## 3 Route Choice Modeling
### Estimation Result  
Apart from the explanatory variables above, the sensitivity of waiting time is another crucial factor when evaluating passengers' choice preferences with emergency-caused delays. Obviously, the commuters could be more pleased to reduce their waiting time in their trip, while those who travel during the nonpeak period may be more unconcerned about the length of waiting time. This distinction of delay time perception is captured by our survey and is shown in Figure 3. Passengers traveling during morning peak periods are the most sensitive to waiting time, and as the waiting time increases, fewer people will be able to tolerate it. Evening peak period follows the same tendency thatmost of the metro passengers can endure 5 to 10 min delays, and, afterward, the number of passengers who willing to wait decreases with the waiting time extends.  
However, during the nonpeak period, the tendency is exactly the opposite that the passengers' acceptance of longer waiting time is much higher than peak periods. Moreover, as the longest waiting time extends, the proportion of the nonpeak period is monotonically increasing. It indicates that passengers that travel during the nonpeak period are more tolerant of longer waiting time than passengers who travel during peak periods.  
The significantly different tendency about waiting time under different periods reflects passengers' heterogeneity in route choices under metro emergencies. Therefore, apart from the route choice model that describes passengers' routing behaviors of the entire day (M1), route choice models for peak periods (M2) and nonpeak periods (M3) are also estimated to investigate the detailed distinctions of passengers' preferences under metro emergency-caused delays. The estimation results are listed in Table 2.  
As is shown in Table 2, all models' adjusted rho-square are larger than 0.2 indicating good model fit of these three models [45]. All the parameters have reasonable signs, and most of the estimated parameters are statistically significant at the 95% level for the absolute values of the t-test are larger than 1.96.  
Variables like ASC 1 to ASC 5 are alternative specific constants added to alternatives route 1 to route 5 in order to capture passengers' unobserved preferences in route choices. Their values are all positive indicating that passengers have tendencies to choose these routes under the emergency-caused delays comparing with the last alternative route 6 (using taxis to reach their destination). It is worth noting that parameters like AC and transfer times show positive effects on metro passengers' routing behaviors. The estimation result seems against our common knowledge that detour and more transfers should have negative effects when passengers considering which way to go.  
However, it is reasonable considering the particular delayed condition caused by metro emergencies. Since the delays have altered the passengers' original choosing environment and the choice set is changed as well, which weakens the advantages of the original choice (the time shortest route) with delay time. These changes make other routes (with more transfer between different metro lines or detours) look like better choices. The alter of the decision-making environment urges passengers to move rather than just standing still and wait, and this phenomenon is much distinguished when the delay time becomes longer, which is in line with what we analyzed above. With the estimated route choice model, we can predict metro passengers' distribution in the network during the delay period, and it is the foundation of simulation.  
Figure 3: Passengers’ endurance of delay time in different period.