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Sharp results on convergence rates for the distribution of GI/M/1/K queues as K tends to infinity

Part of: Special processes Operations research and management science

Published online by Cambridge University Press:  14 July 2016

Bong Dae Choi  and
Bara Kim
Bong Dae Choi*
Affiliation:
Korea University
Bara Kim*
Affiliation:
Korea University
*
∗ Postal address: Department of Mathematics, Korea University, 1, Anam-dong, Sungbuk-ku, Seoul, 136–701, Korea.
∗ Postal address: Department of Mathematics, Korea University, 1, Anam-dong, Sungbuk-ku, Seoul, 136–701, Korea.
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Abstract

In this paper, we investigate how fast the stationary distribution π(K) of an embedded Markov chain (time-stationary distribution q(K) of the GI/M/1/K queue converges to the stationary distribution π of the embedded Markov chain (time-stationary distribution q) of the GI/M/1 queue as K tends to infinity. Simonot (1997) proved certain equalities. We obtain sharper results than these by finding limit values limK→∞σ-K||π(K) - π|| and limK→∞σ-K||q(K) - q|| explicitly.

Keywords

GI/M/1/K queuedual sequencestationary measurestationary distributionconvergence rate

MSC classification

Primary: 60K25: Queueing theory
Secondary: 90B22: Queues and service
Type
Research Papers
Information
Journal of Applied Probability , Volume 37 , Issue 4 , December 2000 , pp. 1010 - 1019
Copyright
Copyright © by the Applied Probability Trust 2000 

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Footnotes

This work was supported in part by a research program from KOSEF (98-0101-02-01-3).

References

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