## 6 Simulation Results and Analysis
### Simulation Scenario  
In the simulation scenario of this paper, a LEO satellite network is built using the STK satellite tool (version 6.0), which includes 24 medium-orbit satellites distributed in three orbital planes with an altitude of 1000 km, 10 observation satellites, and one ground station. This section uses MATLAB (version 2024a) the Python programming language (version 3.8) and a Pytorch (version 2.1.2) simulation environment based on the Gym reinforcement learning environment to simulate the DQN network. During the simulation process, the number of training steps is set to 4000 steps, and the number of training episodes is set to 30 h. The parameters of the DQN network and other parameters are shown in Table 2. This section averages the simulation results of 600 independent experiments and compares the proposed algorithm with the algorithm in the literature. Figures 4 and 5 show the impact of different learning rates and discount factors on long-term rewards. As shown in the figure, a learning rate of 0.1 is very clear that the DQN network does not converge and fluctuates significantly. This is because the learning rate is too large, and the network jumps directly to the local optimal value, resulting in suboptimal results. When the learning rate is 0.0001, the network converges slowly, and even after 400 training steps, there is still a large fluctuation. This is because, during the learning process, the network converges slowly and requires more training steps to reach the final reward. When the learning rate is 0.001, the network can reach the optimal reward after 1000  
Figure 5 illustrates the impact of different discount factors \(\gamma\) on the long-term rewards during the training of our DQN-based task offloading and computation scheduling algorithm. The discount factor is a critical parameter in reinforcement learning algorithms, determining how future rewards are valued relative to immediate rewards. When \(\gamma=0.1\), the agent exhibits slow convergence with high fluctuations in rewards. This low discount factor implies that the agent undervalues future rewards, leading to shortsighted decisions that do not contribute to long-term system optimization. For \(\gamma=0.5\), the agent shows improved convergence and reduced fluctuations. The balance between immediate and future rewards allows the agent to learn better policies but still falls short of optimal performance. With \(\gamma=0.9\), the agent achieves rapid convergence and higher steady-state rewards. The high emphasis on future rewards enables the agent to learn strategies that significantly minimize the long-term system cost. This result indicates that a higher discount factor is beneficial in the context of our satellite edge computing network, where long-term planning is essential due to the dynamic and continuous nature of tasks and resources. In Figure 6, we illustrate the connection between the relay satellite's maximum queue length and the system cost, alongside analysis of varied scenarios concerning task computation difficulty. The figure reveals that as the relay satellite's maximum queue length grows, the system cost declines. This occurs because a longer queue allows the satellite to manage more data transmission tasks and adjust computation task scheduling, enhancing the system's capacity to prevent data loss and stabilize cost fluctuations. Notably, the system cost achieved by our proposed method in this study is lower than that reported in prior research, and with a task computation difficulty of 1000 cycles, the cost reduction using our approach is slower compared to the method from the literature [40]. Figure 5: Long-term reward versus number of training steps (with different discount factors). Figure 7 presents the correlation between the relay satellite's computation capability and system cost. It demonstrates that as the satellite's computation capability increases, the system cost decreases unevenly across various methods.