Statistical Science

Self-Similarity in High-Speed Packet Traffic: Analysis and Modeling of Ethernet Traffic Measurements

Walter Willinger, Murad S. Taqqu, Will E. Leland, and Daniel V. Wilson

Full-text: Open access

Abstract

Traffic modeling of today's communication networks is a prime example of the role statistical inference methods for stochastic processes play in such classical areas of applied probability as queueing theory or performance analysis. In practice, however, statistics and applied probability have failed to interface. As a result, traffic modeling and performance analysis rely heavily on subjective arguments; hence, debates concerning the validity of a proposed model and its predicted performance abound. In this paper, we show how a careful statistical analysis of large sets of actual traffic measurements can reveal new features of network traffic that have gone unnoticed by the literature and, yet, seem to have serious implications for predicted network performance. We use hundreds of millions of high-quality traffic measurements from an Ethernet local area network to demonstrate that Ethernet traffic is statistically self-similar and that this property clearly distinguishes between currently used models for packet traffic and our measured data. We also indicate how such a unique data set (in terms of size and quality) (i) can be used to illustrate a number of different statistical inference methods for self-similar processes, (ii) gives rise to new and challenging problems in statistics, statistical computing and probabilistic modeling and (iii) opens up new areas of mathematical research in queueing theory and performance analysis of future high-speed networks.

Article information

Source
Statist. Sci., Volume 10, Number 1 (1995), 67-85.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.ss/1177010131

Digital Object Identifier
doi:10.1214/ss/1177010131

Zentralblatt MATH identifier
1148.90310

JSTOR
links.jstor.org

Keywords
Self-similarity long-range dependence Hurst effect $R/S$ analysis variance-time analysis periodogram-based estimation traffic modeling for high-speed networks queueing theory

Citation

Willinger, Walter; Taqqu, Murad S.; Leland, Will E.; Wilson, Daniel V. Self-Similarity in High-Speed Packet Traffic: Analysis and Modeling of Ethernet Traffic Measurements. Statist. Sci. 10 (1995), no. 1, 67--85. doi:10.1214/ss/1177010131. https://projecteuclid.org/euclid.ss/1177010131


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