## 4 Numerical Studies
### Single-Vehicle Simulation with a Communication Delay  
To verify the effectiveness of the proposed model, a particle swarm optimisation algorithm [49] and regularisation method [50, 51] were employed to compare the optimal driving model considering a communication delay with an unguided model (IDM) using  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Weighting Coefficient** & **CPS** & **BPS** & **TPS** \\ \hline \(\omega_{1}\) & 0.6–0.8 & 0.2–0.4 & 0.1–0.2 \\ \(\omega_{2}\) & 0.1–0.2 & 0.4–0.6 & 0.1–0.2 \\ \(\omega_{3}\) & 0.1–0.2 & 0.2–0.4 & 0.6–0.8 \\ \hline \hline \end{tabular} \(\overline{\text{CPS}}\), charging priority strategy; BPS, balance priority strategy; TPS, time priority strategy.  
\end{table}
Table 2: Weighting coefficients of different passing strategies.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value** & **Parameter** & **Value** \\ \hline \(v_{max}\) (m/s) & 20 & \(\eta_{d}\) & 0.94 \\ \(v_{min}\) (m/s) & 2 & \(\eta_{m}\) & 0.96 \\ \(a_{max}\) (m/s\({}^{2}\)) & 4.88 & \(\eta_{b}\) & 0.97 \\ \(a_{min}\) (m/s\({}^{2}\)) & \(-3  
the same initial state parameters. Based on the simulation parameters listed in Table 3, comparison experiments were conducted for the same initial state, including an initial speed of 20 m/s and charging area of 200 m.  
In Figure 2a, the minimum speed of the vehicle without a control strategy is 0 m/s, and the vehicle remains stationary at the stop line of the signalised intersection. For the CAEFVs controlled by the optimal driving control model, no STOP-GO behaviour is observed in the CPS, BPS, and TPS, and the vehicles pass through the signalised intersection without stopping in different modes. After introducing a communication delay, the speed curves of the three modes become different. The time required for the CAEFVs driving in the CPS mode to cross the entire signalised intersection is approximately 70 s, and the largest difference between their lowest speeds is 0.24 m/s. However, the times required for the CAEFVs driving in the BPS and TPS modes to cross the entire signalised intersection are equal to 48 and 40 s, and the corresponding minimum speed differences are 0.33 and 0.18 m/s, respectively. Figure 2b illustrates the vehicle passing process through a signalised intersection. In the scenario without a control strategy, the vehicle is affected by the red light and remains idle before the stop line at the signalised intersection. The CAEFVs that consider a communication delay can receive road and signal-light status information in advance, enabling effective decision-making optimisation control and avoiding the idling of vehicles at the signalised intersections.  
The numerical simulation results obtained for the four scenarios are listed in Table 4. The time required for CAEFVs to cross the signalised intersection in the TPS mode is the lowest one. The power consumption of the vehicles operating in this mode is also relatively low, the energy recovered by the regenerative braking system without a control strategy is relatively high, and the charging efficiency of EVs driving in the CPS mode is the highest. Compared with the vehicles without a control strategy, the vehicle driving in the CPS mode saves 0.2014 kWh of electricity; the vehicle operating in the BPS mode saves slightly more than 0.0896 kWh of electricity, and the vehicle driving in the TPS mode saves slightly more than 0.0457 kWh of electricity. However, it takes longer times for the vehicles driving in the CPS mode to pass through the signalised intersection. In contrast, the vehicles driving in the TPS mode save less electricity than those operated using the other two strategies, which significantly reduces the passing time and increases the passing efficiency.  
Figure 2: Simulation results obtained with and without a model control strategy and communication delay: (**a**) velocity and (**b**) trajectory.