Performance evaluation of a single server autoregressive queue

This paper provides an approximation for stationary statistics of the unfinished work in a FIFO single server queue with unlimited buffer fed by a first-order autoregressive input. The method is based on modelling the queue as a semi-Markov queue and using the Wiener-Hopf factorization technique. It has been established that the tail of the unfinished work or waiting time distribution of such queues is negative exponential, and in this paper we provide estimates for the parameters of that exponential term. Simulation results which demonstrate that the formula leads to accurate results are presented.