Convergence and Tradeoff of Utility-Optimal CSMA

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Executive Summary

It has been recently suggested that in wireless networks, CSMA-based distributed MAC algorithms could achieve optimal utility without any message passing. The authors present the first proof of convergence of such adaptive CSMA algorithms towards an arbitrarily tight approximation of utility-optimizing schedule. They also briefly discuss the tradeoff between optimality at equilibrium and short-term fairness practically achieved by such algorithms. Consider a wireless network composed by a set L of L interfering links. Interference is modeled by a symmetric, boolean matrix A ?? {0, 1}L?~L, where Alk = 1 link l interferes link k. Define by N ?? {0, 1}L the set of feasible link activation profiles, or, schedules. A schedule m ?? N is a subset of non-interfering active links.

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