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Parallel fluid queues with constant inflows and simultaneous random reductions

Part of: Special processes Operations research and management science

Published online by Cambridge University Press:  14 July 2016

Offer Kella  and
Masakiyo Miyazawa
Offer Kella*
Affiliation:
The Hebrew University of Jerusalem
Masakiyo Miyazawa*
Affiliation:
Science University of Tokyo
*
∗ Postal address: Department of Statistics, The Hebrew University of Jerusalem, Mount Scopus, Jerusalem 91905, Israel.
∗∗ Postal address: Department of Information Sciences, Science University of Tokyo, Noda-City, Chiba 278-8510, Japan. Email address: miyazawa@is.noda.sut.ac.jp
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Abstract

We consider I fluid queues in parallel. Each fluid queue has a deterministic inflow with a constant rate. At a random instant subject to a Poisson process, random amounts of fluids are simultaneously reduced. The requested amounts for the reduction are subject to a general I-dimensional distribution. The queues with inventories that are smaller than the requests are emptied. Stochastic upper bounds are considered for the stationary distribution of the joint buffer contents. Our major interest is in finding exponential product-form bounds, which turn out to have the appropriate decay rates with respect to certain linear combinations of buffer contents.

Keywords

Parallel fluid queuesmultidimensional stationary distributionstochastic upper boundexponential product formdecay rate

MSC classification

Primary: 60K25: Queueing theory
Secondary: 90B15: Network models, stochastic
Type
Research Papers
Information
Journal of Applied Probability , Volume 38 , Issue 3 , September 2001 , pp. 609 - 620
Copyright
Copyright © by the Applied Probability Trust 2001 

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