Large Deviations for Slotted ALOHA Random Access

The effective bandwidth of a source measures the amount of burstiness besides the data generation rate. The effective bandwidths provide a means to guarantee qualityof-service in terms of packet loss probabilities. The classical theory of effective bandwidth, however, does not apply to a random access system, since the queues are coupled, i.e., the service statistics at one queue depend on the states of the other queues. In this paper, we argue that a similar theory of effective bandwidth can be developed for the slotted ALOHA random access. However, one should also account for the effective bandwidth of the channel, besides the source. We derive the buffer overflow exponent in a finite user ALOHA system, and express it as an optimization problem which can be solved numerically. We then consider natural upper and lower bounds on the exponent, and use the bounds to obtain worst-case performance guarantees.