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The queue with impatience: construction of the stationary workload under FIFO

Part of: Special processes Limit theorems Probability theory on algebraic and topological structures

Published online by Cambridge University Press:  14 July 2016

Pascal Moyal
Pascal Moyal*
Affiliation:
Université de Technologie de Compiègne
*
∗Postal address: Laboratoire de Mathématiques Appliquées de Compiègne, Université de Technologie de Compiègne, Département Génie Informatique, Centre de Recherches de Royallieu, BP 20 529, 60 205 Compiegne Cedex, France. Email address: pascal.moyal@utc.fr
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Abstract

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In this paper we study the stability of queueing systems with impatient customers and a single server operating under a FIFO (first-in-first-out) discipline. We first give a sufficient condition for the existence of a stationary workload in the case of impatience until the beginning of service. We then provide a weaker condition of existence on an enriched probability space using the theory of Anantharam et al. (1997), (1999). The case of impatience until the end of service is also investigated.

Keywords

Stochastic recursionstationary solutionqueues with impatiencerenovative eventenrichment of probability space

MSC classification

Secondary: 60F17: Functional limit theorems; invariance principles 60K25: Queueing theory 60B12: Limit theorems for vector-valued random variables (infinite-dimensional case)
Type
Research Article
Information
Journal of Applied Probability , Volume 47 , Issue 2 , June 2010 , pp. 498 - 512
Copyright
Copyright © Applied Probability Trust 2010 

References

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