# Research on the Evacuation Characteristics of Cruise Ship Passengers in Multi-Scenarios
## 2 The Description of Research Problems
### The Indicators of Evacuation  
Within the evacuation process, evacuation time is one of the most important criteria. The IMO guidelines point out that the evacuation time is divided into three parts. The first part is the response duration (\(R\)), during which passengers perceive the initial notification of an emergency and begin to evacuate. The second part is total travel duration (T), during which all passengers move from where they perceive the initial notification to the evacuation destinations. The third part is the embarkation and launching duration (E + L), which starts from passengers being assembled and the abandon ship signal being given. The evacuation time of passengers can be calculated by Equation (1) [47]:  
\[1.25(R+T)+2/3(E+L)<n \tag{1}\]  
where \(R\) represents the response duration. This begins when the initial notification of an emergency is received and ends when the passenger has realized the situation and has begun to evacuate. \(T\) is the total travel duration. \((E+L)\) represents the embarkation and launching duration, which should be equal to 30 min when this duration cannot be obtained from manufacturers, similar ships, or embarkation analysis. \(n\) is the performance standard of evacuation. \(n\) is 60 if the passenger ship has no more than three MVZs, or \(n\) is 80 if the MVZs of the ship number more than three. This paper mainly studies the evacuation process of passengers moving from the initial position to the embarkation station when an accident occurs. The evacuation time refers to \((R+T)\) in subsequent parts of this paper. Generally, the response duration of passengers is different in an emergency. The SAFEQUARD project measured the response duration of thousands of cruise passengers during a variety of scenarios and recommends Equations (2) and (3) to represent the response duration under day and night scenarios, respectively [49]. \[\mathrm{P_{Day}}=\frac{1.0548}{\sqrt{2\pi}\cdot 0.702\cdot R}exp[-\frac{(\ln(R)-4. 562)^{2}}{2\times 0.702^{2}}]\;0<R<300 \tag{2}\]  
\[\mathrm{P_{Night}}=\frac{1.1074}{\sqrt{2\pi}\cdot 0.817(R-400)}exp[-\frac{(\ln(R -400)-5.49)^{2}}{2\times 0.817^{2}}]\;400<R<700 \tag{3}\]  
where \(\mathrm{P_{Day}}\) and \(\mathrm{P_{Night}}\) represent the probability density in the response duration \(R\) in the day and night scenarios, respectively. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & **Passengers** & \multicolumn{2}{c}{**Percentage of Passengers (\%)**} & \multicolumn{2}{c}{**Walking Speed on Flat Terrain (m/s)**} & \multicolumn{3}{c}{**Walking Speed on Stairs (m/s)**} \\ \cline{3-10}  & & & **Min.** & **Max.** & **Min.** & **Max.** & **Min.** & **Max.** \\ \hline
1 & Females younger than 30 years & 7 & 0.93 & 1.55 & 0.56 & 0.94 & 0.47 & 0.79 \\
2 & Females 30–50 years old & 7 & 0.71 & 1.19 & 0.49 & 0.81 & 0.44 & 0.74 \\
3 & Females older than 50 years & 16 & 0.56 & 0.94 & 0.45 & 0.75 & 0.37 & 0.61 \\
4 & Females older than 50, mobility impaired (1) & 10 & 0.43 & 0.71 & 0.34 & 0.56 & 0.28 & 0.46 \\
5 & Females older than 50, mobility impaired (2) & 10 & 0.37 & 0.61 & 0.29 & 0.49 & 0.23 & 0.39 \\
6 & Males younger than 30 years & 7 & 1.11 & 1.85 & 0.76 & 1.26 & 0.5 & 0.84 \\
7 & Males 30–50 years old & 7 & 0.97 & 1.62 & 0.64 & 1.07 & 0.47 & 0.79 \\
8 & Males older than 50 years & 16 & 0.84 & 1.4 & 0.5 & 0.84 & 0.38 & 0.64 \\
9 & Males older than 50, mobility impaired (1) & 10 & 0.64 & 1.06 & 0.38 & 0.64 & 0.29 & 0.49 \\
10 & Males older than 50, mobility impaired (2) & 10 & 0.55 & 0.91 & 0.33 & 0.55 & 0.25 & 0.41 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The percentage and walking speed of passengers. The IMO Guidelines stipulate that the convergence of evacuation time should be checked every 50 simulations. The convergence of the time should meet the provisions of Equation (4) [47]. \[\left|\,T_{\text{lim}}-T_{0.95}^{\text{mean50}}\right|\,\geq T_{0.95}^{\text{ max50}}-T_{0.95}^{\text{min50}} \tag{4}\]  
where \(T_{\text{lim}}=(n-(2/3)(E+L))/1.25\).