## 5 Case Study
### Optimization of Timetable During Trial Operation  
The Shanghai Suburban Railway airport link line is scheduled to initiate trial operations on 1 September 2024, and is expected to be officially operational by the end of 2024. The simulation in this section primarily focuses on optimizing the timetable during the trial operation phase. To demonstrate the validity and accuracy of the proposed model and method, the T-TPOS is compared with the TUOS-ELS. As can be seen from Figure 9, there is a large difference between the upstream and downstream passenger arrival rates, i.e., \(\mathcal{O}_{sk}\) in Equation (14). This is a key factor in determining the number of trains running in both directions. Based on the trial operation timetable of the Shanghai Suburban Railway airport link line, it is evident that the headway between trains is 15 min, and an all-stop behavior is adopted. Consequently, five trains operate in both the upstream and downstream directions. The timetable obtained by T-TPOS is shown in Figure 10. The number of passengers waiting on the stations is shown in Figures 11 and 12. The train numbers in Figures 11 and 12 are assigned based on the departure sequence of trains shown in Figure 10. For example, the train departing around 8:00 is assigned train number 1, while the train departing between 8:10 and 8:20 is assigned train number 2. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \(\mathbf{H_{\text{max}}}\) & \(\mathbf{H_{\text{min}}}\) & \(\mathbf{I_{\mathbf{ds}}}\) & \(\mathbf{I_{dt}}\) & \(\mathbf{I_{ta}}\) & \(\mathbf{b_{\text{min}}}\) \\ \hline
1800 (s) & 400 (s) & 90 (s) & 90 (s) & 90 (s) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Time-related parameter settings. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \(\mathbf{Station}\) & \begin{tabular}{c} **Minimum** \\ **Dwell Time (s)** \\ \end{tabular} & \begin{tabular}{c} **Maximum** \\ **Dwell Time (s)** \\ \end{tabular} & \
\begin{tabular}{c} **Maximum** \\ **Running Time (s)** \\ \end{tabular} &
\begin{tabular}{c} **Minimum** \\ **Running Time (s)** \\ \end{tabular} \\ \hline Honggiao Airport Terminal 2 & 35 & 65 & - & - \\ Zhongchun Road & 27 & 57 & 382 & 191 \\ Jinghong Road & 27 & 57 & 890 & 445 \\ South Sanlin & 40 & 70 & 356 & 178 \\ East Kanggiao & 41 & 71 & 714 & 357 \\ Shanghai International Resort & 45 & 75 & 412 & 206 \\ Pudong Airport Terminal 1\&2 & 39 & 69 & 812 & 406 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Operation data setting. Figure 9: OD passenger flow arrival rate. The optimized timetable of TUOS-ELS obtained by the GUROBI solver is shown in Figure 13. In Figure 13, the red dashed line and the blue dashed line indicate the time-station paths of trains in the downstream direction and the upstream direction, respectively. The double purple circles indicate the stations skipped by express trains in the downstream direction. Figure 11: Number of passengers waiting of upstream. Figure 12: Number of passengers waiting of downstream. Figure 10: The timetable of T-TPOS. The number of stops, the number of stranded passengers, and the total travel time of each train were counted for the two schemes, as shown in Table 3. Passengers' total waiting time and on-board time are counted in Table 4. The value of objective function represents the total cost of the operator and the passenger in RMB, which is determined by setting the values of \(z_{1},z_{2},z_{3}\), i.e., \(z_{1}=150,z_{2}=10,z_{3}=1\). The term \(z_{1}=150\) is derived from a simulation calculation, primarily including the energy consumption of train stopping, acceleration, deceleration, and equipment maintenance costs. Based on the fare range of 4-26 RMB for the Shanghai Suburban Railway airport link line, and considering the dissatisfaction of stranded passengers, \(z_{2}\) is chosen as the middle value of the fare range, i.e., \(z_{2}=10\). For suburban trains running at 160 km/h, according to literature [6], it is known that the train consumes approximately 1 RMB per second, i.e., \(z_{3}=1\).