The integrated satellite-terrestrial network (ISTN) system has experienced significant growth, offering seamless communication services in remote areas with limited terrestrial infrastructure. However, designing a routing scheme for ISTN is exceedingly difficult, primarily due to the heightened complexity resulting from the inclusion of additional ground stations, along with the requirement to satisfy various constraints related to satellite service quality. To address these challenges, we study packet routing with ground stations and satellites working jointly to transmit packets, while prioritizing fast communication and meeting energy efficiency and packet loss requirements. Specifically, we formulate the problem of packet routing with constraints as a max-min problem using the Lagrange method. Then we propose a novel constrained Multi-Agent reinforcement learning (MARL) dynamic routing algorithm named CMADR, which efficiently balances objective improvement and constraint satisfaction during the updating of policy and Lagrange multipliers. Finally, we conduct extensive experiments and an ablation study using the OneWeb and Telesat mega-constellations. Results demonstrate that CMADR reduces the packet delay by a minimum of 21% and 15%, while meeting stringent energy consumption and packet loss rate constraints, outperforming several baseline algorithms.
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