A Bibliographical Guide to Self-Similar Traffic and Performance Modeling for Modern High-Speed Netwo

This paper provides a bibliographical guide to researchers and traac engineers who are interested in self-similar traac modeling and analysis. It lists some of the most recent network traac studies and includes surveys and research papers in the areas of data analysis, statistical inference, mathematical modeling, queueing and performance analysis. It also contains references to other areas of applications (e.g., hydrology, economics, geophysics, biology and biophysics) where similar developments have taken place and where numerous results have been obtained that can often be directly applied in the network traac context. Heavy tailed distributions, their relation to self-similar modeling, and corresponding estimation techniques are also covered in this guide. A fundamental feature of self-similar or fractal phenomena is that they encompass a wide range of time scales. In the teletraac literature, the notion of burstiness is often used in this context. Mathematical models that attempt to capture and describe self-similar, fractal, or bursty phenomena in a parsimonious manner include certain self-similar stochastic processes and appropriately chosen dynamical systems. A common characteristic of these models is that their space-time dynamics is governed parsimoniously by power-law distribution functions (the "Noah EEect") and hyperbolically decaying autocorrelations(the "Joseph EEect"). In sharp contrast, traditional approaches to modeling frac-tal phenomena typically rely on highly parameterized multilevel hierarchies of conventional models which, in turn, are characterized by distribution and auto-correlation functions that decay exponentially fast. 1 2 Willinger, Taqqu and Erramilli Although bursty or fractal phenomena have been observed in virtually all branches of science and engineering, and fractal models have been applied with with some success in areas, such as hydrology, nancial economics, and bio-physics, they are new to teletraac theory and represent a recent addition to the already large class of alternative models for describing traac in packet switched networks. While most applications of fractal models in science and engineering have been based on empirical ndings, they have almost exclusively focused on the models' powerful descriptive capabilities; their engineering implications and analyses have been largely ignored, mainly because fractal models are generally viewed to be very diicult to analyze. In contrast, the success of fractal models in teletraac theory will only partly depend on how well they describe actual network traac, but will also depend to a large degree on the ability to use these models in network analysis and control. To this end, this bibliographical guide brings together many of the references that (i) report …