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On a property of a refusals stream

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Vyacheslav M. Abramov
Vyacheslav M. Abramov*
Affiliation:
Chaim Sheba Medical Center
*
∗Postal address: Institute of Clinical Epidemiology, The Chaim Sheba Medical Center, Tel Hashomer, Ramat-Gan 52621, Israel. Present address: 26/7 Rambam St., Petach Tiqwa 49542, Israel.
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Abstract

This paper consists of two parts. The first part provides a more elementary proof of the asymptotic theorem of the refusals stream for an M/GI/1/n queueing system discussed in Abramov (1991a). The central property of the refusals stream discussed in the second part of this paper is that, if the expectations of interarrival and service time of an M/GI/1/n queueing system are equal to each other, then the expectation of the number of refusals during a busy period is equal to 1. This property is extended for a wide family of single-server queueing systems with refusals including, for example, queueing systems with bounded waiting time.

Keywords

REFUSALSM/GI/1/N QUEUEING SYSTEMBUSY PERIODRENEWAL PROCESS

MSC classification

Primary: 60K25: Queueing theory
Type
Short Communications
Information
Journal of Applied Probability , Volume 34 , Issue 3 , September 1997 , pp. 800 - 805
Copyright
Copyright © Applied Probability Trust 1997 

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Footnotes

Research was supported by the Nate H. and Beatrice G. Sherman Fellowship at the Technion — Israel Institute of Technology.

References

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