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Limit Behavior of Fluid Queues and Networks

Author

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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)

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.

Suggested Citation

  • Bernardo D’Auria & Gennady Samorodnitsky, 2005. "Limit Behavior of Fluid Queues and Networks," Operations Research, INFORMS, vol. 53(6), pages 933-945, December.
    • Handle: RePEc:inm:oropre:v:53:y:2005:i:6:p:933-945
    DOI: 10.1287/opre.1050.0215
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    References listed on IDEAS

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    1. David Heath & Sidney Resnick & Gennady Samorodnitsky, 1998. "Heavy Tails and Long Range Dependence in On/Off Processes and Associated Fluid Models," Mathematics of Operations Research, INFORMS, vol. 23(1), pages 145-165, February.
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    Cited by:

    1. Dejian Lai, 2010. "Group sequential tests under fractional Brownian motion in monitoring clinical trials," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 19(2), pages 277-286, June.
    2. Mihalis G. Markakis & Eytan Modiano & John N. Tsitsiklis, 2018. "Delay Analysis of the Max-Weight Policy Under Heavy-Tailed Traffic via Fluid Approximations," Mathematics of Operations Research, INFORMS, vol. 43(2), pages 460-493, May.
    3. Hongshuai Dai, 2022. "Tandem fluid queue with long-range dependent inputs: sticky behaviour and heavy traffic approximation," Queueing Systems: Theory and Applications, Springer, vol. 101(1), pages 165-196, June.

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