Lyapunov-Based Tri-Stage Online On-Demand Resource Allocation and Task Offloading in SAGIN

The rapid development of 6G makes space-air-ground integrated networks (SAGIN) a promising solution to the coverage and capacity limitations of traditional cellular systems. However, time-varying topologies, stochastic channels, imbalanced user demands, and limited resources hinder on-demand service provisioning in wide-area environments. To address this challenge, this paper proposes an on-demand service framework that prioritizes users who contribute greater system utility once their demands are satisfied. The objective is to improve system utility through on-demand services without requiring prior knowledge of user demands or channel statistics. We first develop an on-demand utility model that captures diminishing returns in demand satisfaction while incorporating heterogeneous priority levels and latency constraints. Based on this model, we formulate a joint on-demand resource allocation and task offloading problem (ODRA-TO) to maximize system utility under long-term queue stability constraints. To efficiently solve ODRA-TO, we design an alternating direction method with three-stage iterations (ADMI) that decomposes the problem into learning-assisted task offloading, swap-stable matching based subchannel assignment, and gradient-based successive convex approximation for power control. Simulation results show that ADMI reduces the average queue length by 44.18%, improves on-demand utility by 34.59%, and achieves a 99.00% completion rate for high-priority services under dynamic SAGIN conditions.