## 6 Performance Evaluation
### Performance Analysis  
In order to verify the performance of the algorithm proposed in this paper, we compared the performance of multiple algorithms under different environmental parameters. We set up four baseline algorithms as follows:  
* Local processing (LP): All tasks are processed locally on the IoT device's CPU, and the processing computational frequency is set to the IoT's maximum available computational frequency. * Pure HAP processing (PHAP): All tasks are offloaded to HAP drones for processing, and the HAP drones do not offload tasks to LEO satellites. The resource allocation strategy can be obtained by solving problem \(\mathcal{SP2}\). * Random offloading (RAND): The tasks are randomly allocated (i.e., the sizes of \(x_{j},y_{j},z_{j}\) and \(w_{j}\) are random and satisfy \(x_{j}+y_{j}+z_{j}+w_{j}=1\)). The resource allocation strategy can be obtained by solving problem \(\mathcal{SP2}\). * Block coordinate descent (BCD-based): Taking the task splitting problem and the resource allocation problem as two sub-problems and alternately solving the two sub-problems iteratively to obtain the optimal solution of the original problem. The original solution of the algorithm is obtained by the RAND algorithm. In Figure 6, the changes in total system delay under five different algorithms are depicted for various task data sizes. It can be observed from the figure that with the increase in task data size, the overall system delay shows an upward trend for all schemes. This is attributed to the fact that as the data volume increases, devices require more time to transmit and process user tasks. Among them, the curve of the RAND algorithm shows occasional decreases at some points due to its random nature, leading to unstable solution quality. The performance of the BCD-based algorithm depends largely on the quality of the original solution. Therefore, in this figure, the overall system delay obtained by it is better than RAND but inferior to LP and the algorithm proposed in this paper. Among the five algorithms, the proposed algorithm consistently achieves the minimum total delay in all scenarios, confirming the effectiveness of the proposed approach. Figure 7 shows the changes in total delay of the four algorithms under different computing densities. It can be seen from the figure that, as the computing density \(c_{j}(j\in\mathcal{J})\) increases, the total delay obtained by the four algorithms continues to increase. This is because, as the computing density increases, the number of CPU cycles required to process the task continues to increase, and the processing delay of the task increases, resulting in an increase in the total delay. The RAND algorithm has no solution when \(c=1100\) and \(1200\). This is because the task splitting strategy obtained by the RAND algorithm cannot  
Figure 5: Impact of learning rate. allow the resource allocation problem to meet all constraints, resulting in task timeout for some IoT devices. The initial solution of the BCD-based algorithm is obtained through the RAND algorithm; therefore, when \(c=1100\) and \(c=1200\), the BCD-based algorithm has no solution. Among the five algorithms, the algorithm proposed in this paper can always obtain the smallest total delay, which proves that the algorithm proposed in this article can effectively reduce the total system delay. Figure 8 shows the total system delay compared with the computing capacity of terrestrial IoTs. With the increase in local computing capacity, except for the PHAP solution, the total system delay of other solutions shows a downward trend. This is because, as the local computing capacity increases, terrestrial IoT devices can process more tasks on the local CPU, thereby reducing overall system delay. In the PHAP solution, no task is processed locally, so the total system delay of this solution does not change with changes in local computing capabilities. Compared with the other four schemes, the proposed algorithm in this paper achieves the smallest total system delay.