Loss probability in a finite discrete-time queue in terms of the steady state distribution of an infinite queue

Loss probability in a finite discrete-time queue in terms of the steady state distribution of an infinite queue

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Article ID: iaor20003189
Country: Netherlands
Volume: 31
Issue: 3/4
Start Page Number: 317
End Page Number: 326
Publication Date: Jan 1999
Journal: Queueing Systems
Authors: ,
Keywords: markov processes
Abstract:

We consider a discrete-time single-server queue with arrivals governed by a stationary Markov chain, where no arrivals are assumed to occur only when the Markov chain is in a particular state. This assumption implies that off-periods in the arrival process are independent, identically distributed and geometrically distributed. For this queue, we establish the exact relationship between queue length distributions in a finite-buffer queue and the corresponding infinite-buffer queue. With the result, the exact loss probability is obtained in terms of the queue length distribution in the corresponding infinite-buffer queue. Note that this result enables us to compute the loss probability very efficiently, since the queue length distribution in the infinite-buffer queue can be efficiently computed when off-periods are geometrically distributed.

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