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Stability of feed-forward fluid networks with Lévy input

Part of: Special processes Operations research and management science

Published online by Cambridge University Press:  14 July 2016

Haya Kaspi  and
Offer Kella
Haya Kaspi*
Affiliation:
Technion — Israel Institute of Technology
Offer Kella*
Affiliation:
The Hebrew University of Jerusalem
*
∗Postal address: Faculty of Industrial Engineering and Management, Technion — Israel Institute of Technology, Haifa 32000, Israel.
∗∗Postal address: Department of Statistics, The Hebrew University of Jerusalem, Mount Scopus, Jerusalem 91905, Israel.
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Abstract

We consider a stochastic fluid network with independent subordinator inputs to the various stations and deterministic internal flow which is of feed-forward type. We show that under suitable conditions the process of fluid contents in the station has a limiting distribution, where the limit holds in total variation and is independent of the initial condition. We also show that this limiting distribution is of product form only for trivial setups.

Keywords

FLUID NETWORKSSTORAGE MODELSSUBORDINATORLEVY PROCESS

MSC classification

Secondary: 60K30: Applications (congestion, allocation, storage, traffic, etc.) 90B05: Inventory, storage, reservoirs 90B15: Network models, stochastic
Type
Research Papers
Information
Journal of Applied Probability , Volume 33 , Issue 2 , September 1996 , pp. 513 - 522
Copyright
Copyright © Applied Probability Trust 1996 

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Footnotes

Supported in part by grant 92–00035 from the United States - Israel Binational Science Foundation.

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