On a Class of Lévy Stochastic Networks |
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Authors: | Konstantopoulos Takis Last Günter Lin Si-Jian |
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Institution: | 1.Department of Mathematics, University of Patras, 26500, Patras, Greece ;2.Institut für Mathematische Stochastik, Universit?t Karlsruhe (TH), Englerstr. 2, 76128, Karlsruhe, Germany ;3.Axiowave Networks, 200 Nickerson Road, Marlborough, MA, 01752, USA ; |
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Abstract: | We consider a Lévy stochastic network as a regulated multidimensional Lévy process. The reflection direction is constant on each boundary of the positive orthant and the corresponding reflection matrix corresponds to a single-class network. We use the representation of the Lévy process and Itô's formula to arrive at some equations for the steady-state process; the latter is shown to exist, under natural stability conditions. We specialize first to the class of Lévy processes with non-negative jumps and then add the assumption of self-similarity. We show that the stationary distribution of the network corresponding the the latter process does not has product form (except in trivial cases). Finally, we derive asymptotic bounds for two-dimensional Lévy stochastic network. |
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