Stability Analysis of $p$-Persistent Slotted CSMA Systems With Finite Population

When multiple users are communicating with an access point based on a random access, the stability region is known as all possible combinations of the mean packet arrival rates to keep their queue lengths bounded. This paper investigates the stability region of p-persistent carrier sense multiple access (CSMA) systems, where two users have different mean packet arrival rates and (re)transmission probabilities. We then extend our results to p-persistent CSMA systems with N users and discuss applicability of our results to IEEE 802.11 systems with the basic and request-to-send/clear-to-send access mechanisms. In numerical studies, we show the stability region by varying system parameters such as packet arrival rates, (re)transmission probabilities, and radio channel errors, and how the stability region of p-persistent CSMA systems gets close to that of a time-sharing system.