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On the waiting-time and busy period distributions for a general birth-and-death queueing model

Published online by Cambridge University Press:  14 July 2016

Bent Natvig
Bent Natvig*
Affiliation:
University of Sheffield
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Abstract

A general birth-and-death queueing model is considered with N waiting positions (0 ≦ N ≦ ∞), s servers (1 ≦ s ≦ ∞) and a first-come-first-served queueing discipline. The first and second order moments of the steady-state waiting-time (excluding service) for a non-lost arriving customer are given. By setting the busy period equal to the time where at least one service is in progress, we obtain the first and second order moments of the length of a busy period and also the distribution of the number served during it, given an arbitrary number of customers present originally. Using a direct approach all expressions are given in explicit forms which, although being far from elegant, are suitable for evaluation on a computer.

Keywords

GENERAL BIRTH-AND-DEATH QUEUEING MODELSTATE-DEPENDENTWAITING TIMEBUSY PERIODDIRECT METHODEXPLICIT RESULTS
Type
Research Papers
Information
Journal of Applied Probability , Volume 12 , Issue 3 , September 1975 , pp. 524 - 532
Copyright
Copyright © Applied Probability Trust 1975 

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