Advances in Applied Probability

A fluid cluster Poisson input process can look like a fractional Brownian motion even in the slow growth aggregation regime

Vicky Fasen and Gennady Samorodnitsky

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We show that, contrary to common wisdom, the cumulative input process in a fluid queue with cluster Poisson arrivals can converge, in the slow growth regime, to a fractional Brownian motion, and not to a Lévy stable motion. This emphasizes the lack of robustness of Lévy stable motions as `birds-eye' descriptions of the traffic in communication networks.

Article information

Adv. in Appl. Probab. Volume 41, Number 2 (2009), 393-427.

First available in Project Euclid: 6 July 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 90B22: Queues and service [See also 60K25, 68M20]
Secondary: 60F17: Functional limit theorems; invariance principles

Cluster Poisson process fluid queue fractional Brownian motion input model slow growth regime scaling limit workload process


Fasen, Vicky; Samorodnitsky, Gennady. A fluid cluster Poisson input process can look like a fractional Brownian motion even in the slow growth aggregation regime. Adv. in Appl. Probab. 41 (2009), no. 2, 393--427. doi:10.1239/aap/1246886617.

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