## 2 Methodologies
### Proposed Computational Model  
(1) Movement speed model. According to MSC/Cir.1033, the composition of personnel on cruise ships is determined from the perspective of age and gender, as shown in Table 4. The movement speed of people in the corridor can be calculated according to the walking speed of age and gender function (Figure 1) and the proportion of cruise personnel, as shown in Equation (6). The movement speed of passengers in corridors is computed and listed in Table 5.  
\[v_{c-w}=\sum_{i=1}^{n}w_{i}\times v_{c-i} \tag{6}\]  
where \(w_{i}\) is the proportion of passengers of different ages and genders, \(v_{c-i}\) is the maximum or minimum movement speed of passengers in the corridor, \(v_{c-w}\) is the weighted movement speed of passengers. This paper takes into account the movement speed of specific groups such as well-trained crew whose movement speed is significantly faster than passengers. According to the maximum and minimum values of the movement speed in Table 5, the movement speed in the corridor is corrected; see Table 6. \begin{table}
\begin{tabular}{c c} \hline
**Population Groups—Passengers** & **Percentages (\%)** \\ \hline Females \(<\) 30 years & 7 \\ Females 30–50 years old & 7 \\ Females \(>\) 50 years & 16 \\ Females \(>\) 50, mobility impaired (1) & 10 \\ Females \(>\) 50, mobility impaired (2) & 10 \\ Males \(<\) 30 years & 7 \\ Males 30–50 years old & 7 \\ Males \(>\) 50 years & 16 \\ Males \(>\) 50, mobility impaired (1) & 10 \\ Males \(>\) 50, mobility impaired (2) & 10 \\ \hline \end{tabular}
\end{table} 
Table 4: Population composition on cruise ships [22]. Figure 1: Movement speeds of passengers of different ages and genders. Based on the movement speed of passengers in the stairway given in Ref. [13] and the weight determined by the age of passengers as shown in Table 4, the maximum and minimum speeds of passengers when going up and down stairs in the stairway can be calculated using Equation (7), and the results are given in Tables 7 and 8. \[v_{s-w}=\sum_{i=1}^{n}w_{i}\times v_{s-i} \tag{7}\]  
where \(v_{s-i}\) is the maximum or minimum movement speed of passengers of different ages and genders, \(v_{s-w}\) is the movement speed of passengers in the stairway. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Facility** & **Initial Density** & **Conventional Used** & **Corrected by the Proposed** \\  & **_D_ **(p/m2)** & **_S_ **(m/s)** & **Method \(S\) **(m/s)** \\ \hline  & 0 & 1.2 & 1.14 \\ Corridors & 0.5 & 1.2 & 1.14 \\ (Initial density) & 1.9 & 0.67 & 0.68 \\  & 3.2 & 0.20 & 0.2 \\  & \(\geq\)3.5 & 0.10 & 0.1 \\ Corridors & 0 & 1.2 & 1.14 \\ (Flow) & 0.65 & 1.2 & 1.14 \\  & 1.3 & 0.67 & 0.68 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The movement speed of passengers in corridor. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Passenger Group** & **Weights** & **Min. Stairs Down** & **Max. Stairs Down** & **Min. Stairs Up** & **Max. Stairs Up** \\  & & **Speed (m/s)** & **Speed (m/s)** & **Speed (m/s)** \\ \hline Females \textless{} 30 years & 0.07 & 0.56 & 0.94 & 0.47 & 0.79 \\ Females 30–50 years old & 0.07 & 0.49 & 0.81 & 0.44 & 0.74 \\ Females \textgreater{} 50 years & 0.16 & 0.45 & 0.75 & 0.37 & 0.61 \\ Females \textgreater{} 50, mobility & 0.1 & 0.34 & 0.56 & 0.28 & 0.46 \\ impaired (1) & & & & & \\ Females \textgreater{} 50, mobility & 0.1 & 0.29 & 0.49 & 0.23 & 0.39 \\ impaired (2) & & & & & \\ Males \textless{} 30 years & 0.07 & 0.76 & 1.26 & 0.5 & 0.84 \\ Males 30–50 years old & 0.07 & 0.64 & 1.07 & 0.47 & 0.79 \\ Males \textgreater{} 50 years & 0.16 & 0.5 & 0.84 & 0.38 & 0.64 \\ Males \textgreater{} 50, mobility & 0.1 & 0.38 & 0.64 & 0.29 & 0.49 \\ impaired (1) & & & & & \\ Males \textgreater{} 50, mobility & 0.1 & 0.33 & 0.55 & 0.25 & 0.41 \\ impaired (2) & & & & & \\ Weights & & 0.46 & 0.76 & 0.36 & 0.60 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Weighted a movement speed in stairway.