## 4 Numerical Studies
### Multi-Vehicle Simulations in Different Modes
#### 4.3.2 Mixed-Traffic Simulations Using Different MPRs  
In the mixed-traffic simulations, the adaptability and robustness of the proposed model were analysed in different modes by varying the MPRs of CAEFVs to determine their traffic benefits. Based on scenario E in Table 5, the dynamic initial speeds of the IDM and CAEFVs were set to 16-22 and 18-20 m/s, respectively, with an initial time distance of 30-60 m.  
Figure 6 shows the spatiotemporal trajectories of 30 vehicles obtained at different MPRs (0-100%). The vehicle trajectories determined for the TPS, BPS, CPS, and IDM (control) are represented by the dark blue, red, light blue, and black lines, respectively. Overall, as the MPR value increases, the number of vehicles stopping and waiting at the  
Figure 4: Vehicle trajectory and speed distribution curves obtained for different modes.  
Figure 5: Power consumption (consumption, recovery, and charging) values and travel times of the vehicles driving in different modes.  
intersection stop line gradually decreases, and more vehicles travel through the signalised intersection along the optimised or suboptimal trajectories. However, a low penetration rate increases the fluctuations of vehicle trajectories, and even the IDM-controlled vehicles may not be able to cross the CA within the required timeframe. As shown in Figure 6c,d, when the preceding vehicle is a CAEFV, it can effectively shape the trajectory of the following vehicle. However, when the preceding vehicle is an IDM-controlled vehicle, it cannot effectively guide the following vehicle driving in the CPS mode. Therefore, increasing the market share of CAEFVs may significantly improve the passing efficiency of vehicles in the CA.  
Figure 7 shows the average travel times and power consumption values obtained in different modes at MPRs varying from 0 and 100%. According to Figure 7a, the power consumption, regenerative braking recovery energy, charging power, and average travel time determined for the mixed traffic with the TPS at an MPR of 0% are equal to 1.388 kW, 0.56 kW, 0.943 kW, and 39.7 s, respectively. When the MPR value is increased from 20% to 100%, the regenerative braking recovery energy decreases by approximately 4.6-37.2%, and the average travel time saving amounts to 2.1 s. This indicates that as the MPR increases, the TPS has an advantage in terms of the traffic efficiency. When the MPR reaches 100%, the rise in the power consumption as compared with the values obtained at other MPRs is approximately 3.3-37.1%. For the BPS and CPS modes described in Figure 5b,c, the power consumption increases with increasing MPR from 1.388 kW by approximately 11.7-39.4% and 6.8-37.3%, respectively. Meanwhile, the charging power increases from 0.943 kW to 2.073 and 2.276 kW, respectively, while the regenerative braking recovery energy also exhibits a slow upward trend, which indicates that the vehicle has a significant charging advantage when driving through signalised intersections in the CPS mode. For the BPS, the average vehicle travel time increases slightly. In contrast, the average travel time in the CPS mode increases significantly, which also indicates that the vehicle inevitably sacrifices travel time to gain more power while driving. Thus, each mode succeeds in achieving its own objectives.  
Figure 6: Spatial–temporal trajectories obtained at different market penetration rates (0–100%).