Delay and Energy Optimization in Heterogeneous GEO–LEO Satellite Networks: A GNN-Enhanced Game-Theoretic and DRL Approach

As 6G mobile communications evolve, Low Earth Orbit (LEO) satellite mobile edge computing (MEC) enables globally seamless computing. However, the high mobility of LEO satellites disrupts service continuity and resource stability. Existing approaches often use oversimplified models that ignore multi-beam interference and dynamic task queueing. To address this, we establish a hierarchical Geostationary Earth Orbit (GEO)–LEO synergistic architecture, where the integration is implemented by utilizing GEO satellites as stability anchors and remote cloud relays, while LEO satellites provide low-latency edge processing. We formulate fine-grained models for two-level beam-centric communication and preemptive dynamic queueing. The resulting joint task offloading and resource allocation problem is a complex mixed-integer nonlinear program (MINLP). To effectively solve this MINLP, we decouple it hierarchically: first determine discrete offloading decisions, then optimize continuous resource allocations based on them, proposing a novel framework termed G2DRL (GNN-enhanced Game-theoretic and deep reinforcement learning). Simulation results demonstrate that G2DRL significantly reduces the weighted sum of system delay and energy, showing superior convergence stability and performance over state-of-the-art DRL baselines.