# Joint Task Offloading and Power Allocation for Satellite Edge Computing Networks
###### Abstract
The SECN enables low-cost, seamless global coverage and has become one of the key technologies for the future 6G (sixth-generation) network [12,13]. The SECN overcomes the uneven distribution of terrestrial computing resources and the lack of network and computing services over the vast majority of the planet's surface by shifting computing from the ground to space [14]. Because they can achieve seamless global coverage, users can access a variety of services provided by the SECN, including edge computing resources and wireless storage resources, no matter where they are in the world. Users in remote regions do not need to apply for computing and network services from remote cloud centers, and the SECN can greatly reduce queuing and transmission latencies, thereby improving the quality of service [15]. For the cloud center and backbone network, the SECN can share the processing load of numerous tasks, and data do not have to be transmitted through the backbone network, reducing the workload of both. Finally, the SECN processes the data in the satellite MEC in a distributed approach, which greatly reduces the risk of data leakage and improves the security of user data [16]. Although the SECN can improve the user experience and reduce the workload of the network, existing studies only consider the scenario in which each satellite handles a task independently, without considering the complex case when some tasks are too heavy to be handled by a single satellite [17,18]. In such a situation, excessive satellite load happens, which reduces the service lifespan of the satellite and causes a waste of valuable resources. Cooperative satellite computing provide a new solution to this challenge. As shown in Figure 1, this paper considers a multi-satellite cooperative satellite edge computing model where multiple satellites compute in parallel to reduce the maximum latency. The maximum delay minimization problem in the proposed scenario is nonconvex and high-coupled. We consider using the increasing penalty dual decomposition (IPDD) algorithm to minimize the maximum delay of the system under the power and energy constraints, where the IPDD algorithm is a double-loop iterative algorithm that can solve nonconvex nonsmooth optimization problems, especially when the optimization variables are nonlinearly coupled in some nonconvex constraints [19]. While building upon the established IPDD algorithm framework, we present systematic enhancements specifically optimized for latency minimization in satellite edge computing architectures named delay-balanced increasing penalty dual decomposition (DB-IPDD). Our methodological innovations specifically address the unique constraints of multi-satellite collaborative environments. We developed a novel analytical framework that establishes Theorem 1 through rigorous proof-by-contradiction methodology, formally demonstrating that system-wide latency minimization occurs under uniform processing time distribution across satellite nodes. Through evaluating the optimal solution obtained via the IPDD method, we can verify whether it satisfies the optimality criteria established in Theorem 1. If the criteria are not met, we iteratively optimize the resource allocation to balance the processing times between the satellites with the maximum and minimum latencies. This process is repeated until convergence is achieved. This DB-IPDD method ensures progressive refinement toward global optimality, representing a substantial advancement over conventional IPDD implementations. The theoretical foundation established through Theorem 1's proof, combined with our adaptive resource balancing protocol, provides a replicable framework for latency-sensitive distributed space systems. Figure 1: Illustration of the LEO satellite edge computing system. Each satellite has the capability to participate in task offloading and computation, while being subject to resource constraints. During data processing, the data transmission between the MS and the SS occurs over wireless links.