## 4 Examples and Discussion
### Simulation Results and Discussion  
Data from the simulation experiments are meticulously processed to analyze the vehicle's motion characteristics under Krauss, TD3, DDPG, and DQN car-following modes. Regarding the safety aspect of CAV driving, it is noteworthy that unsafe driving behavior is initially observed in the early iterations of the algorithm simulation, where the time to collision exceeds the predefined safety threshold. However, such instances cease to occur in subsequent iterations. This is attributed to the penalty mechanism implemented \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Design hour volume of HVs (veh/h) & 1600 \\ Total driving distance (m) & 525 \\ The speed limit (km/h) & 40 \\ Vehicle acceleration (m/s\({}^{2}\)) & (\(-\)4.500, 4.500) \\ Minimum safety distance between front and rear vehicles (m) & 30 \\ Green time (s) & [41; 37; 64; 46] \\ Yellow time (s) & [3.50, 3.90, 3.50, 3.50] \\ All-red time (s) & [0.50, 1.50, 1.00, 1.00] \\ Maximum training steps & \(10^{5}\) \\ Batch size & 256 \\ Learning rate & \(10^{-4}\) \\ Discount factor & 0.98 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Simulation parameter settings. in the reward function, where a significant penalty is assigned to driving behaviors violating safety protocols, while actions complying with safe driving norms receive equal reward values. Essentially, safety rewards are structured to enforce safe driving as a non-negotiable prerequisite. In summary, given that across all modes, the CAV adheres to the fundamental requirement of safe driving, as evidenced by consistent safety reward values, our comparative analysis focuses on energy consumption, efficiency, and driving comfort among the different approaches. Notably, \"efficiency\" refers to the effectiveness of a vehicle's movement, quantified by factors such as travel time and mean velocity across intersections. The specific evaluation indicators include electricity consumption, travel time, and mean jerk. Findings are summarized in Table 3.  
The vehicle's motion performance, analyzed using various indices, is depicted in Figure 6. Regarding efficiency and comfort, the TD3 algorithm exhibits superior performance over the other three car-following modes. For energy consumption, this study delves into the electric energy consumed by the CAV to evaluate vehicle performance across various car-following modes. The application of the TD3 algorithm in CAV training significantly reduces driving energy consumption--4.33%, 15.79%, and 13.77% compared to DDPG, DQN, and Krauss, respectively. This underscores the proposed algorithm's outstanding effectiveness in energy conservation. Based on trajectory data from simulations, a vehicle spacetime diagram is generated for intuitive comparison and analysis of vehicle traffic efficiency under various car-following modes. As illustrated in Figure 7, the CAV trained by the TD3 algorithm exhibits the longest driving distance per unit of time during most periods. Since the TD3 algorithm is an improvement on the DDPG algorithm, the curves corresponding to these two algorithms are very close in Figure 7. However, the action strategy obtained under DDPG algorithm training has an increased magnitude of variation at the beginning, as evidenced by the \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Car-Following Mode**} & \multicolumn{3}{c}{**Evaluation Indicators**} \\ \cline{2-4}  & **Electricity Consumption** & **Travel Time** & **Mean Jerk** \\  & **(Wh)** & **(s)** & **(m/s3)** \\ \hline TD3 & 101.845 & 188 & 0.674 \\ DDPG & 106.463 & 197 & 0.736 \\ DQN & 120.943 & 215 & 0.949 \\ KRAUSS & 118.102 & 230 & 0.811 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Simulation results under different car-following modes. Figure 6: Comparison of results by several indices. vehicle starting with greater acceleration.