Mean queue size in a queue with discrete autoregressive arrivals of order p

We consider a discrete time single server queueing system where the arrival process is governed by a discrete autoregressive process of order p (DAR(p)), and the service time of a customer is one slot. For this queueing system, we give an expression for the mean queue size, which yields upper and lower bounds for the mean queue size. Further we propose two approximation methods for the mean queue size. One is based on the matrix analytic method and the other is based on simulation. We show, by illustrations, that the proposed approximations are very accurate and computationally efficient.