# A Lyapunov-Optimized Dynamic Task Offloading Strategy for Satellite Edge Computing
## 2 Related Works  
Dynamic task scheduling strategies for collaborative computing among multiple satellites play an essential role in edge computing-enhanced LEO satellite networks. At present, some scholars have carried out the research. [PERSON] et al. [6] proposed a novel system of task-oriented intelligent network architecture to deal with the problems arising in edge computing-enhanced sky-ground-water integrated networks. [PERSON] et al. [7] analyzed the feasibility of MEC-enabled satellites-ground converged networks for processing tasks on satellites. An architecture called STECN is proposed, which discusses the solutions and technical challenges of using the resources of its heterogeneous edge computing clusters for task processing. In the above literature, although the authors propose and emphasize the importance and feasibility of task scheduling and resource allocation for MEC-enabled satellite clusters, none of them elaborated on specific task scheduling strategy schemes. [PERSON] et al. [8] proposed a model for orbital edge computing and described the power and software optimization of the orbital edge. [PERSON] et al. [9] proposed a joint offloading and resource allocation scheme for satellite-assisted vehicle networking. [PERSON] et al. [10] proposed a satellite MEC framework for terrestrial IoT to minimize the energy consumption of IoT mobile devices. They also proposed a computational offloading and resource allocation scheme. In the above works, each of the authors proposed suitable task scheduling and resource allocation schemes; however, none of them included the strategy of multi-satellite cooperative computing in the research model. [PERSON] et al. [11] proposed to form a satellite fog network using a small satellite formation and designing a task scheduling strategy using the improved particle swarm algorithm, which can reduce the task processing latency while meeting energy consumption constraints. However, this paper only considers formation flying satellites, whose topology will not change and has little reference value for task scheduling of highly dynamic LEO satellite constellations. [PERSON] et al. [1] proposed a satellites collaborative computing method using business graph drive in LEO satellite networks. In the paper, [PERSON] combined the computing resources of multiple satellites and ISLs resources to schedule the task to the satellites on the transmission path for processing. However, the authors only considered the scheduling of a single task and did not consider the case of multiple tasks arriving in sequence. [PERSON] et al. [12] proposed to use the steady-state matrix of time-expanded graphs to represent the steady-state topology of dynamic LEO satellite networks. Additionally, the author designed a diffusion algorithm based on the matrix to achieve optimal task assignment for LEO satellite networks, which could efficiently complete the computational tasks while meeting delay constraints. However, this paper only considered the scheduling algorithm for a single-task scenario. Based on this problem, [PERSON] et al. [13] suggested using satellites to assist ground users in computational offloading, where multiple satellites can directly connect to ground users and provide offloading. However, due to orbital coverage issues, most satellites in the actual satellite constellation cannot connect directly to ground users and must be further offloaded through the inter-satellite link. [PERSON] et al. [14] considered using the full satellite constellation for offloading, considering the effects of multi-hop delay and energy consumption. [PERSON] et al. [15] proposed offloading the computing tasks of ground users to the over-the-top satellite. To address the unevenness of satellite network nodes, they proposed transferring computational tasks on under-resourced satellite nodes to more resource-rich nodes for collaborative processing through inter-satellite links, using a linear programming approach to solve related problems.