## 4 Examples and Discussion
### Simulation Results and Discussion
Although the CAV trained by DDPG reaches the first intersection in a shorter time during the initial phase of the vehicle's travel, it consumes more waiting time at the same time. On the other hand, the CAV controlled by the TD3 algorithm travels at a relatively continuous speed overall and spends less time at intersections. Therefore, in terms of the final results, the TD3-controlled CAV consumes the shortest amount of travel time to travel the entire length of the road. The TD3 mode incurs time cost reductions of 4.57%, 12.56%, and 18.26% compared to DDPG, DQN, and Krauss, respectively. This emphasizes the effectiveness of the TD3 algorithm in enhancing travel time efficiency. As the CAV controlled by the TD3 algorithm approaches each intersection, it receives SPaT information from roadside equipment, which is then used to determine the remaining duration of the green light in the current phase. Employing this algorithm enables the determination of whether a smooth intersection passage can be achieved, subsequently allowing for judicious acceleration or deceleration actions. Therefore, optimal algorithmic control effectively reduces the time spent by the CAV to stop and wait at red lights while maintaining a high average velocity. Figure 8 illustrates a violin diagram depicting the velocity distribution, offering a detailed analysis of the speed characteristics of the CAV. With TD3 algorithm training, the speeds of the CAV are notably concentrated in a higher range, achieving the highest average speed in comparison to other car-following modes. Figure 7: Spacetime diagram of CAV under different car-following modes. Figure 9 compares the characteristics of the CAV's speed changes in various car-following modes. As depicted, the vehicle requires prompt speed adjustments near intersections, resulting in noticeable upward or downward shifts in the curve. Moreover, under the intelligent control of RL algorithms, the velocity of the CAV significantly improves compared to the traditional car-following model, with the TD3 algorithm reaching a relatively higher peak. The data reveal that the average driving speeds attained by TD3, DDPG, DQN, and Krauss modes are 13.41 km/h, 12.48 km/h, 11.01 km/h, and 10.46 km/h, respectively. In comparison with the DQN, DDPG, and Krauss modes, the TD3 mode demonstrates significant increases in average driving speed of 7.45%, 21.80%, and 28.20%, respectively. This underscores the effectiveness of the proposed method in enhancing the speed performance of the CAV. The jerk during vehicle operation is utilized as an index for evaluating driving comfort, reflecting sudden speed changes as the CAV navigates through intersections, thereby indicating the smoothness of vehicle operation. Figure 9 visually represents the variation in acceleration during CAV driving under different car-following modes. As depicted in Figure 10, both the DQN and DDPG modes show considerable fluctuations in driving behavior, whereas the TD3 mode maintains more stable acceleration, mostly within the range of [\(-\)3, 4]. Comparative analysis of four car-following modes reveals that in the TD3 car-following mode, the CAV acceleration curve is notably flat, and the average jerk is the smallest. This behavior is attributed to its driving pattern, which is characterized by gradual acceleration or early deceleration. Compared with the DDPG, DQN, and Krauss modes, the jerk is reduced by 8.42%, 28.97%, and 16.89%, respectively. This suggests that the CAV trained with TD3 shows notably better stability in driving performance. Figure 8: Velocity distribution of CAV in different car-following modes. Figure 9: Comparison of velocity curves of CAV in different car-following modes (0\(-\)150 s).