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February 1996 Stability and nonproduct form of stochastic fluid networks with Lévy inputs
Offer Kella
Ann. Appl. Probab. 6(1): 186-199 (February 1996). DOI: 10.1214/aoap/1034968070

Abstract

We consider a stochastic fluid network with inputs which are independent subordinators. We show that under some natural conditions the distribution of the fluid content process converges in total variation to a proper limit and that the limiting distribution has a positive mass at the origin. As a consequence of the methodology used, we obtain upper and lower bounds for the expected values of this limiting distribution. For the two-dimensional case, under certain conditions, explicit formulas for the means, variances and covariance of the steady-state fluid content are given. Further, for the two-dimensional case, it is shown that, other than for trivial setups, the limiting distribution cannot have product form.

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Offer Kella. "Stability and nonproduct form of stochastic fluid networks with Lévy inputs." Ann. Appl. Probab. 6 (1) 186 - 199, February 1996. https://doi.org/10.1214/aoap/1034968070

Information

Published: February 1996
First available in Project Euclid: 18 October 2002

zbMATH: 0863.60070
MathSciNet: MR1389836
Digital Object Identifier: 10.1214/aoap/1034968070

Subjects:
Primary: 60J30
Secondary: 60K30 , 90B05 , 90B15

Keywords: Lévy process , nonproduct form , reflected process , stability , Stochastic fluid networks , tandem networks

Rights: Copyright © 1996 Institute of Mathematical Statistics

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Vol.6 • No. 1 • February 1996
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