Convergence and tradeoff of utility-optimal CSMA

It has been recently suggested by Jiang and Walrand that adaptive carrier sense multiple access (CSMA) can achieve optimal utility without any message passing in wireless networks. In this paper, a generalization of this algorithm is considered. In the continuous-time model, a proof is presented of the convergence of these adaptive CSMA algorithms to arbitrarily close to utility optimality, without assuming that the network dynamics freeze while the CSMA parameters are updated. In the more realistic, slotted-time model, the impact of collisions on the utility achieved is characterized, and the tradeoff between optimality at equilibrium and short-term fairness is quantified.