Journal ArticleDOI
Proof of a fundamental result in self-similar traffic modeling
Murad S. Taqqu,Walter Willinger,Robert Sherman +2 more
- Vol. 27, Iss: 2, pp 5-23
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TLDR
The superposition of many ON/OFF sources with strictly alternating ON- and OFF-periods can produce aggregate network traffic that exhibits the Joseph Effect, and 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.Abstract:
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 Levy 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.read more
Citations
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Journal ArticleDOI
Self-similarity through high-variability: statistical analysis of Ethernet LAN traffic at the source level
TL;DR: In this article, the authors provide a plausible physical explanation for the occurrence of self-similarity in local-area network (LAN) traffic, based on convergence results for processes that exhibit high variability and is supported by detailed statistical analyzes of real-time traffic measurements from Ethernet LANs at the level of individual sources.
Journal ArticleDOI
Long memory and regime switching
Francis X. Diebold,Atsushi Inoue +1 more
TL;DR: The authors show that regime switching is easily confused with long memory, even asymptotically, so long as only a small amount of regime switching occurs, in a sense that they make precise.
Posted Content
Long Memory and Regime Switching
TL;DR: The authors show that regime switching is easily confused with long memory, even asymptotically, so long as only a small' amount of regime switching occurs, in a sense that they make precise.
Proceedings ArticleDOI
Self-similarity through high-variability: statistical analysis of ethernet LAN traffic at the source level
TL;DR: This paper provides a plausible physical explanation for the occurrence of self-similarity in high-speed network traffic based on convergence results for processes that exhibit high variability and is supported by detailed statistical analyses of real-time traffic measurements from Ethernet LAN's at the level of individual sources.
References
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Journal ArticleDOI
An Introduction to Probability Theory and Its Applications
David A. Freedman,William Feller +1 more
Book
Convergence of Probability Measures
TL;DR: Weak Convergence in Metric Spaces as discussed by the authors is one of the most common modes of convergence in metric spaces, and it can be seen as a form of weak convergence in metric space.
Journal ArticleDOI
An Introduction to Probability Theory and Its Applications.
Journal ArticleDOI
On the self-similar nature of Ethernet traffic (extended version)
TL;DR: It is demonstrated that Ethernet LAN traffic is statistically self-similar, that none of the commonly used traffic models is able to capture this fractal-like behavior, and that such behavior has serious implications for the design, control, and analysis of high-speed, cell-based networks.