# Multi-Satellite Task Parallelism via Priority-Aware Decomposition and Dynamic Resource Mapping
## 5 Experiment Results
### Comparative Algorithm and Performance Metrics  
To address the problem's characteristics of temporal variation, complex resource allocation, block structure preservation, network delay, and hierarchical scheduling, we select five comparative algorithms: Optimizing Scheduled Virtual Machine Requests Placement in Cloud Environments: A Tabu Search Approach (TS-SVMPP) [31] with time complexity \(O(n^{2})\); Cooperative Mapping Task Assignment of Heterogeneous Multi-UAV Using an Improved Genetic Algorithm (IDCE-GA) [30] with time complexity \(O(PG)\) (in the genetic algorithm, \(P\) represents the population size in each generation, and \(G\) represents the number of generations); MILP-StuDio: MILP Instance Generation via Block Structure Decomposition (MILP-STUDIO) [25] with time complexity \(O(n^{3})\); Resource Allocation Considering Impact of Network on Performance in a Disaggregated Data Center (RA-CNP) [29] with time complexity \(O(n\log n)\); and Task Decomposition and Hierarchical Scheduling for Collaborative Cloud-Edge-End Computing (VNE-AC) [36] with time complexity \(O(n)\). In addition, the HEFT-LA algorithm [26] is included in the scheduling category with time complexity \(O(n^{2})\), which improves task execution efficiency through a lookahead variant, and the PA-LBIMM algorithm [32] with time complexity \(O(PG)\), which integrates user-priority-based Min-Min scheduling to enhance load balancing. These algorithms are commonly used to solve resource allocation and scheduling problems and have efficient optimization effects. TS-SVMPP and IDCE-GA are often used to optimize virtual machine placement and UAV task allocation, demonstrating good adaptability, while MILP-STUDIO, RA-CNP, and VNE-AC exhibit strong optimization capabilities in large-scale and dynamic environments. For performance evaluation, we employ the following metrics. Task execution rate \(TCR(t)\) is calculated using the equation  
\[TCR(t)=\frac{N_{\text{completed}}(t)}{N_{\text{total}}(t)} \tag{39}\]  
which evaluates the proportion of successfully executed tasks. The objective function value defined in Equation (19) is used to quantify the overall optimization effect of the system. Additionally, resource utilization \(U_{r}(t)\) serves as a metric to evaluate the efficiency of resource allocation, defined as  
\[U_{r}(t)=\frac{\sum_{s\in S}R_{s}^{\text{used}}}{\sum_{s\in S}R_{s}^{\text{ total}}} \tag{40}\]  
To measure communication costs, we introduce the following metrics:  
\[CC=\frac{\sum_{s\in S}\sum_{i,j\in M_{s}}c(T_{ij})}{\sum_{s\in S}C_{s}} \tag{41}\]  
where \(c(T_{ij})\) represents the communication cost for task \(T_{ij}\) in the communication resource request, and \(C_{s}\) represents the total communication capacity of the resource. This metric \begin{table}
\begin{tabular}{l l l l l l l l} \hline \hline
**Datasets** & \(\mathbf{D_{1}}\) & \(\mathbf{D_{2}}\) & \(\mathbf{D_{3}}\) & \(\mathbf{D_{4}}\) & \(\mathbf{D_{5}}\) & \(\mathbf{D_{6}}\) & \(\mathbf{D_{7}}\) \\ \hline
**Satellite Nodes** & \(10\) & \(20\) & \(40\) & \(60\) & \(80\) & \(100\) & \(120\) \\
**Task Quantity** & \(20\) & \(40\) & \(60\) & \(100\) & \(120\) & \(140\) & \(150\) \\ \hline
**Datasets** & \(\mathbf{D_{8}}\) & \(\mathbf{D_{9}}\) & \(\mathbf{D_{10}}\) & \(\mathbf{D_{11}}\) & \(\mathbf{D_{12}}\) & \(\mathbf{D_{13}}\) & \(\mathbf{D_{14}}\) \\ \hline
**Satellite Nodes** & \(140\) & \(160\) & \(180\) & \(200\) & \(220\) & \(240\) & \(300\) \\
**Task Quantity** & \(200\) & \(240\) & \(280\) & \(300\) & \(360\) & \(400\) & \(300\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Number of satellites and tasks in selected datasets. reflects the communication cost incurred during the execution of tasks, with lower values indicating better communication efficiency. The CC helps evaluate the optimization of communication resources and their impact on the overall system.