  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.
