Quasi-Product Forms for Lévy-Driven Fluid Networks

Quasi-Product Forms for Lévy-Driven Fluid Networks

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Article ID: iaor200954129
Country: United States
Volume: 32
Issue: 3
Start Page Number: 629
End Page Number: 647
Publication Date: Aug 2007
Journal: Mathematics of Operations Research
Authors: , ,
Keywords: Levy-stable processes
Abstract:

We study stochastic tree fluid networks driven by a multidimensional Lévy process. We are interested in (the joint distribution of) the steady–state content in each of the buffers, the busy periods, and the idle periods. To investigate these fluid networks, we relate the above three quantities to fluctuations of the input Lévy process by solving a multidimensional Skorokhod reflection problem. This leads to the analysis of the distribution of the componentwise maximums, the corresponding epochs at which they are attained, and the beginning of the first last–passage excursion. Using the notion of splitting times, we are able to find their Laplace transforms. It turns out that, if the components of the Lévy process are “ordered,” the Laplace transform has a so–called quasi–product form.

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