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The equality of the virtual delay and attained waiting time distributions

Published online by Cambridge University Press:  01 July 2016

Hirotaka Sakasegawa  and
Ronald W. Wolff
Hirotaka Sakasegawa*
Affiliation:
University of Tsukuba
Ronald W. Wolff*
Affiliation:
University of California, Berkeley
*
∗Postal address: Institute of Socio-Economic Planning, The University of Tsukuba, Tsukuba, Ibaraki 305, Japan.
∗∗Postal address: Department of Industrial Engineering and Operations Research, University of California, Berkeley, CA 94720, USA.
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Abstract

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It has recently been shown that for the G/G/1 queue, virtual delay and attained waiting time have the same stationary distribution. We present a sample-path derivation of this result.

Keywords

G/G/1 QUEUEFIFOFCFSWORK IN SYSTEM
Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 22 , Issue 1 , March 1990 , pp. 257 - 259
Copyright
Copyright © Applied Probability Trust 1990 

Footnotes

Part of this research was done while R. W. Wolff visited the Department of Information Sciences, Science University of Tokyo, in 1989.

References

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Miyazawa, M. (1983) The derivation of invariance relations in complex queueing systems with stationary inputs. Adv. Appl. Prob. 15, 874–885.Google Scholar
Sengupta, B. (1989) An invariance relationship for the G/G/1 queue. Adv. Appl. Prob. 21, 956–957.Google Scholar