# An Evaluation Framework and Algorithms for Train Rescheduling
## 7 Description of the Experiment
### Train Punctuality  
A general observation is that, in the solutions obtained by ALG2, the percentage of trains exactly on time is typically higher compared to the solutions obtained by ALG1 (see Figure 2b). Furthermore, in the solutions obtained using ALG1, trains often reach their final destination earlier than initially planned in the original timetable, while, in the solutions generated by ALG2, trains rarely arrive at their final station earlier than the originally planned arrival time (see Figure 2a). This makes sense as there is no penalty for early train arrivals in ALG1, whereas one of the objectives of ALG2 is to minimize the end time deviations in train events, albeit the objective with the least priority. What can also be observed from Figure 2b is that the share of affected trains is significantly larger in scenarios 21-30, which primarily is an effect from the initial source of delay, i.e., a temporary infrastructure failure that immediately affects multiple trains. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Algorithm**} & \multicolumn{5}{c}{**Percentage of Trains**} \\ \cline{2-6}  & **Early** & **On-Time** & \multicolumn{3}{c}{**Delayed at Final Section**} \\ \cline{3-6}  & & & **\textless{}3 min** & **[3, 10] min** & **[10, 30] min** & \(\geq\)30 min** \\ \hline ALG1 & 5.10\% & 85.30\% & 7.03\% & 1.43\% & 0.83\% & 0.07\% \\ ALG2 & 0.07\% & 91.83\% & 6.03\% & 1.36\% & 0.50\% & 0.07\% \\ \hline \hline \end{tabular}
\end{table} 
Table 15: An overview of train punctuality: average values over all scenarios. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Algorithm**} & \multicolumn{3}{c}{**Secondary Delays**} \\ \cline{2-4}  & **Early** & **Delayed** & **Travel Times (i)** & **Stops (u)** & **Arriving Earlier** \\ \hline ALG1 & 2.76 min & 0.54 min & 1.54 min & 2.13 & 3.63\% \\ ALG2 & 0.46 min & 0.24 min & 1.92 min & 1.27 & 0\% \\ \hline \hline \end{tabular}
\end{table} 
Table 18: An overview of freight train performance: average values over all scenarios. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Algorithm**} & \multicolumn{3}{c}{**Percentage of Trains**} \\ \cline{2-4}  & **Early** & **On-Time** & \multicolumn{3}{c}{**Delayed at Final Section**} \\ \cline{3-6}  & **\textless{}3 min** & **[3, 10] min** & **[10, 30] min** & \(\geq\)30 min** \\ \hline ALG1 & 5.10\% & 85.30\% & 7.03\% & 1.43\% & 0.83\% & 0.07\% \\ ALG2 & 0.07\% & 91.83\% & 6.03\% & 1.36\% & 0.50\% & 0.07\% \\ \hline \hline \end{tabular}
\end{table} 
Table 16: An overview of train delays: average values over all scenarios. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Algorithm**} & \multicolumn{3}{c}{**Percentage of Trains**} \\ \cline{2-4}  & **Early** & **On-Time** & \multicolumn{3}{c}{**Delayed at Final Section**} \\ \cline{3-6}  & **\textless{}3 min** & **[3, 10] min** & **[10, 30] min** & \(\geq\)30 min** \\ \hline ALG1 & 5.10\% & 85.30\% & 7.03\% & 1.43\% & 0.83\% & 0.07\% \\ ALG2 & 0.07\% & 91.83\% & 6.03\% & 1.36\% & 0.50\% & 0.07\% \\ \hline \hline \end{tabular}
\end{table} 
Table 15: An overview of train punctuality: average values over all scenarios. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Algorithm**} & \multicolumn{3}{c}{**Secondary Delays**} \\ \cline{2-4}  & **\textless{}3 min** & \textgreater{}3 min** \\ \hline ALG1 & 3.8 & 2.4 \\ ALG2 & 2.8 & 1.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 17: An overview of delay propagation: average values over all scenarios. ALG1 typically provides solutions with a higher percentage of delayed trains (see Table 10). In the solutions to scenarios 1-10 obtained using ALG1, no train experiences a delay \(\geq\) 30 min at their final stations. In the solutions obtained by the algorithms for scenarios 21-30, trains are always punctual at their final stations within 10 min (see Table 10). However, in the solutions obtained by ALG1, more trains experience smaller delays.