This Article Full Text (PDF) References Alert me when this article is cited Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via Google Scholar Google Scholar Articles by D’Auria, B. Articles by Samorodnitsky, G. Search for Related Content

Limit Behavior of Fluid Queues and Networks

Dipartimento di Ingegneria dell’ Informazione e Matematica Applicata, University of Salerno, Via Ponte Don Melillo 84084, Fisciano (SA), Italy
School of Operations Research and Industrial Engineering, Cornell University, Ithaca, New York 14853
bdauria{at}unisa.it
dauria{at}diima.unisa.it
gennady{at}orie.cornell.edu

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.

Subject classifications: queue; queueing network; output process; heavy-tailed distribution; long-range dependence; fractional Brownian motion; stable Lévy process; weak convergence.
History: Received January 2004; revision received September 2004; accepted September 2004.