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Convex ordering of the attained waiting times in single-server queues and related problems

Published online by Cambridge University Press:  14 July 2016

Masakiyo Miyazawa  and
Genji Yamazaki
Masakiyo Miyazawa*
Affiliation:
Science University of Tokyo
Genji Yamazaki*
Affiliation:
Tokyo Metropolitan Institute of Technology
*
∗Postal address: Department of Information Sciences, Science University of Tokyo, Noda-city, Chiba 278, Japan.
∗∗Postal address: Department of Engineering Management, Tokyo Metropolitan Institute of Technology, 6–6 Asahigaoka, Hino-city, Tokyo 191, Japan.
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Abstract

The attained waiting time of customers in service of the G/G/1 queue is compared for various work-conserving service disciplines. It is proved that the attained waiting time distribution is minimized (maximized) in convex order when the discipline is FCFS (PR-LCFS). We apply the result to characterize finiteness of moments of the attained waiting time in the GI/GI/1 queue with an arbitrary work-conserving service discipline. In this discussion, some interesting relationships are obtained for a PR-LCFS queue.

Keywords

WORK-CONSERVING DISCIPLINEFCFSLCFSFINITENESS OF MOMENTS
Type
Research Papers
Information
Journal of Applied Probability , Volume 28 , Issue 2 , June 1991 , pp. 433 - 445
Copyright
Copyright © Applied Probability Trust 1991 

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