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A note on losses in M/GI/1/n queues

Published online by Cambridge University Press:  14 July 2016

Rhonda Righter
Affiliation:
Santa Clara University
Corresponding
E-mail address:

Abstract

Let L n be the number of losses during a busy period of an M/GI/1/n queueing system. We develop a coupling between L n and L n+1 and use the resulting relationship to provide a simple proof that when the mean service time equals the mean interarrival time, EL n = 1 for all n. We also show that L n is increasing in the convex sense when the mean service time equals the mean interarrival time, and it is increasing in the increasing convex sense when the mean service time is less than the mean interarrival time.

MSC classification

Type
Short Communications
Copyright
Copyright © Applied Probability Trust 1999 

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References

Abramov, V. M. (1984). Some properties of lost customers. Izv. Akad. Nauk SSSR 3, 148150. (In Russian.)Google Scholar
Abramov, V. M. (1991a). Investigation of a Queueing System with Service Depending on Queue Length. Donish, Dushanbe. (In Russian.)Google Scholar
Abramov, V. M. (1991b). Asymptotic properties of lost customers for one queueing system with refusals. Kibernetika 2, 123124. (In Russian.)Google Scholar
Abramov, V. M. (1997). On a property of a refusals stream. J. Appl. Prob. 34, 800805.CrossRefGoogle Scholar

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