Contact-Capacity-Aware Feasibility and Scheduling-Complexity Boundaries in LEO Satellite–Terrestrial MEC With In-Loop KKT Resource Allocation

Abstract

Low-Earth-orbit (LEO) satellite–terrestrial networks can extend mobile edge computing (MEC) beyond dependable terrestrial coverage, but short orbital contacts and time-varying rates couple task assignment with subsequent resource sharing. Many existing formulations equate geometric visibility with usable service or evaluate a task from a slot-level estimate. We develop a temporal-graph hierarchical graph neural network for satellite–terrestrial integrated networks (TG-HiGNN-STIN), a contact-capacity-aware scheduler with in-loop Karush–Kuhn–Tucker (KKT) resource allocation. A dual-layer switching graph uses a necessary contact-capacity test to remove visible satellite actions whose remaining contact cannot carry the upload even under the maximum rate envelope. Persistent task states retain unfinished access, feeder, and computation work, while closed-form allocations redistribute shared bandwidth and processor capacity at slot boundaries and whenever the active set changes within a slot. An edge-aware graph-attention encoder with recurrent node memory and a feasibility-masked actor then selects the execution path. In a common Walker-constellation benchmark, the screen remains unobtrusive in capacity-rich cases and prevents contact-loss failures for a satellite-priority diagnostic near the service boundary. Load-matched training produces an observed nominal-load crossover in favour of TG-HiGNN-STIN, whereas the transparent rules retain lower mean miss rates under high load and contact stress. Relational queue and contact features also improve group-held-out prediction of coordinated reference decisions. The framework therefore provides a physically grounded decision pipeline and direct evidence for matching scheduling complexity to the operating regime.