In this paper, a framework is proposed to simplify solving the infinite horizon average cost problem for the weakly coupled multi-dimensional systems. Specifically, to address the computational complexity issue, we first introduce a virtual continuous time system (VCTS) and obtain the associated fluid value function. The relationship between the VCTS and the original discrete time system is further established. To facilitate the low complexity distributed implementation and address the coupling challenge, we model the weakly coupled system as a perturbation of a decoupled base system and study the decoupled base system. The fluid value function of the VCTS is approximated by the sum of the per-flow fluid value functions and the approximation error is established using perturbation analysis. Finally, we obtain a low complexity distributed solution based on the per-flow fluid value function approximation. We apply the framework to solve a delay-optimal control problem for the K-pair interference networks and obtain a distributed power control algorithm. The proposed algorithm is compared with various baseline schemes through simulations and it is shown that significant delay performance gain can be achieved.
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