CSMA using the Bethe approximation for utility maximization

CSMA (Carrier Sense Multiple Access), which resolves contentions over wireless networks in a fully distributed fashion, has recently gained a lot of attentions since it has been proved that appropriate control of CSMA parameters guarantees optimality in terms of system-wide utility. Most algorithms rely on the popular MCMC (Markov Chain Monte Carlo) technique, which enables one to find optimal CSMA parameters through iterative loops of simulation-and-update. However, such a simulation-based approach often becomes a major cause of exponentially slow convergence, being poorly adaptive to flow/topology changes. In this paper, we develop a distributed iterative algorithm which produces approximate solutions with convergence in polynomial time. Our approach is motivated by a scheme in statistical physics, referred to as the Bethe approximation, allowing us to express approximate solutions via a certain non-linear system with polynomial size. We provide numerical results to show that the algorithm produces highly accurate solutions and converges much faster than prior ones.