## 6 Case Study on Metro M
### Calculation Results and Analysis
#### 6.3.2 Comparison of the Results  
All train operation plans with virtual coupling trains can reduce passenger waiting time, as shown in Figure 10. As shown in Table 7, the first train operation plan of virtual coupling trains has the minimum passenger waiting time. As shown in Table 8, the first traditional train plan of full-length and short-turn routes has the minimum passenger waiting time. The first train operation plan of virtual coupling trains can reduce the waiting time of passengers by 16.6% and 20.2%, respectively, compared with the first traditional train plan of full-length and short-turn routes and the single train plan. It shows that the train operation plan of virtual coupling trains can greatly reduce the waiting time of passengers and improve the service level. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Minimum Passenger Waiting Time**} & \multicolumn{2}{c}{**Minimum Running Kilometers of Trains**} & \multicolumn{2}{c}{**Optimal Upper Model**} & \multicolumn{2}{c}{**Optimal Lower Model**} \\ \hline Objective functions & Objective function of upper model & 2857.99 & 2904.73 & 2811.09 & 2868.66 \\ Objective functions & Objective function of lower model & 0.16 & 0.18 & 0.12 & 0.03 \\ \hline  & Waiting time for passengers (h) & 2178.46 & 2681.88 & 2234.90 & 2508.91 \\  & Running kilometers of trains (km) & 4342.56 & 3391.60 & 4069.92 & 3654.60 \\ Evaluation index & Number of vehicles used (vehicles) & 180 & 144 & 176 & 168 \\  & Maximum load factor of train (\%) & 97.0 & 114.9 & 95.8 & 120.0 \\  & Average load factor of train (\%) & 60.5 & 76.7 & 63.9 & 75.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: _Cont._ \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Minimum Passenger Waiting Time**} & \multicolumn{2}{c}{**Minimum Running Kilometers of Trains**} & \multicolumn{2}{c}{**Optimal Upper Model**} & \multicolumn{2}{c}{**Single Train Operation Plan**} \\ \hline  & Departure frequency of the full-length train (pairs/h) & 15 & 11 & 14 & 17 \\  & Departure frequency of the short-turn train (pairs/h) & 5 & 11 & 7 & - \\  & Starting station of short-turn route (stations) & 8 & 6 & 8 & - \\ Decision variables & Terminal station of short-turn route (stations) & 15 & 15 & 15 & - \\  & Number of marshalled vehicles of the full-length train (vehicles) & 6 & 6 & 6 & 6 \\  & Number of marshalled vehicles of the short-turn train (vehicles) & 6 & 6 & 6 & - \\ \hline \hline \multirow{4}{*}{\
\begin{tabular}{c} Objective functions \\ Objective functions \\ \end{tabular} } & Objective function of upper model & 3683.39 & 3793.49 & 3712.38 & 3744.74 \\  & Objective function of lower model & 0.67 & 0.51 & 0.77 & - \\ \hline \hline \multirow{4}{*}{
\begin{tabular}{c} Evaluation index \\ \end{tabular} } & Waiting time for passengers (h) & 2610.66 & 2896.18 & 2740.58 & 2728.12 \\  & Running kilometers of trains (km) & 6027.00 & 5753.88 & 5835.48 & 5965.78 \\  & Number of vehicles used (vehicles) & 162 & 162 & 168 & 180 \\  & Maximum load factor of train (\%) & 114.9\% & 112.4\% & 115.2\% & 99.7\% \\  & Average load factor of train (\%) & 72.7\% & 65.8\% & 68.5\% & 55.2\% \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Traditional Train Plan of Full-length and Short-turn Routes and Single Train Plan. Each train operation plan with virtual coupling trains can reduce kilometers of train operation, as shown in Figure 11. As shown in Table 7, the second train operation plan with virtual coupling trains has the minimum running kilometers of trains. In the second train operation plan with virtual coupling trains, there are two marshalling trains on the full-length routes and four marshalling trains on the short-turn routes. This scheme mainly increases the departure frequency of short-turn routes, but decreases the departure frequency of full-length routes.