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November 2003 Limits of on/off hierarchical product models for data transmission
Sidney Resnick, Gennady Samorodnitsky
Ann. Appl. Probab. 13(4): 1355-1398 (November 2003). DOI: 10.1214/aoap/1069786502


A hierarchical product model seeks to model network traffic as a product of independent on/off processes. Previous studies have assumed a Markovian structure for component processes amounting to assuming that exponential distributions govern on and off periods, but this is not in good agreement with traffic measurements. However, if the number of factor processes grows and input rates are stabilized by allowing the on period distribution to change suitably, a limiting on/off process can be obtained which has exponentially distributed on periods and whose off periods are equal in distribution to the busy period of an $M/G/\infty$ queue. We give a fairly complete study of the possible limits of the product process as the number of factors grows and offer various characterizations of the approximating processes. We also study the dependence structure of the approximations.


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Sidney Resnick. Gennady Samorodnitsky. "Limits of on/off hierarchical product models for data transmission." Ann. Appl. Probab. 13 (4) 1355 - 1398, November 2003.


Published: November 2003
First available in Project Euclid: 25 November 2003

zbMATH: 1042.90004
MathSciNet: MR2023880
Digital Object Identifier: 10.1214/aoap/1069786502

Primary: 90B15
Secondary: 60K25

Keywords: $M/G/\infty$ queue , Fluid queue , heavy tales , Infinite divisibility , long-range dependence , product models , Renewal theorems , steady state distribution

Rights: Copyright © 2003 Institute of Mathematical Statistics


Vol.13 • No. 4 • November 2003
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