## 2 Methodologies
### Proposed Computational Model
#### 2.2.2 Flow model. [PERSON] [34] studied the personnel concentration process in the stairway of high-rise buildings. Through the personnel concentration experiment, the influence of the personnel density in the stairway, the opening direction of the stairway, and the state of the exit door on the stairway concentration are analyzed. [PERSON] [38] proposed a mathematical model for calculating the evacuation time of the stairway, considering the impact of the personnel concentration, to evaluate the impact of the concentration of people entering the stairway and people in the stairway on the pedestrian flow and evacuation time. The current cruise flow calculation model based on the flow accumulation method uses the same stairs to escape from each deck. The circulation time is the cumulative sum of the flow of passengers, and the flow rate ratio is computed by:  
\[\mathrm{f_{F-stair}}=\frac{\sum\limits_{i=1}^{n}N_{i}}{F_{s}} \tag{8}\]  
where \(\mathrm{f_{F-stair}}\) is the duration that passengers move within the stairway, \(N_{i}\) is the number of passengers who enter the stairway, \(n\) is the number of decks where people enter the escape ladder, \(F_{s}\) is the personnel flow. Passengers on all decks escape at the same time in case of fire on a cruise ship. When the upper deck passengers move down along the stairway, the middle deck passengers have two movement directions: horizontal movement along the corridor and downward movement through the stairway, i.e., only some middle deck passengers meet with passengers from upper decks at the entrance of the stairway, and the rest of the passengers transfer to the muster station. The current flow-accumulation-based flow calculation model is difficult to map the above actual scenarios. Therefore, this paper proposes a new flow calculation algorithm based on dislocation accumulation, as:  
\[\mathrm{t^{\prime}_{F-stair}}=\frac{\sum\limits_{i=a}^{b}N_{i}-\left(\sum \limits_{i=a}^{b-1}[F_{C_{i}}\times t_{i}]\right)}{F_{s}} \tag{9}\]  
where \(\mathrm{t^{\prime}_{F-stair}}\) is the duration that a person flows through a stairway using a misplaced add-on algorithm, and a, b decks are the lowest and the uppermost deck of the escape using the stairway. The b-1 deck is the lower deck of the b deck. \(N_{i}\) is the number of passengers who enter the stairway, and \(F_{C_{i}}\) is the flow of passengers who move in advance of the convection of the deck except for the upper deck. \(t_{i}\) is the flow duration of the upper deck before it reaches the deck. For example, in the case of b-1 decks, the number of passengers moving in advance on b-1 decks is the result of multiplying the time required to move the human flow from \"b\" deck stairways to b-1 deck stairways and the flow on b-1 deck. In the proposed dislocation accumulation algorithm, it is assumed that the movement time difference of each deck in the corridor is small before entering the stairway, and the passengers on each deck arrive at the stair entrance of a specific floor at the same time. Therefore, when passengers on the upper deck move into the stairway, the passengers on the lower deck before the confluence should be considered. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Type of Facility**} & **Specific Flow \(F\)s** & **Conventional Used** & **Revised by the Proposed** \\  & **(p/(m \(\times\) s))** & **\(S\) (m/s)** & **Method \(S\) (m/s)** \\ \hline \multirow{3}{*}{Stairs (down)} & 0 & 1.0 & 0.76 \\  & 0.54 & 1.0 & 0.76 \\  & 1.1 & 0.55 & 0.46 \\ \hline \multirow{3}{*}{Stairs (up)} & 0 & 0.8 & 0.6 \\  & 0.43 & 0.8 & 0.6 \\ \cline{1-1}  & 0.88 & 0.44 & 0.36 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Weighted average movement speed in stairway. Traditional escape analysis methods based on local rigidity theory consider that the space between passengers is incompressible, and it is difficult to map the flow characteristics under congestion [21; 22]. Therefore, [PERSON] et al.