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Single-server queues with impatient customers

Published online by Cambridge University Press:  01 July 2016

F. Baccelli ,
P. Boyer  and
G. Hebuterne
F. Baccelli*
Affiliation:
INRIA
P. Boyer*
Affiliation:
CNET
G. Hebuterne*
Affiliation:
CNET
*
∗Postal address: INRIA, Domaine de Voluceau, Rocquencourt, BP 105, 78153 Le Chesnay Cedex, France.
∗∗ Postal address: CNET, LAA-SLC-EVP, Route de Tregastel, 22301 Lannion A, France.
∗∗ Postal address: CNET, LAA-SLC-EVP, Route de Tregastel, 22301 Lannion A, France.
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Abstract

We consider a single-server queueing system in which a customer gives up whenever his waiting time is larger than a random threshold, his patience time. In the case of a GI/GI/1 queue with i.i.d. patience times, we establish the extensions of the classical GI/GI/1 formulae concerning the stability condition and the relation between actual and virtual waiting-time distribution functions. We also prove that these last two distribution functions coincide in the case of a Poisson input process and determine their common law.

Keywords

QUEUEING THEORYLIMITED WAITING TIMESERGODIC MARKOV CHAINACTUAL WAITING TIMESVIRTUAL WAITING TIMESREGENERATIVE PROCESSESINVARIANT MEASUREFUNCTIONAL EQUATION
Type
Research Article
Information
Advances in Applied Probability , Volume 16 , Issue 4 , December 1984 , pp. 887 - 905
Copyright
Copyright © Applied Probability Trust 1984 

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