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On the attained waiting time

Published online by Cambridge University Press:  01 July 2016

J. W. Cohen
J. W. Cohen*
Affiliation:
Centre for Mathematics and Computer Science
*
∗Postal address: Stichting Mathematisch Centrum, Centre for Mathematics and Computer Science, Kruislaan 413, 1098 SJ Amsterdam, The Netherlands.
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Abstract

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By using properties of up- and downcrossings of the sample functions of the workload process and of the attained waiting-time process for a G/G/1 queueing model, a direct proof of a theorem proved by Sakasegawa and Wolff is given.

Keywords

WORKLOAD PROCESSSAMPLE FUNCTIONSSTATIONARY DISTRIBUTIONS
Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 23 , Issue 3 , September 1991 , pp. 660 - 661
Copyright
Copyright © Applied Probability Trust 1991 

References

Cohen, J. W. (1977) On up- and downcrossings. J. Appl. Prob. 14, 405–410.Google Scholar
Cohen, J. W. (1982) The Single Server Queue , revised edn. North-Holland, Amsterdam.Google Scholar
Sakasegawa, H. and Wolff, R. W. (1990) The equality of the virtual delay and attained waiting time distributions. Adv. Appl. Prob. 22, 257–259.Google Scholar