The saturation throughput region of p-persistent CSMA

Many modern wireless data networks employ Carrier Sense Multiple Access (CSMA) for efficient medium access. The p-persistent CSMA protocol is an analytically tractable version of CSMA that has been used successfully to model practical medium access protocols such as the IEEE 802.11 Distributed Coordination Function (DCF). We present a closed-form expression to characterize the access probabilities at the boundary of the saturation throughput region of p-persistent CSMA. This expression is a non-trivial generalization of the elegant result, obtained by J. Massey and P. Mathys in 1985, that the boundary of the saturation throughput region for slotted Aloha corresponds to the users adopting independent access probabilities that sum up to 1. We also present a closed form expression for the throughput values obtained at the boundary of the saturation throughput region of p-persistent CSMA for the case of 2 users.