# 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
As shown in Figure 6, with the increase in ground computing power, the task completion rate of all schemes shows an upward trend. In addition, the method with locally all processed (AL) [31] and RA has a lower task completion rate, while the TDISSA has the highest completion rate. When the local computing power was 4 Cycles/s, the completion rate of TDISSA was 100%, while that of the RA and AL were 72.72% and 63.63%, respectively. The reason for this is that the computing resources of the ground terminal are limited and can only handle one task at a time. Therefore, put a part of the application on the ground. In the AL, each application calculates its tasks on the ground, so this leads to a lower task completion rate, and many applications cannot successfully process. However, since the random decision is not optimal, its completion rate is also lower. The completion rate of the method proposed in this paper is higher than the completion rate of the AL, indicating that the satellite ground processing together is effective, and also illustrates the

Figure 4: DAG completion rate versus satellite communications resources. Figure 5: DAG completion rate versus the number of DAG tasks. importance of proper task offloading decisions. The completion rate of the AV is 90.9%, which is lower than the completion rate of the method proposed in this paper, indicating the importance of resource allocation for the tasks offloaded to the satellite. ## 5 Conclusions

In this paper, when considering the dependency between tasks in satellite edge computing, improper resource allocation leads to a too-long subtask processing delay and a low success rate of application processing. To solve this problem, this paper first proposes a satellite-ground joint deployment network architecture based on task dependency, then schedules the subtasks of the application DAG with dependency, and then proposes a scheduling algorithm of TBID. Secondly, to overcome the problem that the traditional spar-row search algorithm falls into local optimality in the search process, this paper improves it and uses the improved sparrow search algorithm to allocate resources. In this paper, opposition-based learning, random search, and Cauchy mutation operators are introduced into the Sparrow search algorithm to improve the convergence and global search ability of the algorithm. The simulation results show that when the satellite computing resource is 14 Gcycles/s, the communication resource is 14 MHz, the number of DAGs to be processed is 16, and the local computing power is 4 Gcycles/s, the completion rate of the scheme is 100%, 90.9%, 12.5%, and 100%, respectively, which has a higher application completion rate than other benchmark methods. In the future, we will consider using the resources of adjacent satellites to schedule processing tasks in a multi-satellite satellite network architecture and consider the problem of real-time task scheduling. Conceptualization, Z.L. and Y.J. ; Methodology, Z.L. ; Software, Y.J. ; Validation, Y.J. and J.R.; Formal analysis, Y.J. ; Investigation, Y.J. and J.R.; Resources, [PERSON]; Data curation, Y.J. ; Writing--original draft, Y.J. ; Writing--review and editing, [PERSON], Y.J. and J.R.; Visualization, Y.J. ; Supervision, J.R.; Project administration, J.R. All authors have read and agreed to the published version of the manuscript. This research received no funding. The processed data required to reproduce these findings cannot be shared as the data also form part of an ongoing study. The writers would like to thank the editor and anonymous reviewers for their helpful comments for improving the quality of this paper. The authors declare no conflict of interest. Figure 6: DAG completion rate versus local computing capacity. ## References

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