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On a single server queue with negative arrivals and request repeated

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

J. R. Artalejo  and
A. Gomez-Corral
J. R. Artalejo*
Affiliation:
Universidad Complutense de Madrid
A. Gomez-Corral*
Affiliation:
Universidad Complutense de Madrid
*
∗Postal address: Departamento de Estadística e I.O., Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, 28040 Madrid, Spain.
∗Postal address: Departamento de Estadística e I.O., Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, 28040 Madrid, Spain.
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Abstract

There is a growing interest in queueing systems with negative arrivals; i.e. where the arrival of a negative customer has the effect of deleting some customer in the queue. Recently, Harrison and Pitel (1996) investigated the queue length distribution of a single server queue of type M/G/1 with negative arrivals. In this paper we extend the analysis to the context of queueing systems with request repeated. We show that the limiting distribution of the system state can still be reduced to a Fredholm integral equation. We solve such an equation numerically by introducing an auxiliary ‘truncated’ system which can easily be evaluated with the help of a regenerative approach.

Keywords

Queueing theorynegative arrivalslinear request repeatedFredholm integral equationstable recursion schemes

MSC classification

Primary: 60K25: Queueing theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 36 , Issue 3 , September 1999 , pp. 907 - 918
Copyright
Copyright © Applied Probability Trust 1999 

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