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On the reversibility of the input and output processes for a general birth-and-death queueing model

Published online by Cambridge University Press:  14 July 2016

Bent Natvig
Bent Natvig*
Affiliation:
University of Oslo
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Abstract

In this paper we consider the general birth-and-death queueing model of Natvig (1975). Define the input and output processes by the steady-state behaviour of respectively successive input and output intervals. Ignoring balking customers, two cases are considered. In the first case we treat a lost customer neither as an input nor as an output, then secondly as both. For both cases we show the input and output processes to be reverse processes. One mistake and two erroneous comments in Natvig (1975) are also corrected.

Keywords

GENERAL BIRTH-AND-DEATH QUEUEING MODELSTATE-DEPENDENTBALKINGDEFECTIVE CUSTOMERSLOSSSTEADY-STATEINPUT PROCESSOUTPUT PROCESSREVERSIBILITY
Type
Short Communications
Information
Journal of Applied Probability , Volume 14 , Issue 4 , December 1977 , pp. 876 - 883
Copyright
Copyright © Applied Probability Trust 1977 

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References

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