# A Novel Multi-Agent-Based Approach for Train Rescheduling in Large-Scale Railway Networks
## 5 Case Study
### Computational Experiments and Discussion  
The final evaluation is based on the total value of the objective function for the five junction dispatching agents. Train cancellations and replatforming actions are not considered. The TTOE strategy, which follows the original train schedule sequence, is \begin{table}
\begin{tabular}{c c c} \hline \hline
**Index** & **Train ID** & **Delay Distribution** \\ \hline Class III\_a & & \(k=0.45\), \(\lambda=4\) \\ \hline Class III\_b & All trains potentially delayed on departure & \(k=0.5\), \(\lambda=6\) \\ \hline Class III\_c & & \(k=0.55\), \(\lambda=8\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Summary of minor perturbation delay scenarios. included for comparison. However, TTOE often performs worse than FCFS and the proposed MAS, and is sometimes not feasible. FCFS is used as the baseline to assess improvements achieved by the MAS over traditional human dispatching. The specific data settings for each local dispatching agent are detailed in the following sections, providing a clear framework for evaluating the MAS approach's effectiveness in optimizing train dispatching in a complex railway network. * \(t_{slot}=30\) min;
* \(N_{gen}=100\);
* \(P_{sel}=0.8\);
* \(N_{ter}=50\). To show the advantages of the proposed MAS approach, an example scenario (M_S28_S4) is detailed and discussed below. In Table 4, each value states the TD in seconds across the whole network; numbers in black indicate that the decisions made from the FCFS and MAS approaches are the same in terms of TD, and in the scenario with two values, the numbers in red and green stand for FCFS and MAS, respectively. To illustrate the difference between the FCFS and MAS approaches, we take the case of S28 with a 1320 s delay and S4 with a 300 s delay as an example. The detailed timetables of the representative trains for FCFS and MAS are shown in Tables 5 and 6 below, and their differences are highlighted in red color:  
S28 and S4 are long-distance services with a single stop in Derby station, originating from Long Eaton station and terminating at Willington and Clay Cross North Junction, respectively. S6 is local service to Matlock station from Long Eaton station with stops at Spondon, Derby, Duffield, Belper, Ambergate, Whatstandwell, Cromford, Matlock Bath, and Matlock stations. S6, S4, and S28 enter the simulation at 7:38:00, 7:39:00, and 7:43:00, respectively; due to their same trajectory between Long Eaton and Derby stations, the movement of S6 blocks the movement of S4 and S28. S6 has a dwell at Spondon station, which means that S4 and S28 have to wait outside Spondon station and extend their delays. As they approach Derby station, S6, S4, and S28 dwell at platforms 6, 4, and 5, respectively. After dwelling at Derby station, S6 and S4 are dispatched to the Ambergate Junction side at 7:52:10 and 7:53:44, respectively. However, S6 and S4 will ask for the same infrastructure between Derby station and Ambergate Junction, so if Derby Station North Junction makes the decision according to FCFS, dispatching S6 before S4, the future movement of S4 will be blocked by S6 and its dwelling at Duffield and Belper stations, resulting in a significant delay of S4 at Ambergate Junction, though FCFS has a smaller value for its local objective function. In the MAS approach, Derby Station North Junction launches S4 first, followed by S6. Besides that, S24 is also a long-distance service having the same trajectory as S28 but with a dwell at Derby station at platform 3, and S12 is a high-speed train that enters the simulation from Derby station and is dispatched to the Long Eaton station side from the same platform as S28. In the context of FCFS, the train will be dispatched by Derby London Road Junction in the sequence S24, S28, S12; that decision will increase the delay of S28 and attach a larger knock-on delay to S12. However, the MAS decides to launch S28 first, with the sequence S28, S24, S12. Then, the delay of S28 will be smaller than under FCFS, and the delay to S24 caused by its conflict with S28 will be