## 3 Case Study
### Results and Analysis of Abnormal Stations
#### 3.2.1 Analysis of Abnormal Stations in the Whole Network  
According to the 3\(\sigma\) principle, the fluctuation threshold of the tap-in passenger flow at all stations during the normal operation was obtained. Then, after comparing the tap-in passenger flow between 7:00 a.m. and 10:00 a.m. on 19 February with that during normal operation, all abnormal stations were identified, as shown in Table 1. It was found that the number of abnormal stations in the whole network increased first and then decreased from 7:00 a.m. to 10:00 a.m. Among all time periods, the number of abnormal stations between 8:00 a.m. and 8:15 a.m. was the highest, with 29 abnormal stations, of which 20 stations presented a decrease in tap-in passenger flow and 9 stations presented an increase in tap-in passenger flow. Moreover, in the early stage of the disruption, the abnormal stations were mainly characterized by a decreased tap-in passenger flow, while in the later stage, the abnormal stations were mainly characterized by an increased tap-in passenger flow.  
To visualize the abnormal stations affected by the disruption, a spatiotemporal diagram was drawn, indicating the location of these abnormal stations during different time periods, as presented in Figure 3. It can be seen from Figure 3a that when the disruption occurred, the first stations to be affected were only those upstream and downstream of Bajiao Amusement Park station. Then, several stations adjacent to Bajiao Amusement Park station were affected by the disruption. Finally, the influence of the disruption gradually propagated from adjacent stations to some stations on line 1 that were far away from the disrupted station as time passed. The tap-in passenger flow at these stations decreased significantly. Generally, the disruption did not affect ordinary stations on other lines. It can be seen from Figure 3c that, at 7:45-8:00 a.m., some ordinary stations on line 1 that were far from the disrupted station were not affected by the disruption any longer. At  
\begin{table}
\begin{tabular}{l l l l} \hline
**Time** & **Number of** & **Number of Stations with Decreased Tap-In** & **Number of Stations with Increased Tap-In** \\
**Period** & **Abnormal Stations** & **Passenger Flow** & **Passenger Flow** \\ \hline
7:00–7:15 & 3 & 3 & 0 \\
7:15–7:30 & 19 & 18 & 1 \\
7:30–7:45 & 25 & 24 & 1 \\
7:45–8:00 & 23 & 20 & 3 \\
8:00–8:15 & 29 & 20 & 9 \\
8:15–8:30 & 15 & 3 & 12 \\
8:30–8:45 & 24 & 6 & 18 \\
8:45–9:00 & 22 & 3 & 19 \\
9:00–9:15 & 13 & 0 & 13 \\
9:15–9:30 & 8 & 4 & 4 \\
9:30–9:45 & 10 & 6 & 4 \\
9:45–10:00 & 9 & 4 & 5 \\ \hline \end{tabular}
\end{table}
Table 1: Number of abnormal stations affected by the disruption.  
45 min after the disruption, the issue of signal interruption had been well resolved. The tap-in passenger flow at most transfer stations that were affected by the disruption began to increase, as shown in Figure 3d. Meanwhile, the passenger flow at ordinary stations that were far from the disruption station recovered to a normal level. In contrast to the transfer stations, these ordinary stations did not suffer an increased tap-in passenger flow. However, the adjacent stations were still suffering a decreased tap-in passenger flow in the meanwhile. As time passed, all stations returned to normal, except for the transfer stations affected by the disruption, as can be seen in Figure 3e-h. This indicates that the duration for which transfer stations were affected by the disruption was the longest. In summary, all stations affected by the disruption were ranked according to their recovery speed, from fastest to slowest, as follows: ordinary stations that were far away from the disrupted station, adjacent stations, and transfer stations. Since there was a significant difference between ordinary stations and transfer stations in terms of recovery speed, a detailed analysis of the two types of stations will be presented in the following subsection.  
Figure 3: _Cont._