# Resource Allocation Strategy for Satellite Edge Computing Based on Task Dependency
## 3 System Models and Problem Formulation
### Task Scheduling Model
#### 3.3.1 Scheduling Model Based on Subtask Degree
When the scroungers sense that the producer has found a better food source, they will continue to search for food in the vicinity of the producer. Select a subset of individuals from the individuals as investigators. Updating investigator's location:

\[X_{i,j}^{t+1}=\left\{ \begin{array}{l}X_{best}^{t}+\beta\left|X_{i,j}^{t}-X_ {best}^{t}\right|\ \ f_{i}>f_{g}\\ X_{i,j}^{t}+\frac{\left|X_{i,j}^{t}-X_{worst}^{t}\right|}{(f_{i}-f_{g})+\epsilon }\ \ f_{i}=f_{g}\end{array} \right. \tag{15}\]\(X_{best}^{t}\) is the current global optimal position. The step control parameter \(\beta\) is a random number following a normal distribution with a mean of 0 and a variance of \(1.k\in[-1,1]\) is a random number, and \(f_{i}\) is the fitness value of the current individual sparrow. \(f_{g}\) and \(f_{w}\) are the current global best and worst fitness values, respectively. \(\varepsilon\) is the smallest constant to avoid zero in the denominator. 3. Population disturbance combined with Cauchy variation

In the later stages of the algorithm, the sparrow population gradually approaches the optimal individual, which leads to the lack of population diversity and premature convergence of the algorithm. Therefore, the Cauchy variant operator is added in the late stage of the sparrow search. In the iterative process of the search algorithm, the locally optimal solution is continuously disturbed, while the sparrows with better fitness value are retained. Such a strategy is aimed at avoiding situations in which the sparrow population falls into a locally optimal solution during the search process, and the position is updated to:

\[X_{best}^{*}=X_{best}^{t}+X_{best}^{t}.\;Chuchy(0,1) \tag{16}\]

## 4 Discussion

This simulation experiment uses STK 11 simulation software to simulate the information transmission network. In the simulation, we consider a circular coverage area, a LEO satellite with a radius of 1000 km, where the height of the satellite is 500 km. The parameter settings for the simulation in this chapter are shown in Table 3[29; 30; 31; 32]. This section compares and analyzes application completion rates. The simulation results are displayed and analyzed from three aspects: resource changes, processing methods, and the number of DAGs. As shown in Figure 3, with the increase in satellite computing resources, the task completion rates of all schemes show an upward trend. In addition, the method of all satellite processing (AS) [20] and random processing (RA) [29] has a low task completion rate, while the resource allocation scheme based on task degree and the improved Sparrow search algorithm (TDISSA) has a high completion rate compared to other algorithms. When the satellite computing resources were 14 Gcycles/s, the completion rate of TDISSA was 100%, while that of RA and AS were 63.63% and 54.54%, respectively. The more computing resources a satellite has, the more computing resources can be allocated to tasks, which reduces task computing latency. However, the computing resources of the satellite's MEC server are still limited and there is currently only one satellite node, which can process limited tasks. Therefore, the algorithm proposed in the article only offloads a part of the application to the satellite for calculation. In the AS, each application offloads its tasks to the satellite for calculation, so this leads to its lower task completion rate, and many applications cannot successfully process. The RA method adopts random decisions, which are not optimal strategies, resulting in a lower task completion rate as well. The completion