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

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Rhonda Righter
Rhonda Righter*
Affiliation:
Santa Clara University
*
∗Postal address: Department of Operations and Management Information Systems, Santa Clara University, Santa Clara, CA 95053, USA. Email address: rrighter@scu.edu
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Abstract

Let Ln be the number of losses during a busy period of an M/GI/1/n queueing system. We develop a coupling between Ln and Ln+1 and use the resulting relationship to provide a simple proof that when the mean service time equals the mean interarrival time, ELn = 1 for all n. We also show that Ln 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.

Keywords

Loss systemsM/GI/1/n queuesstochastic coupling

MSC classification

Primary: 60K25: Queueing theory
Type
Short Communications
Information
Journal of Applied Probability , Volume 36 , Issue 4 , December 1999 , pp. 1240 - 1243
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, 148–150. (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, 123–124. (In Russian.)Google Scholar
Abramov, V. M. (1997). On a property of a refusals stream. J. Appl. Prob. 34, 800–805.CrossRefGoogle Scholar