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Non-product form of two-dimensional fluid networks with dependent Lévy inputs

Part of: Stochastic processes Operations research and management science Special processes

Published online by Cambridge University Press:  14 July 2016

Offer Kella
Offer Kella*
Affiliation:
The Hebrew University of Jerusalem
*
∗ Postal address: Department of Statistics, The Hebrew University of Jerusalem, Mount Scopus, Jerusalem 91905, Israel. Email address: mskella@mscc.huji.ac.il
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Abstract

We show that the stationary distribution of a two-dimensional stochastic fluid network with (possibly dependent) Lévy inputs does not have product form other than in truly obvious cases. This is in contrast to queueing networks, where product form exists for non-obvious situations in which the inputs are independent, and for Brownian networks, where it typically exists for cases where the driving processes are actually dependent.

Keywords

Stochastic fluid networksLévy processreflected processnon-product form

MSC classification

Primary: 60G51: Processes with independent increments; L'evy processes
Secondary: 60K30: Applications (congestion, allocation, storage, traffic, etc.) 90B05: Inventory, storage, reservoirs 90B15: Network models, stochastic
Type
Short Communications
Information
Journal of Applied Probability , Volume 37 , Issue 4 , December 2000 , pp. 1117 - 1122
Copyright
Copyright © by the Applied Probability Trust 2000 

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Footnotes

Supported in part by grant 794/97 from the Israel Science Foundation.

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