Throughput Upper-Bound of Slotted CSMA Systems with Unsaturated Finite Population

In this paper we propose a new Markovian model for p-persistent carrier sense multiple access (CSMA) systems with a finite population of unsaturated single-buffered terminals. Focused on the distribution of the number of backlogged terminals in the steady state, our model allows the optimal persistent probability p from the number of backlogged terminals, which enables us to determine the throughput upper-bound (or mean access delay lower-bound) of slotted CSMA systems. We compare the performance of slotted CSMA systems with binary exponential backoff (BEB) algorithm and with p-persistent protocol against the throughput upper-bound and examine the stability of these systems. We show how closely slotted CSMA systems with BEB algorithm or p-persistent protocol approaches the throughput upper-bound in accordance with the minimum contention window size or the persistent probability p. Further, we propose a generalized Bertsekas' (backoff) algorithm (GBA) based on backlog size estimation, which is a generalization of the existing algorithm proposed by Bertsekas, in order to achieve the throughout upper-bound. Our study shows that in slotted CSMA systems, the access fairness of BEB algorithm is worse than those of p-persistent protocol and GBA algorithm, while the BEB and GBA algorithms show throughput performance close to optimality.