Matrix analytical model of an ATM output buffer with self-similar traffic

Renewal processes with asymptotically hyperbolic interarrival time distributions are shown to exhibit self-similar behavior. An output buffer of an ATM switch is modeled as a discrete time queue with a single server, deterministic service times and self-similar renewal process input. A matrix geometric solution is found for the stationary distribution of states. For the case of hyperbolically distributed interarrival times, the mean and standard deviation of queue length are plotted for various values of the queue utilization and the self-similarity parameter of the arrival process. The self-similarity is found to have a significant impact on the performance of the queue.