## 4 Simulation Case and Analysis  
Based on the simulation environment and the construction of the amphibious aircraft agent and the PDT agent, the effectiveness and applicability of the TPM is verified with cases in this section. In addition, the simulation environment could perform the TPM smoothly for different situations in the simulation case. The simulation case was designed to be a capsized ship case that occurred in the distant sea region of the East China Sea. At 9:00 am on 11 June 2022, a ship capsized at the position 31\({}^{\circ}\)12\({}^{\prime}\)28.8\({}^{\prime\prime}\) N, 127\({}^{\circ}\)043.2\({}^{\prime\prime}\) E. The persons on the ship were all overboard. The average water temperature at the ship's position was 16 \({}^{\circ}\)C. In addition, the ocean wind speed and the ocean flow speed in the distress position could be obtained through weather monitoring applications. Assuming that the number of PDTs was 45,the PDTs were randomly generated within a 2 km square around the distress position as the initial position. For each PDT, 50 samples were carried out in Monte Carlo experiments to predict their drifting trajectories based on the simulated time advance. Considering that the predicted trajectories were not the accurate positions, some extra time (5 min) was needed for the lifeboat to rescue one PDT. The amphibious aircraft was located at Shanghai Pudong International Airport. The main performance parameters of the amphibious aircraft in the simulation environment are listed in Table 1.  
To the best of our knowledge, the distress information sent by the PDT cannot be immediately available to the rescue base in practical applications. Apart from that, the response and the preparation of the TPM will also take some time. Therefore, the start of the rescue may be delayed for some time while the PDTs are in distress. The TPM-X is used to indicate that the start of the rescue is delayed by X hours. Taking the TPM-0.5 as an example, the main screenshots of the TPM-0.5 and the simulation results for 45 PDTs are shown in Figure 12 and Table 2. To illustrate the TPM-0.5 of SRP in detail, the rescue time of each stage is shown in Figure 13. \begin{table}
\begin{tabular}{c c} \hline
**Performance Parameters** & **Value** \\ \hline initial position & 31\({}^{\circ}\)9\({}^{\prime}\)0\({}^{\prime\prime}\) N, 121\({}^{\circ}\)48\({}^{\prime}\)21.6\({}^{\prime\prime}\) E \\ cruising speed (km/h) & 480 \\ aircraft guarantee time & 30 \\ (refuel, transfer of the persons in distress, etc.) (min) & 30 \\ the maximum rescue capability (person) & 30 \\ number of lifeboats & 1 \\ lifeboat speed (km/h) & 28 \\ lifeboat voyage (km) & 92.6 \\ the maximum rescue capability of the lifeboat (person) & 5 \\ time to rescue one person of lifeboat (min/person) & 5 \\ \hline \end{tabular}
\end{table} 
Table 1: Performance parameters of the amphibious aircraft. The simulation results show that the TPM-0.5 had a high successful rescue rate and a short rescue time, which meant that the TPM-0.5 had greater effectiveness for 45 PDTs. The result shows that the amphibious aircraft needed to rescue the PTDs twice when there were 45 PDTs. The percentage of time taken to rescue the PDTs was the largest. This means it is necessary to optimize the SRP for medium/distant maritime rescue. To verify the adaptability of the TPM for different rescue situations, a simulation experiment with 70 PDTs was conducted with other parameters equal to those mentioned in this study. Moreover, the initial positions of the PDTs were randomly generated, which caused uncertainties. The prediction trajectories of the PDTs also caused uncertainties in the Monte Carlo experiments, and the simulation results might be different for the same case because of uncertainty factors, including the hardware platform that supports the simulation environment. Therefore, to reduce the impact of random factors on the simulation results, the simulation of the TPM-0.5 for 45 and 70 PDTs was conducted fifty times separately.