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Stability and nonproduct form of stochastic fluid networks with Lévy inputs. (English) Zbl 0863.60070
Summary: 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.

MSC:
60J99 Markov processes
90B05 Inventory, storage, reservoirs
90B15 Stochastic network models in operations research
60K30 Applications of queueing theory (congestion, allocation, storage, traffic, etc.)
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