## 5 Analytical Evaluation
### Robustness Analysis  
We present the robustness analysis here in order to consider not only the rescue efficiency of cooperative rescue plan under normal conditions, but also the reliability under extreme operative situations. In the robustness analysis, a series of simulations have been executed to measure the rescue plan's adaptability to unexpected situations. Let \(LRS\) be an indicator to measure robustness of the model [33], shown in Equation (12). \[LRS=\frac{\sum\left(x_{i}-\overline{x_{i}}\right)\left(E_{i}-\overline{E_{i}} \right)}{\sum\left(x_{i}-\overline{x_{i}}\right)^{2}} \tag{12}\]  
where \(x_{i}\) (\(i=1,\,2,\,3\,\ldots\)) denotes specified values of the parameter that we have considered for variations, \(E_{i}\) denotes the corresponding rescue efficiency, \(\overline{x_{i}}\) and \(\overline{E_{i}}\) denote the average values. The more significant the \(LRS\) is, the less robust the model becomes, and vice versa. The parameters that we have considered for variations in robustness analysis are search radius \(s_{r}\) and scope of cooperation \(s_{c}\). Search radius could decrease for severe visibility conditions. Scope of cooperation could be affected by extreme operating environment and severe communication conditions. In Figure 8, \(x\)-axis denotes independent variables, i.e., the parameters that have considered for variations, and \(y\)-axis denotes dependent variables. We have explored the impact of varying search radius from 3 m to 8.1 m with an interval of 0.3 m; the scope of cooperation from 5 m to 125 m with an interval of 5 m. For every case described here, the simulation was repeated 200 times. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & & \(P_{rs}\) & \(P_{r}\) & \(t_{a}\) \\ \hline \multirow{2}{*}{Fatal} & Cooperation & 7.5\%, [0.7\%, 16.2\%] & 6.9\%, [0.5\%, 14.9\%] & 8.7\%, [0.8\%, 20.3\%] \\  & No-cooperation & 10.3\%, [0.8\%, 23.9\%] & 9.4\%, [0.3\%, 24.4\%] & 8.6\%, [0.9\%, 20.5\%] \\ \hline \multirow{2}{*}{Serious} & Cooperation & 5.8\%, [0.8\%, 13.8\%] & 5.6\%, [0.6\%, 14.4\%] & 8.2\%, [0.7\%, 20.7\%] \\  & No-cooperation & 6.6\%, [0.2\%, 16.1\%] & 5.9\%, [0.5\%, 15.2\%] & 6.8\%, [0.4\%, 17.1\%] \\ \hline \multirow{2}{*}{Normal} & Cooperation & 4.4\%, [0.2\%, 10.7\%] & 3.4\%, [0.2\%, 8.5\%] & 6.5\%, [0.8\%, 17.0\%] \\  & No-cooperation & 4.6\%, [0.4\%, 12.5\%] & 4.7\%, [0.4\%, 12.1\%] & 6.1\%, [0.5\%, 15.1\%] \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The relative error of three indicators in three scenarios. The results of robustness analysis show a number of interesting and reasonable dynamics. As the search radius increases, the rescue efficiency improves significantly, as shown in Figure 8a. When the rescue operations occur in the night, the search radius would decrease for low visibility, resulting in the lowering of rescue efficiency. The correlation between search radius and rescue efficiency is significant at 1% significance level, and the indicator \(LRS\) is 0.011, which indicates that rescue efficiency is easily affected by the variation of visibility conditions. As can be seen from Figure 8b, the rescue efficiency does not show a regular change with the scope of cooperation \(s_{c}\), especially when \(s_{c}\) is larger than 20 m, the rescue efficiency changes very little, and falls in [0.60, 0.615] basically. When the scope of cooperation is small, rescue teams' request for cooperation cannot be satisfied. However, as the scope of cooperation \(s_{c}\) increases to \(s_{c}=25\) m, the cooperation could be reached within a short time. When \(s_{c}\) is larger than 20 m, the indicator \(LRS\) is \(-3.6\times 10^{-5}\), indicating no correlation between rescue efficiency and scope of cooperation. To summarize, when \(s_{c}\) falls in [5 m, 20 m], it is not easy to reach cooperation, and the increase of \(s_{c}\) could result in improvement in rescue efficiency.