# A Novel Multi-Agent-Based Approach for Train Rescheduling in Large-Scale Railway Networks
## 5 Case Study
### Computational Experiments and Discussion
\begin{table}
\begin{tabular}{l l l l l l l l} \hline  & **S6** & **S4** & **S28** & **S24** & **S12** & **S50** & **S14** \\ \hline North Stafford Jn & – & – & 08:02:21 & 08:11:40 & – & 07:55:51 & 08:03:42 \\ \hline Derby LNW Jn & – & – & 07:58:02 & 08:07:19 & – & 08:00:45 & 07:59:25 \\ \hline Derby London Road Jn & 07:48:15 & 07:49:17 & 07:50:45/ 07:57:06 & 08:06:24 & 07:59:09 & – & – \\ \hline Derby Station & 07:49:10– & 07:50:18– & 07:51:43– & 07:59:17– & 07:53:00 & 08:02:54– & 07:53:00– \\ \hline Derby North Jn & 07:53:58 & 07:53:44 & – & – & – & 08:10:30 & 07:52:08 \\ \hline Ambergate Jn & 08:08:12 & 08:01:09 & – & – & – & – & 07:30:10 \\ \hline \end{tabular}
\end{table} 
Table 6: Rescheduled timetable for representative trains in MAS. \begin{table}
\begin{tabular}{l l l l l l l l} \hline  & **S6** & **S4** & **S28** & **S24** & **S12** & **S50** & **S14** \\ \hline North Stafford Jn & – & – & 08:04:37 & 08:11:40 & – & 07:55:51 & 08:01:50 \\ \hline Derby LNW Jn & – & – & 07:59:53 & 08:07:19 & – & 07:59:15 & 07:57:51 \\ \hline Derby London Road Jn & 07:48:15 & 07:49:17 & 07:50:45/ 07:58:00 & 08:06:24 & 07:58:42 & – & – \\ \hline Derby Station & 07:49:10– & 07:50:18– & 07:51:43– & 07:58:00– & 07:53:00 & 08:01:07– & 07:53:00– \\ \hline Derby North Jn & 07:52:10 & 07:53:18– & 07:56:43 & 08:06:00 & 07:53:00 & 08:10:00 & 07:57:00 \\ \hline Derby North Jn & 07:52:25 & 07:53:44 & – & – & – & 08:10:30 & 07:52:08 \\ \hline Ambergate Jn & 08:07:28 & 08:08:51 & – & – & – & – & 07:30:10 \\ \hline \end{tabular}
\end{table} 
Table 5: Rescheduled timetable for representative trains in FCFS. easily absorbed by the dwell time at Derby station. The detailed passing sequence in scenario M_S28(1320s)_S4(300s) is shown in Table 7 below, and the difference in sequence is highlighted in the table. In this single scenario, due to the global voting mechanism proposed in this paper, the delays of trains S4 and S28 are reduced and the delays of trains S6, S24, S12, S50 and S14 are enlarged against the FCFS dispatching rule. The improvements in delays for S4 and S28 are larger than the values of deterioration for S6, S24, S12, S50, and S14, so the value of total delay across the whole network is reduced. With the changes in the passing sequence between the solutions of FCFS and MAS, the maximum value of prolonged delay for trains S6, S24, S12, S50, and S14 is up to 3 min, and the mean value is about 1 min, and the reduced delays for S4 and S28 are up to 5 min and 2.5 min, respectively. Although improving the performance of S4 and S28 results in more delays for other trains, the prolonged delays are usually around 1 min, which is acceptable for daily operations. Furthermore, S4 and S28 are long-distance services that are more sensitive to punctuality, so it is worth changing the train passing sequence to the MAS version. In brief, 11.8% and 20.64% of the solutions generated by the MAS are better than those by FCFS in class I and class II, respectively. The improvement based on FCFS in terms of the values of the objective function is up to 34.11%, 28.7%, and 21.27% in class I, class II, and class III, respectively. Figure 4 illustrates the detailed average values of the objective function in class III, and Figure 5 shows the computational time of each agent in the MAS.