The Annals of Applied Probability

Stability and nonproduct form of stochastic fluid networks with Lévy inputs

Offer Kella

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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.

Article information

Source
Ann. Appl. Probab. Volume 6, Number 1 (1996), 186-199.

Dates
First available: 18 October 2002

Permanent link to this document
http://projecteuclid.org/euclid.aoap/1034968070

Mathematical Reviews number (MathSciNet)
MR1389836

Digital Object Identifier
doi:10.1214/aoap/1034968070

Zentralblatt MATH identifier
0863.60070

Subjects
Primary: 60J30
Secondary: 60K30: Applications (congestion, allocation, storage, traffic, etc.) [See also 90Bxx] 90B05: Inventory, storage, reservoirs 90B15: Network models, stochastic

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

Citation

Kella, Offer. Stability and nonproduct form of stochastic fluid networks with Lévy inputs. The Annals of Applied Probability 6 (1996), no. 1, 186--199. doi:10.1214/aoap/1034968070. http://projecteuclid.org/euclid.aoap/1034968070.


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