The Annals of Applied Probability

Self-similar communication models and very heavy tails

Sidney Resnick and Holger Rootzén

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Several studies of file sizes either being downloaded or stored in the World Wide Web have commented that tails can be so heavy that not only are variances infinite, but so are means. Motivated by this fact, we study the infinite node Poisson model under the assumption that transmission times are heavy tailed with infinite mean. The model is unstable but we are able to provide growth rates. Self-similar but nonstationary Gaussian process approximations are provided for the number of active sources, cumulative input, buffer content and time to buffer overflow.

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Ann. Appl. Probab., Volume 10, Number 3 (2000), 753-778.

First available in Project Euclid: 22 April 2002

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Zentralblatt MATH identifier

Primary: 60K25: Queueing theory [See also 68M20, 90B22]
Secondary: 60F05: Central limit and other weak theorems 60F10: Large deviations 60F17: Functional limit theorems; invariance principles 60G18: Self-similar processes 60G55: Point processes

Heavy tails regular variation Pareto tails self-similarity scaling data communication traffic modeling infinite source Poisson connections


Resnick, Sidney; Rootzén, Holger. Self-similar communication models and very heavy tails. Ann. Appl. Probab. 10 (2000), no. 3, 753--778. doi:10.1214/aoap/1019487509.

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