Before revision:  We prove that , unlike the standard CSMA algorithm, this simple distributed access scheme is optimal in the sense that the network is stable for all traffic intensities in the capacity region of the network. Simulations show that capacity (in terms of maximum sustainable traffic) increases by a factor ranging from 1.5 to 2.5 compared to the standard CSMAalgorithm, depending on the network topology and the number of available radio channels .
After revision:  We prove that , unlike the standard CSMA algorithm, this simple distributed access scheme is optimal in ad-hoc mode but not in infrastructure mode, when all data flows originate from or are destined to some access points, due to the inherent bias of CSMA against downlink traffic. We propose a slight modification of CSMA, that we refer to as flow-aware CSMA, which corrects this bias and makes the algorithm optimal in all cases. The analysis is based on some time-scale separation assumption which is proved valid in the limit of large flow sizes .