# Double-Track One-Direction Operation Mode for Overnight Trains on High-Speed Railway
## 4 Case Study
### Results  
All trains rendezvous at the Zhengzhoudong Station, and the double-track one-direction section is from Xuzhoudong to Xi'anbei. The optimal solution of the objective function obtained by calculation and manual correction was converted into tabular form as shown in Table 2.  
Because of the limited number of arrival and departure tracks, the same amount of time can be consumed by slowing down instead of stopping at stations. Entering the double-track one-direction operation too early or too late may affect the operation of other trains. According to the actual operation situation, the operation period of the double-track one-direction mode should be limited from 23:30 to 05:30 of the next day as far as possible. On the premise of ensuring the maintenance disruption of 180 min in each section, passenger trains are allowed 20 min for the entire journey in each direction. When \(\Delta t\) equals 5 min, 10 pairs of trains can be accommodated. Figure 11 shows the fully operational diagram. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**ID**} & \multirow{2}{*}{**Station Name**} & **Mileage** & **250 km/h Trains** & **350 km/h Trains** & **Number of Arrival and** \\  & & **(km)** & **Pass-through Time** & **Pass-through Time** & **Departure Tracks** \\ \hline
0 & Xuzhoudong & 0 & 0 & 0 & 28 \\
1 & Xiaoxianbei & 47 & 12 & 9 & 6 \\
2 & Yongchengbei & 83 & 21 & 15 & 4 \\
3 & Dangshannan & 126 & 32 & 23 & 4 \\
4 & Shangqiu & 182 & 46 & 33 & 7 \\
5 & Minquanbei & 248 & 63 & 45 & 4 \\
6 & Lankaonan & 282 & 72 & 51 & 4 \\
7 & Kaifengbei & 338 & 86 & 61 & 4 \\
8 & Zhengzhoudong & 361 & 92 & 66 & 32 \\
9 & Zhengzhouxi & 441 & 113 & 80 & 4 \\
10 & Gongyianan & 475 & 121 & 86 & 4 \\
11 & Luoyang & 509 & 130 & 93 & 7 \\  & Longmen & 579 & 148 & 105 & 4 \\
12 & Minchinan & 640 & 163 & 116 & 4 \\
13 & Sammenxian & 693 & 177 & 126 & 4 \\
14 & Lingbaoi & 755 & 193 & 137 & 6 \\
15 & Huashanbei & 813 & 208 & 148 & 4 \\
16 & Weinanbei & 866 & 221 & 157 & 34 \\
18 & Xianyangxi & 901 & 230 & 166 & 5 \\
19 & Yanglingnan & 960 & 245 & 181 & 6 \\
20 & Qshshan & 998 & 255 & 191 & 4 \\
21 & Baojian & 1033 & 264 & 200 & 14 \\
22 & Dongcha & 1097 & 280 & 216 & 4 \\
23 & Tianshuinan & 1189 & 304 & 240 & 7 \\
24 & Qinan & 1243 & 317 & 253 & 4 \\
25 & Tongwei & 1307 & 334 & 270 & 4 \\
26 & Dingxibei & 1346 & 344 & 280 & 6 \\
27 & Yuzhong & 1390 & 355 & 291 & 4 \\
28 & Lanzhouxi & 1434 & 366 & 302 & 28 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of the Xuzhou-Lanzhou high-speed railway. Down-direction trains passing this section used 5 h and 23 min, and the average speed was 161 km/h; the up-direction trains used 5 h and 24 min, and the average speed reached 197 km/h. The double-track one-direction operation section started at 23:38 and ended at 05:20. All of the maintenance disruption was finished by 06:50, satisfying the current schedule, and it did not affect the morning and evening trains. According to the sleeping habits of passengers, the full time of the sunset-departure and sunrise-arrival trains controlled in 10-13 h is quite reasonable. A distance range of \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Station ID** & **Station Name** & \
\begin{tabular}{c} **Stop Time for** \\ **down-Direction Train (min)** \\ \end{tabular} &
\begin{tabular}{c} **Stop Time for** \\ **up-Direction Train (min)** \\ \end{tabular} \\ \hline
0 & Xuzhoudong & - & - \\
1 & Xiaoxinbein & - & - \\
2 & Yongchengbei & - & - \\
3 & Dangshannan & - & - \\
4 & Shangqiu & 9 & 15 \\
5 & Minquanbei & - & - \\
6 & Lankaonan & - & - \\
7 & Kaifengbei & 9 & 8 \\
8 & Zhenghoudong & - & - \\
9 & Zhengzhouxi & - & - \\
10 & Gongyian & - & - \\
11 & Luoyang & - & - \\
12 & Longmen & - & - \\
12 & Mianchinan & - & - \\
13 & Sammerxianan & 28 & 6 \\
14 & Lingbaoxi & - & - \\
15 & Huashanbei & - & - \\
16 & Weinanbei & - & - \\
17 & Xianbei & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The optimal solution of the fully operational diagram. Figure 11: Fully operational diagram.