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

Offer Kella

doi:10.1239/jap/1014843090

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

Offer Kella^*

^*Corresponding author for this work

Department of Statistics

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

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.

Original language	English
Pages (from-to)	1117-1122
Number of pages	6
Journal	Journal of Applied Probability
Volume	37
Issue number	4
DOIs	https://doi.org/10.1239/jap/1014843090 https://doi.org/10.1017/S0021900200018295
State	Published - 1 Jan 2000

Keywords

Lévy process
Non-product form
Reflected process
Stochastic fluid networks

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abstract = "We show that the stationary distribution of a two-dimensional stochastic fluid network with (possibly dependent) L{\'e}vy 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.",

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AB - 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.

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

Abstract

Keywords

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