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August 2000 Self-similar communication models and very heavy tails
Sidney Resnick, Holger Rootzén
Ann. Appl. Probab. 10(3): 753-778 (August 2000). DOI: 10.1214/aoap/1019487509


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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Sidney Resnick. Holger Rootzén. "Self-similar communication models and very heavy tails." Ann. Appl. Probab. 10 (3) 753 - 778, August 2000.


Published: August 2000
First available in Project Euclid: 22 April 2002

zbMATH: 1083.60521
MathSciNet: MR1789979
Digital Object Identifier: 10.1214/aoap/1019487509

Primary: 60K25
Secondary: 60F05 , 60F10 , 60F17 , 60G18 , 60G55

Keywords: data communication , heavy tails , infinite source , Pareto tails , Poisson connections , regular variation , scaling , self-similarity , traffic modeling

Rights: Copyright © 2000 Institute of Mathematical Statistics


Vol.10 • No. 3 • August 2000
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