# 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} \hline \hline
**Passing sequences of trains in each junction in FCFS** \\ \hline The order for **North Strafford Junction** is: S5, S1, S51, S2, S19, S13, S22, S23, S15, S52, S50, S18, S14, S28, S31, S24, S35, S41, S37, S42, S33, S36, S40, S43, S32, S44, S54; \\ The order for **Derby LNW Junction** is: S5, S1, S51, S2, S13, S19, S22, S15, S23, S52, S14, S50, S28, S18, S24, S31, S41, S35, S37, S42, S33, S43, S36, S40, S44, S32, S54; \\ The order for **Derby London Road Junction** is: S53, S51, S47, S5, S49, S9, S51, S5, S57, S47, S2, S25, S49, S11, S10, S19, S15, S19, S15, S19, S16, S4, S52, S28, S24, S28, S12, S50, S26, S24, S50, S55, S16, S29, S42, S35, S42, S35, S38, S43, S36, S39, S30, S36, S44, S45, \\ The order for **Derby Station North Junction** is: S53, S58, S9, S47, S53, S49, S47, S8, S25, S57, S57, S49, S52, S6, S4, S26, S29, S55, S43, S38, S30, S39, S45; \\ The order for **Ambergate Junction** is: S58, S9, S8, S25, S13, S1, S14, S27, S52, S26, S22, S16, S6, S29, S4, S23, S41, S18, S55, S43, S30, S37, S45, S38, S39, S40. \\ \hline
**Passing sequences of trains in each junction in MAS** \\ \hline The order for **North Strafford Junction** is: S5, S1, S51, S2, S19, S13, S22, S23, S15, S52, S50, S18, S28, S14, S31, S24, S35, S41, S37, S42, S33, S36, S40, S43, S32, S44, S54; \\ The order for **Derby LNW Junction** is: S5, S1, S51, S2, S13, S19, S22, S15, S23, S52, S28, S14, S50, S18, S24, S31, S41, S35, \\ S37, S42, S33, S43, S36, S40, S44, S32, S54; \\ The order for **Derby London Road Junction** is: S53, S51, S47, S5, S49, S9, S51, S55, S57, S47, S2, S25, S49, S11, S10, S19, S15, S15, S19, S15, S19, S6, S4, S52, S28, S24, S12, S50, S55, S56, S29, S42, S35, S42, S35, S38, S43, S36, S39, S30, S36, S44, S45; \\ The order for **Derby Station North Junction** is: S53, S58, S9, S47, S53, S49, S47, S8, S25, S57, S27, S49, S57, S52, S4, S6, S26, S16, S29, S55, S43, S38, S30, S39, S45; \\ The order for **Ambergate Junction** is: S58, S9, S8, S25, S13, S1, S14, S27, S526, S22, S16, S4, S29, S6, S23, S41, S18, S55, S43, S30, S37, S45, S38, S39, S40. \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Passing sequence of trains in all junctions considered in FCFS and MAS. In summary, the MAS effectively addresses the train dispatching problem during delays, achieving up to a 34.11% improvement in network-wide delay reduction. The computational times for the junction agent and collaborative agent are 13.49 s and 7.62 s, respectively. The overall computational time for the system, which depends on the slowest junction agent and the collaborative agent's voting process, averages 27.39 s, with a maximum of 33.87 s. A key advantage of the MAS is its ability to offer a global perspective to each junction agent, enabling it to balance solutions across the network. This collaborative strategy ensures that overly greedy decisions made by individual junction agents can be corrected, thereby enhancing the overall feasibility and optimization of train dispatching solutions. The collaborative agent plays a crucial role in validating the global feasibility of the solutions and selecting the optimal approach from the junction agents under its control.