Statistical Analysis of Ethernet LAN Traffic at the Source Level

A number of recent empirical studies of traf- fic measurements from a variety of working packet net- works have convincingly demonstrated that actual net- work traffic is self-.szmdar or long-range dependent in na- ture (i. e., bursty over a wide range of time scales) - in sharp contrast to commonly made traffic modeling as- sumptions. 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 con- vergence results for processes that exhibit hagh uariabihty (i.e., infinite variance) and is supported by detailed sta- tistical analyses of real-time traffic measurements from Ethernet LAN's at the level of individual sources. Our key mathematical result states that the superpo- sition of many ON/OFF sources (also known as packet trams) whose ON-periods and OFF-periods exhibit the Noah Effect (i. e., have high variability or infinite vari- ance) produces aggregate network traffic that features the Joseph E~ect (i.e., is self-similar or long-range de- pendent). There is, moreover, a simple relation be- tween 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 con- sistent with the Noah Effect. We also discuss implica- tions of this simple physical explanation for the presence of self-similar traffic patterns in modern high-speed net- work traffic for (i) parsimonious traffic modeling, (ii) effi- cient synthetic generation of realistic traffic patterns, and (iii) relevant network performance and protocol analysis.