Date: 09 Jun 2005

The BMAP/G/1 queue: A tutorial

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We present an overview of recent results related to the single server queue with general independent and identically distributed service times and a batch Markovian arrival process (BMAP). The BMAP encompasses a wide range of arrival processes and yet, mathematically, the BMAP/G/1 model is a relatively simple matrix generalization of the M/G/1 queue. Stationary and transient distributions for the queue length and waiting time distributions are presented. We discuss numerical algorithms for computing these quantities, which exploit both matrix analytic results and numerical transform inversion. Two-dimensional transform inversion is used for the transient results.