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Supplementary variable method applied to the MAP/G/1 queueing system

Published online by Cambridge University Press:  17 February 2009

Bong Dae Choi ,
Gang Uk Hwang  and
Dong Hwan Han
Bong Dae Choi
Affiliation:
Center for Applied Mathematics and Department of Mathematics, Korea Advanced Institute of Science and Technology, 373–1 Kusong-Dong, Yusong-Gu, Taejon, 305–701, Korea
Gang Uk Hwang
Affiliation:
Center for Applied Mathematics and Department of Mathematics, Korea Advanced Institute of Science and Technology, 373–1 Kusong-Dong, Yusong-Gu, Taejon, 305–701, Korea
Dong Hwan Han
Affiliation:
Department of Mathematics, Sun Moon University, Asan-Kun, Chungnam, 337–840, Korea
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Abstract

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In this paper we consider the MAP/G/1 queueing system with infinite capacity. In analysis, we use the supplementary variable method to derive the double transform of the queue length and the remaining service time of the customer in service (if any) in the steady state. As will be shown in this paper, our method is very simple and elegant. As a one-dimensional marginal transform of the double transform, we obtain the generating function of the queue length in the system for the MAP/G/1 queue, which is consistent with the known result.

Type
Research Article
Information
The ANZIAM Journal , Volume 40 , Issue 1 , July 1998 , pp. 86 - 96
Copyright
Copyright © Australian Mathematical Society 1998

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