## 2 Methodologies  
### Evacuation Time Model  
According to the MSC.1/Circular.1533 issued by IMO, the escape time \(T\) can be calculated by:  
\[T=(\gamma+\delta)\times t_{I}+R \tag{1}\]  
where \(\gamma\) is the correction factor, \(\delta\) is the counterflow correction factor equal to 0.3; \(t_{I}\) is the maximum travel duration in ideal conditions, \(R\) is the response duration, and it equals 10 min for the nighttime scenarios and 5 min for the day scenarios [22]. Generally, the escape sequence of passengers is from corridor to stairway and to the stairway exit where the muster station is located. The escape routes are considered to be a hydraulic network. To be specific, corridors and stairs are regarded as pipelines, and doors are treated as valves. Therefore, the time to pass an escape route until the assigned muster station is defined as:  
\[t_{\text{I}}=t_{\text{F}}+t_{\text{deck}}+t_{\text{stair}}+t_{\text{assembly}} \tag{2}\]  
where \(t_{\text{F}}\) is the maximum duration of passengers within all stairways and corridors in an escape route; \(t_{\text{deck}}\) is the travel duration(s) to move from the farthest point of the escape route of a deck to the stairway; \(t_{\text{stair}}\) is the stairway travel duration(s) of the escape route to the assembly station; \(t_{\text{assembly}}\) is the travel duration(s) to move from the end of the stairway to the entrance of the assigned muster station. Specifically, the calculation steps for the durations above are as follows:  
(1) \(t_{\text{deck}}\): Assuming that cabin passengers move into the corridor instantaneously at the same time, the personnel density (\(D\)) in the corridor area is decided by the area of the corridor and the number of people escaping [22]; The initial moving speed (\(S\)) of personnel is listed in Table 1. Then, the farthest escape distance and deck movement time (the ratio of the farthest escape distance to the initial movement speed of the personnel) of passengers in the cabin to the exit is calculated according to the corridor layout. (2) \(t_{\text{F}}\): The flow time of passengers is the maximum flow time of each entrance and exit on the escape channel. The flow time of each entrance and exit is the ratio of the number of passengers to the flow. The passenger flow time in the corridor exit is based on the area of the corridor and the number of people, which is then used to calculate parameter \(D\); According to the initial specific flow, \(F\)s of passengers, the ratio of the total number of people \(N\) in the area to the specific flow, is determined. On the other hand, the flow time at the exit of the stairway can be computed according to the principle that has been shown in \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Facility**} & **Initial Density \(D\)** & **Initial Density \(F\)s** & **Initial Personnel Movement** \\  & **(p/m2)** & **(p/(m \(\times\) s))** & **Speed \(S\) (m/s)** \\ \hline \multirow{4}{*}{Corridors} & 0 & 0 & 1.2 \\  & 0.5 & 0.65 & 1.2 \\ \cline{1-1}  & 1.9 & 1.3 & 0.67 \\ \cline{1-1}  & 3.2 & 0.65 & 0.20 \\ \cline{1-1}  & \(\geq\)3.5 & 0.32 & 0.10 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Initial movement speed and flow of personnel. Equation (3). It should be noted that the current analysis sets the maximum flow rate \(F\)s in different locations as listed in Table 2.  
\[\sum F_{c}(in)=\sum F_{c}(out) \tag{3}\]  
where \(F_{c}(in)\) is the flow of route arriving at transition point; \(F_{c}(out)\) is the route departing from transition point. (3) \(t_{\text{stair}}\): The flow in the stairway is determined by Equation (4). The moving speed (5) in the stairway refers to Table 3, in which the moving time in the stairway is the ratio of the length of the ramp to the moving speed, as:  
\[t_{\text{stair}}=\frac{L_{ri}}{S} \tag{4}\]  
where \(L_{ri}\) is the length of the ramp of route \(i\).