Journal of Applied Probability

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

Offer Kella

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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.

Article information

J. Appl. Probab. Volume 37, Number 4 (2000), 1117-1122.

First available in Project Euclid: 27 February 2002

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G51: Processes with independent increments; Lévy processes
Secondary: 60K30: Applications (congestion, allocation, storage, traffic, etc.) [See also 90Bxx] 90B05: Inventory, storage, reservoirs 90B15: Network models, stochastic

Stochastic fluid networks Lévy process reflected process non-product form


Kella, Offer. Non-product form of two-dimensional fluid networks with dependent Lévy inputs. J. Appl. Probab. 37 (2000), no. 4, 1117--1122. doi:10.1239/jap/1014843090.

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