###### Abstract  
Satellite edge computing (SEC) plays an increasing role in earth observation, due to its global coverage and low-latency computing service. In SEC, it is pivotal to offload diverse observation-data-processing tasks to the appropriate satellites. Nevertheless, due to the sparse intersatellite link (ISL) connections, it is hard to gather complete information from all satellites. Moreover, the dynamic arriving tasks will also influence the obtained offloading assignment. Therefore, one daunting challenge in SEC is achieving optimal offloading assignments with consideration of the dynamic delay-sensitive tasks. In this paper, we formulate task offloading in SEC with delay-sensitive tasks as a mixed-integer linear programming problem, aiming to minimize the weighted sum of deadline violations and energy consumption. Due to the limited ISLs, we propose a fully-decentralized method, called the PI-based task offloading (PITO) algorithm. The PITO operates on each satellite in parallel and only relies on local communication via ISLs. Tasks can be directly offloaded on board without depending on any central server. To further handle the dynamic arriving tasks, we propose a re-offloading mechanism based on the match-up strategy, which reduces the tasks involved and avoids unnecessary insertion attempts by pruning. Finally, extensive experiments demonstrate that PITO outperforms state-of-the-art algorithms when solving task offloading in SEC, and the proposed re-offloading mechanism is significantly more efficient than existing methods. s 2024 16 2184 11.1  
Unfortunately, due to the distributed and dynamic nature of SEC [7], it is tough to obtain offloading assignments for delay-sensitive tasks. Specifically, on the one hand, there are sparse ISL connections in SEC; thus, it is hard to gather all the necessary information from all satellites, and sending information from satellites to the control center also involves unnecessary delays. Additionally, the satellite states change rapidly during task processing, collecting such information leading to a huge communication burden on the satellite network. On the other hand, due to the dynamics in SEC, delay-sensitive tasks are continually generated by observation satellites, which causes a daunting challenge for task offloading. That is because newly generated tasks may have the same time horizon as the offloaded ones, affecting the original offloading assignment, and even make it infeasible. Thus, task offloading problems should be carefully addressed to resolve the above challenges. The task offloading problem in SEC has received increasing attention recently. Specifically, recent works [14; 15; 16; 17; 18; 19; 20; 21; 22; 23] obtain offloading assignments by various centralized approaches deploying on the access satellites or gateway stations. Meanwhile, considering the non-centrality of SEC, works [24; 25; 26; 27; 28] adopt the distributed algorithm to reduce the latency caused by long-distance communication [25]. Unfortunately, some practical issues are still neglected, such as the sparsity of ISLs, the limited network resources, and the dynamic arrival of delay-sensitive tasks. To the best of our knowledge, task offloading problems jointly considering the aforementioned practical issues, have not been addressed for SEC. In this paper, we investigate the task offloading problem in SEC with delay-sensitive tasks by jointly considering the distributed satellites and the dynamic environment. The main contributions of this article are summarized as follows:  
* This paper establishes a mixed-integer linear programming (MILP) model for delay-sensitive task offloading in SEC, which aims to reduce the deadline violation of delay-sensitive tasks while minimizing the system's energy consumption. * Considering the limited ISL connections, we propose a fully decentralized PITO algorithm. The PITO operates on each satellite in parallel and only relies on local communication via ISLs. It iterates between two stages, called _task inclusion_ and _consensus and task removal_.