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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

Information

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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