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On a Property of a Refusals Stream

Vyacheslav M. Abramov
Journal of Applied Probability
Vol. 34, No. 3 (Sep., 1997), pp. 800-805
DOI: 10.2307/3215106
Stable URL: http://www.jstor.org/stable/3215106
Page Count: 6
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On a Property of a Refusals Stream
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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/Gl/I/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.

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