Limit behavior of fluid queues and networks

Limit behavior of fluid queues and networks

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Article ID: iaor2008990
Country: United States
Volume: 53
Issue: 6
Start Page Number: 933
End Page Number: 945
Publication Date: Nov 2005
Journal: Operations Research
Authors: ,
Abstract:

A superposition of a large number of infinite source Poisson inputs or that of a large number of ON–OFF inputs with heavy tails can look like either a fractional Brownian motion or a stable Lévy motion, depending on the magnification at which we are looking at the input process. In this paper, we investigate what happens to a queue driven by such inputs. Under such conditions, we study the output of a single fluid server and the behavior of a fluid queueing network. For the network we obtain random field limits describing the activity at different stations. In general, both kinds of stations arise in the same network: the stations of the first kind experience loads driven by a fractional Brownian motion, while the stations of the second kind experience loads driven by a stable Lévy motion.

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