# Offloading of Atomic Tasks in Satellite Networks:
## 5 Numerical Experiments
### Results Analysis  
The time cost consumption of task \(c(q_{i})\) includes the task waiting time \(w(q_{i})\) and the task execution time \(e(q_{i})\). Ideally, if the resources are sufficient, then the task does not need to wait and the time cost of the task only includes the task execution time. However, the Ideal Scenario of Sufficient Resources (ISSR) is extremely difficult to occur on spatial information networks. In this experiment, the approach that approximates the time cost consumption of ISSR is more effective. In addition, the First Come, First Service (FCFS) scheduling method executes the task queues on the satellite according to the task order. Therefore, the waiting time of the current task includes the sum of the execution time of the previous tasks and the waiting time, i.e., \(w(q_{i+1})=c(q_{i})\), then \(c(q_{i+1})=c(q_{i})+e(q_{i+1})\). We analyze the task time cost incurred by the method OCMF with the cost consumption of ISSR, FCFS, PSO, GA, and DE methods. The numerical results of the simulation experiments are shown in Table 4. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \(gamma\) & \(n\_clusters\) & \(n\_neighbors\) & \(Degree\) \\ \hline
0.01, 0.1, 1, 10 & \(2,3,4,5,6\) & 10 & 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Spectral clustering parameters setting in OCMF process. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Algorithms** & \(lb\) & \(ub\) & \(prob\_mut\) & \(w\) & \(c1\) & \(c2\) & \(F\) & \(size\_pop\) \\ \hline PSO & 0 & - & - & 0.8 & 0.5 & 0.5 & - & 200 \\ GA & 0 & - & 0.001 & - & - & - & - & 200 \\ DE & 0 & - & 0.001 & - & - & - & 0.5 & 200 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Experimental parameter setting of baseline model. As shown in Table 4, we can observe the task time calculation results of OCMF and multiple baseline algorithms on six datasets. The experimental results show that the task time consumed by the OCMF approach increases with the growing datasets. The incremental time cost of OCMF on datasets D1 and D2 are relatively small. However, the increment of time cost increases by the increasing amount of the datasets. Moreover, OCMF has lower time consumption than ISSR, FCFS, PSO, GA, and DE algorithms on multiple datasets. The ISSR time cost includes executing all tasks themselves without the waiting time consumption. We can notice that the OCMF time consumption is slightly lower than ISSR, which is caused by the caching mechanism in the proposed method OCMF. If a task has been executed in the previous time and the task execution result is cached, then the same task can be accessed without repeated execution and the result data can be obtained from the cache of the high-orbiting satellite. FCFS is a traditional task scheduling method that considers the task wait time and the task execution time. The task waiting time includes the execution time of the previous tasks and the waiting execution time. Although FCFS does not include the inter-satellite link transmission time consumption, the algorithm has the disadvantage of large waiting time consumption. Therefore, the FCFS scheduling method is inferior to OCMF. Although the swarm intelligence algorithm has a good performance in various application scenarios, the results on space-based information networks are not promising due to the tall task offloading operations times of the group intelligence algorithm, which leading a large time consumption for inter-satellite link transmission. As the Table 4 shows, we can observe that the PSO, GA, and DE algorithms have more significant time cost consumption, whereas the GA algorithm has lower time cost consumption. PSO time cost on dataset D4 is much lower than the DE time cost on dataset D4. However, PSO the time consumption on dataset D6 is much larger than that of DE on dataset D6. As the dataset increases, the growth rate of PSO cost consumption is greater than that of DE.