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Etude d'une file GI/G/1 à service autonome (avec vacances du serveur)

Published online by Cambridge University Press:  01 July 2016

C. Fricker
C. Fricker*
Affiliation:
Université Paris VI
*
∗Postal address: Université Paris VI, Laboratoire de Probabilités, 4 Place Jussieu—Tour 56, 75230 Paris Cedex 05, France.
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Abstract

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The purpose of this letter is to study a modified GI/G/1 queueing system in which the server becomes unavailable for (independent) random periods each time he is free. This problem was first studied by Gelenbe and Iasnogorodski [6] who obtained the stationary law of the waiting time of a customer. We construct a simple probabilistic model coupling a G//G/1 queue with an autonomous server (in Borovkov's terminology [1]) with a GI/G/1 queue of classical type having the same characteristics, to compare them stochastically. We prove that the waiting time is a Markov chain, using a renewal process property which has not previously been noted.

Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 18 , Issue 1 , March 1986 , pp. 283 - 286
Copyright
Copyright © Applied Probability Trust 1986 

References

Bibliographie

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