Self-Similarity Through High-Variability: Statistical Analysis of Ethernet LAN Traffic at the Source Level

Walter Willinger
Murad S. Taqqu
Robert Sherman
Daniel V. Wilson


A number of recent empirical studies of traffic measurements from a variety of working packet networks has convincingly demonstrated that actual network traffic is self-similar or long-range dependent in nature (i.e., bursty over a wide range of time scales) -- in sharp contrast to commonly made traffic modeling assumptions. In this paper, we provide a plausible physical explanation for the occurrence of self-similarity in high-speed network traffic. Our explanation is based on convergence results for processes that exhibit high variability (i.e., infinite variance) and is supported by detailed statistical analyses of real-time traffic measurements from Ethernet LAN's at the level of individual sources.

Our key mathematical result states that the superposition of many on/off sources (also known as packet trains) whose on-periods and off-periods exhibit the Noah Effect (i.e., have high variability or infinite variance) produces aggregate network traffic that features 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). An extensive statistical analysis of two sets of high time-resolution traffic measurements from two Ethernet LAN's (involving a few hundred active source-destination pairs) confirms that the data at the level of individual sources or source-destination pairs are consistent with the Noah Effect. We also discuss implications of this simple physical explanation for the presence of self-similar traffic patternsin modern high-speed network traffic for (i) parsimonious traffic modeling, (ii) efficient synthetic generation of realistic traffic patterns, and (iii) relevant network performance and protocol analysis.