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Murad S. Taqqu
Daniel V. Wilson
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.