## 5 Case Study
### Capacity Assessment of Xuzhou-Bengbu Section  
The Xuzhou-Bengbu Section is generally considered to be the busiest and most tightly utilized section of the Beijing-Shanghai high-speed railway, including three stations of Xuzhou East, Suzhou East, and Bengbu South. According to the statistics of the existing timetable, the number of trains in the Xuzhou-Bengbu section is 152. As shown in Figure 10, these trains are divided into four continuous train group groups after sorting and grouping steps. The occupancy time of each continuous train group is calculated in turn and summed to obtain a total occupancy time \(OT_{total}\) of 911.4 min. The total available time in this section is: \(T_{available}=1052.67(\text{min})\). The capacity utilization rate of timetable is: \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Sections** & **Departure Station** & **Arrival Station** & **Number of** & **Length (km)** & \(TT_{s}\) \\ \hline Beijing-Tianjin & Beijing South & Tianjin South & 3 & 131 & 0:26:40 \\ Tianjin-Jinan & Tianjin South & Jinan West & 4 & 288 & 0:51:10 \\ Jinan-Xuzhou & Jinan West & Xuzhou East & 6 & 269 & 0:50:45 \\ Xuzhou-Bengbu & Xuzhou East & Bengbu South & 3 & 156 & 0:27:20 \\ Bengbu-Nanjing & Bengbu South & Nanjing South & 4 & 174 & 0:34:00 \\ Nanjing-Shanghai & Nanjing South & Shanghai & 8 & 284 & 0:55:05 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Sections of the Beijing–Shanghai high-speed railway. Figure 10: Timetable of the Xuzhou–Bengbu section. \(\mu=911.4/1052.67=86.57\%\). The maximum number of trains in the timetable is: \(N_{capacity}=152/86.57\%=175\). Based on the existing train timetable, the algorithm characteristics are compared with the compression method by randomly generating train timetables with different train numbers for thousands of times. The capacity, utilization and computing time under different train number of both methods are recorded. A part of the results is shown in Table 3.  
The results show that, for both of the two methods, as the number of trains in the timetable increased, the section capacity also increased. This phenomenon occurs because when the number of trains is small, the trains are laid sparsely, and the average occupancy time is longer. When the number of trains in the timetable increases, to make full use of the time, the new trains will overlap with the original trains so that the average occupancy time decreases, and the calculated carrying capacity becomes larger. In addition, we can see that although the calculation time of the two methods is both increasing, the combined method is obviously much faster than the compression method because the relationship between trains is simplified. Figure 11 shows the calculation results for the capacity of the two methods of the combined method and compression method when the number of trains in the timetable is different. The calculation result of the compression method is higher than the calculation result of the combined method in all cases because the compression method does not consider the buffer time between trains, which will cause the calculation result to be relatively large. In addition, when the number of trains in the timetable is small, the calculation results differ greatly because when the number of trains is small, the trains are often spread evenly, and the compression process for the compression method changes the trains into centralized, which changes the characteristics of the train timetable.