Stability and nonproduct form of stochastic fluid networks with Lévy inputs

Offer Kella*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

31 Scopus citations


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.

Original languageAmerican English
Pages (from-to)186-199
Number of pages14
JournalAnnals of Applied Probability
Issue number1
StatePublished - Feb 1996


  • Lévy process
  • Nonproduct form
  • Reflected process
  • Stability
  • Stochastic fluid networks
  • Tandem networks


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