## 4 Discussion
### Validations  
To further verify the results of the proposed method, this paper takes the shipping platform as the object and uses the same ship layout scheme, passenger allocation scheme, assembly station location, and other environmental information as the input of the conventional method. Meanwhile, according to MSC.1/Circular.1533 [22], this simulation method of estimating the evacuation duration is based on the following assumptions: (i) The passengers and crew are represented as unique individuals with specified individual abilities and response durations; (ii) A safety factor having a value of 1.25 is introduced in the calculation to take account of model omissions, assumptions, and the limited number and nature of the benchmark scenarios considered; (iii) The population's composition is defined as shown in Tables 14 and 15; (iv) The response duration is not fixed for all the people, and the response duration distributions for the night-time scenario should be truncated logarithmic normal distributions as follows:  
\[y=\frac{1.01875}{\sqrt{2\pi}\times 0.84\times(x-400)}\exp\left[-\frac{(\ln(x-400 )-3.95)^{2}}{2\times 0.84^{2}}\right] \tag{11}\]  
This paper constructs the three-dimensional simulation model using the escape simulation analysis software maritime EXODUS. The simulation of MVZs 1, 4, and 5, are listed in Figure 9.  
Combined with the scenarios where passengers were located in various areas in the three main vertical areas, 50 simulations were carried out. Considering the uncertainties of the analysis, 95% of the simulated time is selected to represent all, which is marked with orange color in the Figures; see Figures 10-12.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Population Groups—Passengers** & **Percentages (\%)** \\ \hline Females \textless{} 30 years & 7 \\ Females \textgreater{} 30–50 years old & 7 \\ Females \textgreater{} 50 years & 16 \\ Females \textgreater{} 50, mobility impaired (1) & 10 \\ Females \textgreater{} 50, mobility impaired (2) & 10 \\ Males \textless{} 30 years & 7 \\ Males \textgreater{} 30–50 years old & 7 \\ Males \textgreater{} 50 years & 16 \\ Males \textgreater{} 50, mobility impaired (1) & 10 \\ Males \textgreater{} 50, mobility impaired (2) & 10 \\ \hline \hline \end{tabular}
\end{table}
Table 14: Population’s composition of passengers.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Population Groups—Crew** & **Percentages (\%)** \\ \hline Crew females & 50 \\ Crew males & 50 \\ \hline \hline \end{tabular}
\end{table}
Table 15: Population’s composition of crew.  
Figure 9: Simulation model of maritime EXODUS software.  
Figure 11: Convergence result of advanced evacuation analysis in MVZ 4.  
Figure 10: Convergence result of advanced evacuation analysis in MVZ 1.  
The comparison results of travel durations between the MVZs computed by the proposed method, the traditional method, and the simulation tools are listed in Table 16. The comparison demonstrates that the deviations of the traditional model are 40.2% (MVZ 1), 9.7% (MVZ 4), and 21.9% (MVZ 5), respectively. The proposed method, however, reduced such deviations to 14% (MVZ 1), 0.2% (MVZ 4), and 11.9% (MVZ 5). It confirms the accuracy of the proposed method in this paper over the traditional one. Meanwhile, the time required for the preparation, calculation, and presentation of the results of the proposed method, the traditional method, and the simulation tools are listed in Table 17. The comparison demonstrates that the model-based method's efficiency is