The Waiting Time Analysis of A Discrete Time Queue with Arrivals as A Discrete Autoregressive Process of Order 1

Abstract

We consider a discrete time queueing system with the discrete autoregressive process of order 1 (shortly, the DAR(1)) as an input process and obtain the actual waiting time distribution and the virtual waiting time distibution. As shown in the analysis, our approach provides natural numerical algorithm to compute the waiting time distributions, based on the theory of the GI/G/1 queue, and consequently we can easily investigate the effect of the parameters of the DAR(1) on the waiting time distribution. We also derive a simple approximation of the asymptotic decay rate of the tail probabilities for the virtual waiting time in the heavy traffic case.