Explicit solution for the stationary distribution of a discrete-time finite buffer queue

Bara  Kim; Jeongsim  Kim

doi:10.3934/jimo.2016.12.1121

Article Contents

2016, Volume 12, Issue 3: 1121-1133. Doi: 10.3934/jimo.2016.12.1121

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Explicit solution for the stationary distribution of a discrete-time finite buffer queue

Bara Kim^1, and
Jeongsim Kim^2,

1.
Department of Mathematics, Korea University, 145, Anam-ro, Seongbuk-gu, Seoul, 02841
2.
Department of Mathematics Education, Chungbuk National University, 1, Chungdae-ro, Seowon-gu, Cheongju, Chungbuk, 28644

Received: September 30, 2013

Revised: January 31, 2015

Published: June 2016

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Abstract

We consider a discrete-time single server queue with finite buffer. The customers arrive according to a discrete-time batch Markovian arrival process with geometrically distributed batch sizes and the service time is one time slot. For this queueing system, we obtain an exact closed-form expression for the stationary queue length distribution. The expression is in a form of mixed matrix-geometric solution.

Keywords:

Discrete-time queue,
discrete-time batch markovian arrival process,
stationary distribution,
quadratic matrix equation,
mixed matrix-geometric solution.

Mathematics Subject Classification: Primary: 60K25; Secondary: 60J10.

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