## 4 Experimental Results  
### Test Scenario  
The satellite system under consideration is a cluster satellite configuration, specifically a Walker Delta constellation. This constellation is comprised of eight planes, with satellites ranging from 1 to 5 per plane, amounting to a maximum of 40 satellites. These satellites orbit at an altitude of 500 km and are equipped with state-of-the-art active phased array Synthetic Aperture Radar (SAR) sensors. The orbital trajectories and configuration of this satellite constellation are graphically represented in Figure 9, providing a clear visual understanding of the spatial arrangement.  
Targets are randomly generated within the geographic boundaries of the Korean Peninsula, between latitude 32-42\({}^{\circ}\) N and longitude 124-131\({}^{\circ}\) E, with their count progressively increasing from 100 up to a maximum of 1000 in increments of 100. Figure 10 illustrates the spatial distribution of these targets within the mission area. Additionally, each target is randomly assigned a urgency and significance value, chosen from 0.3, 0.6, or 0.9, adding layers of complexity to the target prioritization process.  
The mission planning period is set from 00:00 on 1 January 2024 to 00:00 on 8 January 2024, spanning 7 days. The test scenarios involve varying numbers of satellites, from 8 (one per plane) to 40 in total, and targets ranging from 100 to 1000. This results in 50 unique test cases for the numerical simulation. Detailed simulation parameters are listed in Table 2.  
The simulation environment is a crucial aspect, primarily focusing on the computing power and related resources required for the effective execution of the simulation. The specific simulation environment is provided in Table 3.  
Figure 9: Satellite constellation on 3D map.  
The workflow of our simulation is a multi-step process, initiated with user-inputted target information and satellite parameters fed into the STK program. Utilizing this input, STK generates target data and propagates satellite orbit. A critical output of this process is the VTW report, which becomes the foundational input for the MDP and greedy algorithms, both written in Python language. These algorithms are used to derive the solution of the optimal mission scheduling. The entirety of this workflow, from initial input to final algorithmic processing, is depicted in Figure 11, offering a comprehensive visual guide to the simulation process.  
\begin{table}
\begin{tabular}{c l} \hline \hline
**Parameter** & **Value** \\ \hline Scheduling period (day) & \{1, 2, 3, 4, 5, 6, 7\} \\ Mission area (\({}^{\circ}\)) & 32–42\({}^{\circ}\) N, 124–13\({}^{\circ}\) E \\ Number of targets & \{100, 200, 300, 400, 500, 600, 700, 800, 900, 1000\} \\ Walker Delta constellation & 44.1\({}^{\circ}\): 40/8/1 \\ Altitude (km) & 500 \\ Incidence angle (\({}^{\circ}\)) & 25–45 \\ \(\tau_{ijk}^{o}\) (s) & 20 \\ \(\tau_{j}^{o}\) (s) & 10 \\ \(d_{i}\) (s) & 60 \\ \(n_{i}^{min}\), \(n_{i}^{max}\) & 1 \\ \(p_{i}\), \(u_{i}\) & \{0.3, 0.6, 0.9\} \\ \(\alpha\), \(\beta\) & 0.7, 0.3 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Simulation parameters.  
Figure 10: Distribution of 1000 targets in mission area.  
\begin{table}
\begin{tabular}{c l} \hline \hline
**Index** & **Specification** \\ \hline Processor & Intel® CoreTM i7-11700 \\ Memory (RAM) & 32 GB \\ Orbit analysis tool & AGI® STK (Systems Tool Kit) \\ Orbit propagator in STK & J2 perturbation \\ Implement tool & VS Code \\ Framework & Python 3.10 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Simulation environments.