## 3 Route Choice Modeling
### Explanatory Variables  
Generally, many variables could influence passengers' mode and route preferences under the delays caused by metro emergencies, such as route attributes, topological properties of the metro network and delay specific variable. In this study, route attributes such as travel time, travel cost and transfer time are taken into consideration. The topological properties of the metro network are designed as indicators to evaluate the importance of stations and routes in the network. Passengers always prefer the fastest, shortest or the most convenient route between origin and destination and unwilling to take detours when the metro system is normally operating. However, when the chosen route is delayed by the emergencies, passengers may have to weigh between taking detours and waiting for the original route. Angular cost (AC) is the indicator designed to demonstrate passengers' unwillingness about taking detours and the penalty of detoured routes. As metro routes do not directly connect origin and destination, especially when origin and destination are not on the same line. The deviation between the chosen metro routes and the direct connect of origin-destination have a significant influence on passengers' route choices [40,41]. The angular cost increases with the increase of the deviation angles and the length of the route. [PERSON] et al. [42] modified the original formula by using the tangent function, as shown in Equation (1). With this modification, the AC is more sensitive to the changes in deviation angle and the impact on passengers' route choice behaviors is more significant. \[AC_{k}^{\text{ad}}=\sum_{s}^{N_{s}}L_{s}\times\tan\frac{\theta_{s}}{4} \tag{1}\]  
Figure 2: Respondents attribute in the SP survey. where, route \(k\)'s AC from station \(o\) to station \(d\) is represented by \(AC_{k}^{od}\), assume route \(k\) goes through \(N_{s}\) stations between \(o\) and \(d\), and the section from station \(s\) to station \(s+1\) is represented by \(L_{s}\), \(s\in S\), where \(S\) is the set of stations in the metro network. The angular deviation between section \(s\) and the direct connection of \(o\) and \(d\) is represented by \(\theta_{s}\), \(\theta_{s}\in[0,\,\pi]\). Moreover, different metro stations play different roles in the network, and transfer stations and non-transfer stations may be valued differently for different passengers. Especially, when an emergency occurs in the metro system, a route with more transfer stations can offer more route alternatives than the ones with fewer transfer stations, but a transfer station always means more passengers and the station could be very crowded. The differences between stations are represented by station betweenness centrality (BC), which is the ratio between the amount of the shortest routes through the particular station and all the shortest routes in the network. BC derives from graph theory, and it measures metro stations' importance by their ability to control the shortest routes. A station with higher BC means stronger control capability over the entire network, and if it is disabled by metro emergencies, all the shortest routes that go through this station have to stop operating [43; 44]. In our research, we do not only focus our attentions on metro stations' BC, but also consider the betweenness of the routes, and it can be calculated by the following equation:  
\[BC_{k}=\sum_{s}^{N_{s}}bc_{s}=\sum_{s}^{N_{s}}\sum_{p\
eq q\
eq s}\frac{N_{pq} (s)}{N_{pq}} \tag{2}\]  
where \(N_{pq}(s)\) is the amount of shortest routes between station \(p\) and station \(q\) that go through station \(s\), \(N_{pq}\) is the total amount of shortest routes between \(p\) and \(q\) in the entire network, \(s\), \(p\), \(q\in S\). Apart from the aforementioned explanatory variables that describe characteristics of the routes and the networks, another explanatory variable is designed in this research to demonstrate the feature of emergency-caused delays, not just take the delay time as a variable.