## 5 Empirical Study  
In order to testify the performance of passengers' routing behavior based congestion propagation rate in the propagation process in the metro network, a small scale of the metro network is selected to reduce the amount of computation and improve operation accuracy. The network we choose is in the central part of Guangzhou metro, as shown in Figure 10, which takes Hesha (HS) station (non-transfer station on Line 6) as the origin station and takes Yangji (Y) station (transfer station of Line 1 and Line 5) as the destination. The augmented metro network is established, where 38 stations (including 26 actual stations and 12 virtual stations) and 52 links (36 actual links and 16 virtual links) are constructed to reflect passengers travel in the system. With the \(k\)-shortest path algorithm, 4 metro routes are selected to construct the route choice set for the passengers, alongside with 1 bus route and 1 taxi rout. The attributes of the 6 routes are listed in Table 3. Where, route 1 is the shortest metro route in travel time (transfer time is included in travel time), route 2 to route 4 are backup routes in the metro system from HS station to YJ station, route 5 travels by bus, route 6 travel by taxi which costs the most among all the routes. Among the metroroutes, a total of 26 metro stations are included (about 10% of the stations in the entire metro network), including 4 transfer stations: Tanwei (TW) station, Huangsha (HSha) station, Quzhuang (QZ) station and Dongshankou (DSK) station. There are 3 transfer stations (the gray transfer stations in Figure 10) that do not provide transfer function in this scenario. Therefore, we just regard them as non-transfer stations on the routes. The interrupted area is placed on route 1 from QZ station to the destination, YJ station, and lead to a delay of about 20 min on route 1, while the other routes are not infected by the metro emergency-caused delay. During the metro delay, passengers can choose all the available routes from route 1 to route 6. Based on the estimated route choice models with the RRM principle in Section 3, the probability of choosing each route is calculated and is shown in Table 4. As in line with what we analyzed before, passengers who suffered the metro emergency-caused delays in the peak periods are more likely to abandon the metro and choose taxi as a back option to ensure punctuality. Fewer passengers want to stand still and wait for the resume of the delayed metro line in all periods of the day. In the ASEIR model, the parameters of M2 and M3 are used, and the simulation results are shown in Figure 11. During peak periods, if there are no intervention measures, it takes 126 time steps (about 4 h) for the network from HS station to HJ station to get rid of the influence of congestion caused by metro emergencies. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Route** & **M1** & **M2** & **M3** \\ \hline
1 & 8.61\% & 6.75\% & 10.86\% \\
2 & 49.83\% & 48.16\% & 51.28\% \\
3 & 34.03\% & 37.59\% & 30.13\% \\
4 & 3.91\% & 3.41\% & 4.73\% \\
5 & 0.89\% & 0.72\% & 1.10\% \\
6 & 2.73\% & 3.37\% & 1.91\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Choice probabilities of each route. Figure 10: Available routes from HS station to YJ station. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Route** & **AC/m** & **BC** & **RSC** & **Travel Time/min** & **Transfer Times** & **Travel Cost/CNY** \\ \hline
1 & 2770.73 & 0.92 & 1 & 23.72 & 1 & 5 \\
2 & 2888.46 & 0.81 & 0.43 & 23.93 & 1 & 5 \\
3 & 3219.03 & 1.01 & 0.58 & 30.88 & 3 & 5 \\
4 & 3020.31 & 0.79 & 0.49 & 26.75 & 1 & 5 \\
5 & - & - & 2.25 & 63 & 0 & 2 \\
6 & - & - & 0.64 & 33 & 0 & 33 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Route attributes from HS to YJ. In peak periods, the susceptible stations decrease rapidly in the beginning, nearly all the stations are influenced by metro emergency before time step 50.