# Multi-Satellite Task Parallelism via Priority-Aware Decomposition and Dynamic Resource Mapping
## 5 Experiment Results
### Numerical Analysis
\begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline
**Datasets** & HEFT-LA [26] & PA-LBIMM [32] & IDCE-GA [30] & TS-SVMPP [31] & MILP-STUDIO [25] & RA-CNP [29] & VNE-AC [26] & HADRM \\ \hline \(D_{1}\) & 12,031.12 & 11,530.57 & 12,058.48 & 9102.37 & 9524.48 & 9500.25 & 8964.25 & **11,031.12** \\ \(D_{2}\) & 24,041.98 & 23,012.32 & 13,548.48 & 12,001.33 & 11,584.88 & 12,314.66 & 12,865.36 & **22,541.99** \\ \(D_{3}\) & 76,841.25 & 75,341.26 & 578,412.13 & 520,147.66 & 508,741.13 & 525,478.99 & 553,284.27 & **75,321.26** \\ \(D_{4}\) & 107,481.54 & 105,486.17 & 98,521.48 & 89,214.65 & 84,215.48 & 90,214.55 & 95,632.62 & **105,481.55** \\ \(D_{5}\) & 265,145.89 & 252,347.36 & 198,754.68 & 194,512.37 & 174,795.48 & 198,523.13 & 406,654.30 & **252,145.90** \\ \(D_{6}\) & 425,512.34 & 40,134.12 & 451,478.33 & 412,664.75 & 386,621.13 & 4352,554.74 & 426,587.11 & **4014.52** \\ \(D_{7}\) & 765,648.25 & 752,218.74 & 851,478.65 & 1,014,520.85 & 964,587.33 & 1,023,020.99 & 1,045,549.59 & 745,648.25 \\ \(D_{8}\) & 1,021,457.15 & 1,051,342.28 & 1,158,452.12 & 1,302,541.66 & 1,224,587.66 & 1,350,005.15 & 1,359,596.65 & **1,152,145.15** \\ \(D_{9}\) & 1,223,521.25 & 1,122,356.98 & 1,387,482.15 & 1,554,798.94 & 1,458,741.21 & 1,574,215.65 & 1,800,205.24 & **1,203,521.25** \\ \(D_{10}\) & 1,387,582.36 & 1,378,620.54 & 1,958,412.66 & 1,812,254.513 & 1,752,412.65 & 1,823,654.55 & 1,865,833.00 & **1,366,582.37** \\ \(D_{11}\) & 1,652,465.29 & 1,556,321.27 & 1,854,285.21 & 1,925,874.66 & 1,798,541.15 & 1,954,785.55 & 1,972,285.36 & **1,542,645.30** \\ \(D_{12}\) & 1,63,684.88 & 1,534,625.72 & 2,254,784.21 & 2,230,547.21 & 2,145,874.21 & 2,245,214.99 & 2,270,253.69 & **1,23,653,68.48** \\ \(D_{13}\) & 1,774,511.54 & 1,611,241.28 & 2,458,741.66 & 2,365,412.15 & 2,314,789.65 & 2,385,412.66 & 2,402,569.55 & **1,604,511.55** \\ \(D_{14}\) & 2,258,836.49 & 2,062,354.12 & 3,685,412.33 & 3,502,541.65 & 3,414,789.33 & 3,502,148.66 & 3,595,541.00 & **2,038,363.49** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Objective function value results across 14 datasets. maintain stable optimization effects when task loads increase; however, MILP-STUDIO and RA-CNP rely on complex integer programming methods, leading to a rapid increase in computational overhead in large-scale environments. In addition, the static scheduling mechanism of VNE-AC also limits its adaptability in rapidly changing and complex environments. Although HEFT-LA and PA-LBIMM performed well, especially the PA-LBIMM algorithm, which showed competitive results in multiple datasets, HADRM maintained more balanced and efficient resource utilization overall. As shown in Table 6 and Figure 4(a), we measure the task execution time of each algorithm at different task scales, providing a comprehensive quantitative comparison. From these results, it is evident that algorithms such as MILP-STUDIO and TS-SVMPP perform well in small-scale datasets with shorter execution times; however, as the task scale increases, HADRM demonstrates notable advantages. For example, in dataset D14, the execution time of HADRM is 29,652.15, which is substantially lower than MILP-STUDIO's 37,254.12 and the times of IDCE-GA and TS-SVMPP, both around 39,874.12. Next, to investigate how the iteration count affects task execution time, we conducted a parameter-tuning experiment. As shown in Figure 3(b), HADRM not only achieves lower execution times, but also converges more rapidly over successive iterations, indicating that in large-scale, complex task scenarios, HADRM can more efficiently handle task scheduling and resource allocation. The advantage of HADRM lies in its adoption of a scheduling strategy that integrates hierarchical adaptive decomposition and reinforcement learning. Specifically, HADRM  
Figure 4: Comparative resource utilization in static and iterative scenarios. (**a**) Resource utilization. (**b**) Resource utilization over varying iterations.