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Proof of a fundamental result in self-similar traffic modeling

Taqqu, Murad S. and Willinger, Walter and Sherman, Robert (1997) Proof of a fundamental result in self-similar traffic modeling. ACM SIGCOMM Computer Communication Review, 27 (2). pp. 5-23. ISSN 0146-4833. doi:10.1145/263876.263879.

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We state and prove the following key mathematical result in self-similar traffic modeling: the superposition of many ON/OFF sources (also known as packet trains) with strictly alternating ON- and OFF-periods and whose ON-periods or OFF-periods exhibit the Noah Effect (i.e., have high variability or infinite variance) can produce aggregate network traffic that exhibits the Joseph Effect (i.e., is self-similar or long-range dependent). There is, moreover, a simple relation between the parameters describing the intensities of the Noah Effect (high variability) and the Joseph Effect (self-similarity). This provides a simple physical explanation for the presence of self-similar traffic patterns in modern high-speed network traffic that is consistent with traffic measurements at the source level. We illustrate how this mathematical result can be combined with modern high-performance computing capabilities to yield a simple and efficient linear-time algorithm for generating self-similar traffic traces.We also show how to obtain in the limit a Lévy stable motion, that is, a process with stationary and independent increments but with infinite variance marginals. While we have presently no empirical evidence that such a limit is consistent with measured network traffic, the result might prove relevant for some future networking scenarios.

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Additional Information:© 1997 ACM. M. S. Taqqu and W. Willinger were partially supported by the NSF grant NCR-9404931. M. S. Taqqu was also partially supported by the NSF grant DMS-9404093. Part of this research was done when M. S. Taqqu was visiting Academia Sinica in Taipei. He would like to thank the Institute of Statistical Science and Dr. Hwai-Chung Ho for their hospitality. This extended version of our ACM SIGCOMM'95 paper [21] has benefited from many helpful and specific suggestions by Vern Paxson and discussions with Joe Abate and Ward Whitt concerning the inversion problem of Laplace transforms.
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Official Citation:Murad S. Taqqu, Walter Willinger, and Robert Sherman. 1997. Proof of a fundamental result in self-similar traffic modeling. SIGCOMM Comput. Commun. Rev. 27, 2 (April 1997), 5-23. DOI=
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:73035
Deposited On:21 Dec 2016 18:25
Last Modified:11 Nov 2021 05:10

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