Self-similarity through high-variability: Statistical analysis of ethernet LAN traffic at the source level

A number of recent empirical studies of traffic measurements from a variety of working packet networks have 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 local-area network (LAN) traffic, Our explanation is based on new convergence results for processes that exhibit high variability (i.e., infinite variance) and is supported by detailed statistical analyzes of real-time traffic measurements from Ethernet LAN's at the level of individual sources, This paper is an extended version of [52] and differs from it in significant ways, In particular, we develop here the mathematical results concerning the superposition of strictly alternating ON/OFF sources. Our key mathematical result states that the superposition of many ON/OFF sources (also known as packet-trains) with strictly alternating ON- and OFF-periods and whose ON-periods or OFF-periods exhibit the Noah Effect (i.e., have high variability or infinite variance) produces aggregate network traffic that exhibits 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 high time-resolution Ethernet LAN traffic traces (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 patterns in modern high-speed network traffic for 1) parsimonious traffic modeling, 2) efficient synthetic generation of realistic traffic patterns, and 3) relevant network performance and protocol analysis.