## 5 Case Study
### Optimization of Timetable During Trial Operation
Moreover, the values marked with * are used in the calculation of the objective function. In Table 3, TUOS-ELS saves 38.59% in the total cost of the operator and the passenger compared to T-TPOS. The number of trains in the upstream direction was increased from 5 to 7, creating a shortened headway. The obtained headways for each train in the upstream direction are shown in Figure 16. All headways in the downstream direction are 1800 s. As a result, the number of stranded passengers decreased from 2489 to 196, and the total waiting time of passengers was greatly shortened from 2581.1 h to 1841.1 h in the upstream direction in Table 4. However, in the downstream, at the expense of a small number of stranded passengers, the reduction in the number of trains and the use of an express train (train 2) have significantly decreased the total travel time of trains from 10,185 s to 6139 s. Moreover, passengers' on-board time were reduced by 8 h as compared with T-TPOS in the downstream direction. It is worth noting that TUOS-ELS can improve the trains' loading rate in both directions. In Figure 17,b, the maximum loading rates of TUOS-ELS and T-TPOS in the upstream \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Total Waiting Time (h)**} & \multicolumn{2}{c}{**Total On-Board Time (h)**} & \multirow{2}{*}{**Calculation Time (s)**} & \multirow{2}{*}{**Gap of GUROBI**} \\ \cline{2-2} \cline{5-6}  & **Upstream** & & & & & \\ \hline TUOS-ELS & 1841.1 & 723.6 & 2666.5 & 330.8 & 1000 & 0.45\% \\ T-TPOS & 2581.1 & 388.7 & 2189.9 & 338.8 & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison results including passengers’ total travel time. Figure 16: Headway between trains. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Total Travel Time (s)**} & \multicolumn{2}{c}{**Number of Stops**} & \multicolumn{2}{c}{**Stranded Passengers**} & \multirow{2}{*}{**Objective**} \\ \cline{2-2} \cline{5-6}  & **Upstream * & Downstream * & & & & & \\ \hline TUOS-ELS & 14,886 & 6139 & 49 & 20 & 196 & 91 & 34,245 \\ T-TPOS & 10,185 & 10,185 & 35 & 35 & 2489 & 0 & 55,760 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison results including objective function values. direction are 107.64% and 107.82% respectively. Notably, the difference of maximum loading rates between the two schemes is not significant. But, Figure 17a,b illustrate that the trains loading rate under the TUOS-ELS rapidly decreases during the section from 3 to 6, whereas the trains loading rate under the T-TPOS remains consistently high. Meanwhile, in the downstream direction, the maximum loading rates under TUOS-ELS and T-TPOS are 39.27% and 20%. Figure 18a,b clearly demonstrates that the TUOS-ELS effectively enhances the trains' loading rate and minimizes capacity waste. Based on the above analysis, compared to T-TPOS, the implementation advantages of TUOS-ELS can be reflected in both passenger service quality and operating costs. In terms of passenger service quality, TUOS-ELS can effectively reduce the total number of stranded passengers by 2202, the total passenger waiting time by 405.1 h, and the passenger on-board time in the downstream direction by 8 h. Additionally, TUOS-ELS can improve trains' load rate, thereby alleviating passenger congestion. From an operational cost perspective, reducing the total number of train stops can minimize the traction and braking processes, which helps lower energy consumption and equipment maintenance.