A new approximation for slotted buffered Aloha

Few models in wireless communications have been addressed as thoroughly as slotted Aloha, and most important questions regarding its performance have been answered (e.g., stability). Although slotted time finite user Aloha with infinite backlog (no queueing analysis) and fixed (common) contention probability is trivial, incorporating queueing significantly increases the complexity of the problem, with a corresponding major impact on the resulting performance. The stability region of this model is known, as are many other performance aspects, but a review of the literature yields no explicit performance expressions in terms of the fundamental model parameters. This paper approximates the performance of the K coupled queues with K uncoupled geom/geom/1 queues, where the queue parameters are selected to reflect the actual coupling as closely as possible. The throughput match is excellent, and the service delay match is good. The approach can be extended to queue-specific contention probabilities in a straightforward manner.