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Approximation of the queue-length distribution of an M/GI/s queue by the basic equations

Published online by Cambridge University Press:  14 July 2016

Masakiyo Miyazawa
Masakiyo Miyazawa*
Affiliation:
Science University of Tokyo
*
∗Postal address: Department of Information Sciences, Faculty of Science and Technology, Science University of Tokyo, Noda City, Chiba 278, Japan.
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Abstract

We give a unified way of obtaining approximation formulas for the steady-state distribution of the queue length in the M/GI/s queue. The approximations of Hokstad (1978) and Case A of Tijms et al. (1981) are derived again. The main interest of this paper is in considering the theoretical meaning of the assumptions given in the literature. Having done this, we derive new approximation formulas. Our discussion is based on one version of the steady-state equations, called the basic equations in this paper. The basic equations are derived for M/GI/s/k with finite and infinite k. Similar approximations are possible for M/GI/s/k (k < +∞).

Keywords

APPROXIMATION FORMULAQUEUE LENGTHSTEADY-STATE DISTRIBUTIONPOISSON ARRIVAL
Type
Research Paper
Information
Journal of Applied Probability , Volume 23 , Issue 2 , June 1986 , pp. 443 - 458
Copyright
Copyright © Applied Probability Trust 1986 

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References

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