Distributed scheduling of wireless networks: A message passing approach

We consider the problem of scheduling wireless networks with stochastic packet arrivals on the links and constant transmission rates. We propose a scheduling policy based on solving a Maximum Weighted Independent Set (MWIS) problem at each time slot on a conflict graph that incorporates all the interference constraints. Due to the computational difficulty of solving the MWIS on general graphs, we design a novel, low-complexity and distributed two-phase algorithm which solves the linear programming relaxation of the MWIS and then constructs a feasible solution to the original problem. We show that the two-phase algorithm always produces a maximal schedule for general networks, thus, achieving network stability. Numerical results show that our scheduling policy achieves significantly smaller aggregate long-run average queue lengths than some state-of-the-art scheduling algorithms.