Limit Behavior of Fluid Queues and Networks

Bernardo D’Auria () and Gennady Samorodnitsky ()
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Bernardo D’Auria: Dipartimento di Ingegneria dell’ Informazione e Matematica Applicata, University of Salerno, Via Ponte Don Melillo 84084, Fisciano (SA), Italy
Gennady Samorodnitsky: School of Operations Research and Industrial Engineering, Cornell University, Ithaca, New York 14853

Operations Research, 2005, vol. 53, issue 6, 933-945

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 (Mikosch et al. 2002). 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.

Keywords: queue; queueing network; output process; heavy-tailed distribution; long-range dependence; fractional Brownian motion; stable Lévy process; weak convergence (search for similar items in EconPapers)
Date: 2005
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Citations: View citations in EconPapers (3)

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