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

Authors:
Fumio Ishizaki;Tetsuya Takine
Affiliations:
Department of Information Science and Intelligent Systems, Faculty of Engineering, The University of Tokushima, 2-1 Minamijosanjima, Tokushima 770-8506, Japan E-mail: ishizaki@is.tokushima-u.ac ...;Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan E-mail: takine@kuamp.kyoto-u.ac.jp
Venue:
Queueing Systems: Theory and Applications
Year:
1999

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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 i.i.d. 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.