Self - Similarity Through High - Variability :

| A number of recent empirical studies of traf-c measurements from a variety of working packet networks have convincingly demonstrated that actual network traac 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 traac modeling assumptions. In this paper, we provide a plausible physical explanation for the occurrence of self-similarity in high-speed network traac. Our explanation is based on convergence results for processes that exhibit high variability (i.e., innnite variance) and is supported by detailed statistical analyses of real-time traac 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 trains) whose ON-periods and OFF-periods exhibit the Noah EEect (i.e., have high variability or innnite variance) produces aggregate network traac that features the Joseph EEect (i.e., is self-similar or long-range dependent). There is, moreover, a simple relation between the parameters describing the intensities of the Noah EEect (high variability) and the Joseph EEect (self-similarity). An extensive statistical analysis of two sets of high time-resolution traac measurements from two Ethernet LAN's (involving a few hundred active source-destination pairs) connrms that the data at the level of individual sources or source-destination pairs are consistent with the Noah EEect. We also discuss implications of this simple physical explanation for the presence of self-similar traac patterns in modern high-speed network traac for (i) parsimonious traac modeling, (ii) ee-cient synthetic generation of realistic traac patterns, and (iii) relevant network performance and protocol analysis.