# A Lyapunov-Optimized Dynamic Task Offloading Strategy for Satellite Edge Computing
## 1 Introduction  
Satellite networks are widely utilized for emergency communications, navigation and positioning, earthquake relief, and other applications due to their wide coverage, high data transmission rates, large capacity, and ability to operate independently of geographical limitations. Low Earth orbit (LEO) satellites have attracted the attention of scholars owing to their numerous advantages, including minimal transmission delays, support for global on-demand access, and terminal miniaturization, among others [1]. Currently, several countries have launched their own LEO satellite communication projects to supplement terrestrial services, such as Starlink, OneWeb, and O3b. Nevertheless, the majority of current LEO satellite networks employ the bent-pipe mode of data transmission, which involves forwarding large amounts of user data to the ground center for processing through the LEO network. This approach often leads to substantial network loads and long transmission delays due to complex inter-satellite links (ISLs) [2]. Additionally, the underutilization of LEO satellite communication and computing resources often leads to significant resource waste [2]. Multi-access edge computing (MEC) is an emerging computing paradigm that proposes the use of computing and communication resources near the user edge for task processing, instead of relying on cloud-centric resources [3]. This approach allows for data processing to be executed on edge servers, whereas the ground command center is responsible for storing processing results and conducting further data analysis. Drawing inspiration from MEC technology, edge servers are now being deployed on LEO satellite networks, creating what is known as an edge computing satellite (ECS) [4]. In this architecture, in-orbit resources of LEO satellites can be used directly by ground users for task processing, effectively mitigating time delays and network load issues. However, owing to the varying service regions of satellite networks, there are differences in task loads between satellites. The design of a rational computing offloading strategy for a satellite constellation can ensure a more balanced task load among satellites, and expedite task completion. Therefore, a collaborative task processing approach among LEO satellites (MLSCTP) is worthy of investigation as it can effectively mitigate issues related to high transmission delay and network congestion caused by long-distance satellite-ground link transmissions. Moreover, it addresses the problem of high computational latency resulting from the limited computing power of a single satellite. However, the research on MLSCTP still faces several significant challenges [1; 5]:  
* The satellite topology is highly dynamic, and the ISLs are variable at different moments. * Each satellite node is hard to manage during its operational phase as the task load changes, making its computing and communication resources change rapidly. * No defined collaborative strategy between multiple LEO satellites to ensure efficient task scheduling while fully utilizing computing resources. To address the issues mentioned above, this paper proposes a dynamic task offloading method based on the Lyapunov method and the Hungarian algorithm. In particular, for the computing offloading problem among satellites, the Lyapunov method is utilized to convert the long-horizon queue stability-constrained offloading problem into a single time-slot offloading optimization problem. Additionally, the problem is transformed into an assignment problem and solved using the Hungarian algorithm, which has low computational complexity and does not require any prior knowledge or multiple iterations to obtain optimal solutions. This approach provides a valuable reference for dynamic computing offloading among satellite constellations. The contributions of this paper are summarized below:  
* Consider a satellite edge computing scenario where the satellites in a constellation receive varying task loads.