## 4 Case Study
### Evaluation of Multi-Train Control Effect
As shown in Table 8, the DRL-DA algorithm has more state transfers than other algorithms, and the average reward value obtained is higher, indicating that the DRL-DA triggers less termination of training and better learning. Due to the algorithm structure of Q learning, Q learning chooses discrete vectors for the action space, which has some limitations in simulation generalization ability and is slightly less effective. However, due to the relative simplicity of the algorithm, the training time is relatively fast. The DQN algorithm is relatively slow in computing efficiency due to the complexity of the algorithm compared to the reinforcement learning algorithm. At the same time, because the artificial neural network training has a certain degree of randomness, the training results are prone to fluctuations, which can be improved by adjusting the reward function weights and improving the neural network. Compared with other algorithms, the proposed algorithm requires less data. Through the direct interaction between the environment and the agent, it continuously learns and corrects each step of the action without the need for complex operation conditions settings. Therefore, compared with other algorithms, the proposed algorithm is more convenient and shows better performance. Figure 21 shows that in the process of solving with the DRLDA algorithm, there is a convergence curve between the optimal value and the number of iterations. The operating time of multiple trains at Xinjiekou, Pinganli, Xisi and Lingjinghutong stations can be obtained by inputting different train arrival intervals in Figure 22.  
Figure 21 demonstrates that the proposed algorithm converges to a relatively satisfactory solution after more than 100 generations of computation. The time to obtain the optimal solution is about 371 s. As seen in Figure 22, the multi-train operating time optimization diagram, drawn according to the optimization results obtained by the algorithm, can better reflect the variation pattern of passenger flow with time, and the train operating interval changes dynamically with the passenger flow demand. During the morning peak hours of 7:00-9:00 a.m., the operating lines are more closely distributed, which can maximize passenger waiting time, rationalizing train departures and reducing operation costs. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Number of Training** & **Number of State** & **Average Rewards Value** & **Single Training Time [s]** \\ \hline DRL-DA & 10,000 & 751,442 & \(-\)104 & 0.0008 \\ DDPG-RS & 10,000 & 735,117 & \(-\)141 & 0.02 \\ DQN-RS & 10,000 & 680,985 & \(-\)181 & 0.06 \\ DDPG & 10,000 & 640,088 & \(-\)282 & 0.83 \\ DQN & 10,000 & 601,128 & \(-\)369 & 2.04 \\ DRL-DA & 20,000 & 837,022 & \(-\)119 & 0.001 \\ DDPG-RS & 20,000 & 802,441 & \(-\)150 & 0.21 \\ DQN-RS & 20,000 & 750,088 & \(-\)193 & 0.35 \\ DDPG & 20,000 & 721,672 & \(-\)294 & 1.19 \\ DQN & 20,000 & 682,309 & \(-\)382 & 2.20 \\ DRL-DA & 30,000 & 915,147 & \(-\)132 & 0.032 \\ DDPG-RS & 30,000 & 870,036 & \(-\)158 & 0.33 \\ DQN-RS & 30,000 & 834,011 & \(-\)205 & 0.68 \\ DDPG & 30,000 & 802,113 & \(-\)303 & 1.54 \\ DQN & 30,000 & 779,554 & \(-\)394 & 2.31 \\ DRL-DA & 40,000 & 1,012,271 & \(-\)141 & 0.074 \\ DDPG-RS & 40,000 & 953,046 & \(-\)167 & 0.56 \\ DQN-RS & 40,000 & 903,117 & \(-\)218 & 1.04 \\ DDPG & 40,000 & 880,121 & \(-\)312 & 1.81 \\ DQN & 40,000 & 840,455 & \(-\)408 & 2.57 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Comparing the training session results of the proposed method with other algorithms. For verification, the solution results of the DRLDA algorithm were entered into Anylogic. In the multi-train train control model, the relationship between train traction energy consumption and passenger waiting time is mainly studied by changing the arrival interval of the train. The TrainSource module in Anylogic sets the train arrival interval, which can be adjusted in minutes or seconds. According to the solution results, the train arrival interval is adjusted by running the simulation.