| Summary: | This paper investigates the critical issue of maintaining system stability for multipacket reception (MPR) <inline-formula> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula>-persistent carrier sense multiple access (CSMA) systems. When multiple users with individual queues simultaneously transmit a packet to an access point (AP) via CSMA, the number of successful transmissions and their identities are determined probabilistically in the MPR channel. Stability signifies that none of the users’ queues grows unbounded. The stability region is a significant measure, addressing all potential permutations of mean packet arrival rates for the users to maintain bounded queue lengths. The work begins by considering a system with two users characterized by differing mean packet arrival rates and (re)transmission probabilities. Subsequently, it examines an <inline-formula> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula>-user system in which each user shares an identical packet arrival rate and retransmission probability. A backoff algorithm is then proposed for these <inline-formula> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> users to utilize in order to stabilize their queues. The paper concludes with numerical studies illustrating the stability region as a function of user parameters, demonstrating how the proposed backoff algorithm can be used to maximize throughput.
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