Synergistic Task Offloading in 6G Integrated Satellite-Terrestrial Edge Computing Networks Based on Propagation Dynamics

Abstract

Integrated satellite-terrestrial edge computing technology efficiently utilizes the computational resources of low earth orbit (LEO) satellites and terrestrial intelligent terminals to provide low-latency and high-reliability task offloading services for terrestrial terminals. However, excessive task offloading increases the risk of terrestrial network paralysis. Identifying the critical conditions leading to large-scale task overload in intelligent terminals is crucial for ensuring network stability. Therefore, we investigated the dynamic transmission process of task offloading in 6G integrated satellite-terrestrial edge synergistic computing network and proposed a bi-layer coupled Service-Request-Healing ( $SRH$ ) synergistic task offloading propagation model. Within the framework of propagation dynamics theory, two state transition linear threshold functions are incorporated to distinguish the task processing capabilities and capacities of intelligent terminals from those of LEO satellites. Furthermore, the resulting $SRH$ task offloading propagation model is theoretically examined through edge-based compartmental theory. By establishing propagation dynamics equations, we derived the saddle point and perform stability analysis to determine the critical conditions that lead to large-scale task overload in intelligent terminals. This provides a theoretical reference for preventing network paralysis in satellite-terrestrial integrated edge computing networks. Simulation results demonstrated that the model can describe the offloading process, reveal the evolutionary mechanism. In addition, we can effectively prevent the paralysis of 6G integrated satellite-terrestrial edge synergistic computing network by controlling network connectivity density and degree distribution heterogeneity.