turn. Combined with the three-layer optimization model introduced in Chapter 4, the shortest period of time during which there is a green light \(C_{p,r,j}^{min}=\)15 s, the longest possible period of time for the green \(G_{p,j}^{max}=\) 40 s, and the spacing time \(R_{p,j}=\) 5 s are set in the upper-layer model. In the model of the middle layer, the saturated left-turn HV flow (when m is 2, 4, 6, and 8) is 1550 veh/h, and the direct saturated flow of HVs (when m is 1, 3, 5, and 7) is 1650 veh/h. In the model of the base layer, the maximum rate of acceleration \(a^{U}\) of CAVs is 2 m/s\({}^{2}\), the greatest rate of slowdown \(a^{L}\) is \(-\)2 m/s\({}^{2}\), the maximum CAV speed limit is 14 m/s, the total distance \(d_{a^{lim}}^{lim}\) and body-fixed length \(l_{\omega}\) of the front end are 6 m, and the car's response time is 0 s. The beginning speed of the first CAV stepping into the passing zone is generated at random between \(v_{0}^{L}\) (3 m/s) and \(v_{0}^{L}\) (14 m/s). VISSIM 4.3 (PTVAG, 2008) was selected as the simulation software, and Wiedermann 74 was chosen as the CAV-following and lane-change models, which can collect the HV driving behaviour in the simulation.  
Each arm sees an average of 2250 vehicles every hour. The vehicle arrivals during the simulation are divided into uniform distribution and Poisson distribution, where the proportions of vehicles turning left, right, and straight ahead are, respectively, 0.4, 0.2, and 0.4, and 50% of the population are CAVs. The straight and left-turn ahead CAVs operate in a dedicated CAV lane consisting of a passing zone and a variable virtual waiting zone. The prediction range \(T\) is set to 2 min. The sake of simplicity and the frequency of HV arrival obtained from the previous prediction within the prediction horizon \(T\) are considered asthe average HV arrival rate. The arrival information of each CAV within the predicted range is available through communication methods.  
The model for managing traffic at a single crossroads with a dedicated CAV lane in a mixed-traffic environment based on shared-phase dedicated lanes (SPDL) proposed by [PERSON] [11] is used as a benchmark for evaluation. The model proposes that CAVs use a dedicated CAV lane in a queue. The model plans the intersection signal phase and signal duration as well as the vehicle trajectory collaboratively, as shown in Figure 13; however, the model does not fully utilize the space within the intersection area.  
A desktop PC equipped with an Intel 2.6 GHz CPU and 16 GB of RAM is used for all experiments in this study, and the simulation model is constructed in Python 3.7.4. Five threads are utilized in parallel computation to increase the computing performance. During the simulation of each trial, five random seeds are employed to account for the ambiguity of vehicle arrival and HV driving behaviour. With a forecast time T of 2 min and a time step \(\Delta t=\)1 s, every simulation was run for 1000 s.