On the design of efficient CSMA algorithms for wireless networks

Recently, it has been shown that CSMA algorithms which use queue length-based link weights can achieve throughput optimality in wireless networks. In particular, a key result by Rajagopalan, Shah, and Shin (2009) shows that, if the link weights are chosen to be of the form log log(q) (where q is the queue-length), then throughput optimality is achieved. In this paper, we tighten their result by showing that throughput optimality is preserved even with weight functions of the form log(q)/g(q), where g(q) can be a function that increases arbitrarily slowly. The significance of the result is due to the fact that weight functions of the form log(q)/g(q) seem to achieve the best delay performance in practice.