# A Heuristic Approach to Solving the Train Traffic Re-Scheduling Problem in Real Time
## 5 Experimental Application and Performance Assessment
### Experimental Set-Up
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Scenario** & \multicolumn{2}{c}{**Disturbance**} & \multicolumn{2}{c}{**Problem Size: \#Events 1**} \\ \hline
**Category: ID** & **Location** & **Initially Disturbed Train** & \begin{tabular}{c} **Initially Delay** \\ **(min)** \\ \end{tabular} & \
\begin{tabular}{c} **1 h Time** \\ **Window** \\ \end{tabular} &
\begin{tabular}{c} **1.5 h Time** \\ **Window** \\ \end{tabular} \\ \hline
1:1 & Karlshamm-Angságsmossen & 1058 (Eastbound) & 10 & 1753 & 2574 \\
1:2 & Bromolla Solvesborg & 1064 (Eastbound) & 5 & 1717 & 2441 \\
1:3 & Kristianstad-Karpalund & 1263 (Southbound) & 8 & 1421 & 2100 \\
1:4 & Bergdas-Guillenma & 1097 (Westbound) & 10 & 1739 & 2482 \\
1:5 & Barkabe Hopy-Ronneby & 1103 (Westbound) & 15 & 1393 & 2056 \\
1:6 & Flackarp-Hárup & 491 (Southbound) & 5 & 1467 & 2122 \\
1:7 & Eslov-Dammstorp & 533 (Southbound) & 10 & 1759 & 2578 \\
1:8 & Burlov-Akarp & 544 (Northbound) & 7 & 1748 & 2572 \\
1:9 & Burlov-Akarp & 1378 (Northbound) & 4 & 1421 & 2100 \\
1:10 & Hoör-Stehag & 1381 (Southbound) & 10 & 1687 & 2533 \\
2:1 & Karlsham-Angságsmossen & 1058 (Eastbound) & 40\% & 1753 & 2574 \\
2:2 & Bromolla Solvesborg & 1064 (Eastbound) & 20\% & 1717 & 2441 \\
2:3 & Kristianstad-Karpalund & 1263 (Southbound) & 20\% & 1421 & 2100 \\
2:4 & Bergdas-Guillenma & 1097 (Westbound) & 40\% & 1739 & 2482 \\
2:5 & Barkabe Hopy-Ronneby & 1103 (Westbound) & 100\% & 1393 & 2056 \\
2:6 & Flackarp-Hárup & 491 (Southbound) & 100\% & 1467 & 2122 \\
2:7 & Eslov-Dammstorp & 533 (Southbound) & 50\% & 1759 & 2578 \\
2:8 & Burlov-Akarp & 544 (Northbound) & 80\% & 1748 & 2572 \\
2:9 & Burlov-Akarp & 1378 (Northbound) & 40\% & 1421 & 2100 \\
2:10 & Hoör-Stehag & 1381 (Southbound) & 40\% & 1687 & 2533 \\
3:1 & Karlsham-Angságsmossen & All trains passing through & 4 & 1753 & 2574 \\
3:2 & Bromolla Solvesborg & All trains passing through & 2 & 1717 & 2441 \\
3:3 & Kristianstad-Karpalund & All trains passing through & 3 & 1421 & 2100 \\
3:4 & Bergdas-Guillenma & All trains passing through & 6 & 1739 & 2482 \\
3:5 & Brakne Hopy-Ronneby & All trains passing through & 5 & 1393 & 2056 \\
3:6 & Flackarp-Hárup & All trains passing through & 3 & 1467 & 2122 \\
3:7 & Eslov-Dammstorp & All trains passing through & 4 & 1759 & 2578 \\
3:8 & Burlov-Akarp & All trains passing through & 2 & 1748 & 2572 \\
3:9 & Burlov-Akarp & All trains passing through & 2 & 1421 & 2100 \\
3:10 & Hoör-Stehag & All trains passing through & 2 & 1687 & 2533 \\ \hline \hline \end{tabular}  
* The size of the generated graph \(G\) is the squared size of number of events.  
\end{table} 
Table 3: Description of the 30 \(\times\) 2 scenarios that were used in the experimental study. The first number in the scenario-ID specifies which disturbance category it is. For category 2, the disturbance is a percentage increase of the runtime, e.g., 40%. The two rightmost columns specify the size of the problem expressed in a number of train events that are to be re-scheduled. Figure 4: Illustration of the studied railway line Karlskrona-Kristianstad-Malmö. Source: Trafikverket. The _minimum release time goes first_ (DR-1) was the best dispatching rule, considering the \(\sum TFD_{j}^{+3}\) objective function. The average \(\sum TFD_{j}^{+3}\) for the MIP model was 259 s for the 1 h time window and 332 s for the 1.5 h time window. The average \(\sum TFD_{j}^{+3}\) for the _minimum release time goes first_ (DR-1) was 597 and 849 s, respectively. Statistical analyses of the results belonging to disturbance scenario type 1 revealed that the _less real buffer time goes first_ (DR-3) dispatching rule, with an average delay of 361 s for a 1 h time window and 314 s for a 1.5 h time window, works better than the other dispatching rules. Additionally, an inefficient solution is not able to absorb the delays (i.e., the delays after a temporary route blocking may remain in the system until midnight).