# A Lyapunov-Optimized Dynamic Task Offloading Strategy for Satellite Edge Computing
## 5 Simulation and Analysis
### Simulation Analysis  
As we have previously analyzed, the value of \(V\) has a crucial impact on both the task queue length and the performance of the algorithm. As shown in Figure 3, \(\mathrm{M}=50\), \(\beta=0.1\), \(\mathrm{B}=500\)(Mb/s) (a) Average task queue length per satellite vs. V of DOALH algorithm; (b) Average task queue length per satellite vs. different algorithms. Figure 3a, when the value of \(V\) is small, the queue can be kept stable directly. However, when the value of \(V\) is large, the queue grows gradually and eventually converges to an approximately stable state. The stable length of the queue convergence is positively related to the value of \(V\). As Figure 3b reveals, among the different algorithms, the DOALH algorithm guarantees the optimal solution for \(P2\) at each time slot, resulting in the shortest average queue length. The DQN algorithm adopts \(P2\) as the reward function, which also guarantees the convergence of the queue to a lower value. The Greedy algorithm also results in a shorter queue length compared with the Local algorithm due to its greedy strategy. The Local algorithm generates a large queue buildup because it only considers Local processing and does not make rational use of other available satellite resources. According to Figure 4, the Greedy algorithm attains the highest average cost, primarily because it solely focuses on achieving an improved balance in the queue without considering the costs associated with delay and energy consumption resulting from ISL transmission. The Local and Greedy algorithms are simpler and are not impacted by the value of \(V\), enabling them to maintain a consistent trend. However, both the DQN algorithm and the DOALH algorithm exhibit a substantial decreasing trend as the value of \(V\) increases. Eventually, they converge to a stable value. This phenomenon can be attributed to the fact that as the value of \(V\) increases, the algorithm places more emphasis on minimizing the \(Cost\) incurred by the task, which allows it to achieve a more optimal solution. The simulation results align with the preceding analysis of the algorithm. Thus, \(V\) should be chosen for a good trade-off between the overall \(Cost\) and the required t  
Figure 3: \(M=50,\beta=0.1,B=500\) (Mb/s) (**a**) Average task queue length per satellite vs. \(V\) of DOALH algorithm; (**b**) Average task queue length per satellite vs. different algorithms. Furthermore, we need to investigate the impact of the energy consumption weight \(\beta\) on performance. A larger \(\beta\) results in a higher weight of energy consumption. As demonstrated in Figure 5, the _Cost_ clearly increases as \(\beta\) increases. The algorithms exhibit linear growth, albeit with varying slopes, which correspond to the energy consumption per time slot of offloading strategies. The Greedy algorithm aims to balance the queue by offloading more tasks to other satellites, resulting in the highest energy consumption for offloading strategies. On the other hand, the DOLAH algorithm is capable of maintaining the lowest _Cost_. Next, we investigate the correlation between _Cost_ and the number of satellites that receive tasks during each time slot \(M\). The value of \(M\) reflects the operational workload of the satellite constellation, where a larger value indicates that more tasks are assigned to satellites during each time slot, resulting in fewer idle satellites and computing resources in orbit. As depicted in Figure 6, the _Cost_ increases as \(M\) increases. This is due to the longer queue length of tasks with more tasks received in the constellation. With limited computational resources available to assist in processing, tasks require more waiting time. The DOLAH algorithm always achieves optimal cost by ensuring that all satellite resources are fully utilized, regardless of the value of \(M\). The bandwidth of the ISL has a significant impact on the computational offload.