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PROCESSOR SHARING G-QUEUES WITH INERT CUSTOMERS AND CATASTROPHES: A MODEL FOR SERVER AGING AND REJUVENATION

Published online by Cambridge University Press:  24 April 2017

J.-M. Fourneau  and
Y. Ait El Majhoub
J.-M. Fourneau
Affiliation:
DAVID, UVSQ, Université Paris-Saclay, 45, Av. des États-Unis, 78035 Versailles, France E-mail: [email protected]
Y. Ait El Majhoub
Affiliation:
DAVID, UVSQ, Université Paris-Saclay, 45, Av. des États-Unis, 78035 Versailles, France
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Abstract

We consider open networks of queues with Processor-Sharing discipline and signals. The signals deletes all the customers present in the queues and vanish instantaneously. The customers may be usual customers or inert customers. Inert customers do not receive service but the servers still try to share the service capacity between all the customers (inert or usual). Thus a part of the service capacity is wasted. We prove that such a model has a product-form steady-state distribution when the signal arrival rates are positive.

Keywords

agingcatastrophesG-networks with customers and signalsinert customersproduct – form steady-state distributionrejuvenation
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 31 , Special Issue 4: G-Networks and their Applications , October 2017 , pp. 420 - 435
Copyright
Copyright © Cambridge University Press 2017 

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