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Response time distributions in tandem G-networks

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Peter G. Harrison  and
Edwige Pitel
Peter G. Harrison*
Affiliation:
Imperial College, London
Edwige Pitel*
Affiliation:
Imperial College, London
*
Postal address for both authors: Department of Computing, Imperial College, 180 Queen's Gate, London SW7 2BZ, UK.
Postal address for both authors: Department of Computing, Imperial College, 180 Queen's Gate, London SW7 2BZ, UK.
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Abstract

The Laplace transform of the probability distribution of the end-to-end delay in tandem networks is obtained where the first and/or second queue are G-queues, i.e. they have negative arrivals. For the most general case the method is based on the solution of a boundary value problem on a closed contour in the complex plane, which itself reduces to the solution of a Fredholm integral equation of the second kind. We also consider the dependence or independence of the sojourn times at each queue in the two special cases where only one of the queues is a G-queue, the other having no negative arrivals.

Keywords

NEGATIVE CUSTOMERSQUEUEING NETWORKSSOJOURN TIMESEND-TO-END DELAYBOUNDARY VALUE PROBLEMSFREDHOLM INTEGRAL EQUATION

MSC classification

Primary: 60K25: Queueing theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 32 , Issue 1 , March 1995 , pp. 224 - 246
Copyright
Copyright © Applied Probability Trust 1995 

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Footnotes

∗

Supported by the European Commission under ESPRIT BRA QMIPS n° 7269.

†

Supported by the European Commission under ESPRIT bursary n° ERBCHBICT920179.

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