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In order to help design and control the emerging high-speed communication networks, we want source traf®c models (also called offered load models or bandwidth demand models) that can be both realistically ®t to data and successfully analyzed. Many recent traf®c measurements have shown that network traf®c is quite complex, exhibiting phenomena such as heavy-tailed probability distributions, longrange dependence, and self similarity; for example, see Caceres et al. [7], Leland  et al. [23], Paxson and Floyd [24], and Crovella and Bestavros [10]. In fact, the heavy-tailed distributions. | Self-Similar Network Traffic and Performance Evaluation Edited by Kihong Park and Walter Willinger Copyright 2000 by John Wiley Sons Inc. Print ISBN 0-471-31974-0 Electronic ISBN 0-471-20644-X 17 NETWORK DESIGN AND CONTROL USING ON OFF AND MULTILEVEL SOURCE TRAFFIC MODELS WITH HEAVY-TAILED DISTRIBUTIONS N. G. Duffield and W. Whitt AT T Labs-Research Florham Park NJ 07392 INTRODUCTION In order to help design and control the emerging high-speed communication networks we want source traffic models also called offered load models or bandwidth demand models that can be both realistically fit to data and successfully analyzed. Many recent traffic measurements have shown that network traffic is quite complex exhibiting phenomena such as heavy-tailed probability distributions long-range dependence and self similarity for example see Câceres et al. 7 Leland et al. 23 Paxson and Floyd 24 and Crovella and Bestavros 10 . In fact the heavy-tailed distributions may be the cause of all these phenomena because they tend to cause long-range dependence and asymptotic self-similarity. For example the input and buffer content processes associated with an on off source exhibit long-range dependence when the on and off times have heavy-tailed probability distributions for example see Section . Heavy-tailed distributions are known to cause self-similarity in models of asymptotically aggregated traffic see Willinger et al. 27 . In this chapter we propose a way to analyze the performance of a network with multiple on off sources and more general multilevel sources in which the on-time off-time and level-holding-time distributions are allowed to have heavy tails. To do 421 422 NETWORK DESIGN USING HEAVY-TAILED DISTRIBUTIONS so we must go be beyond the familiar Markovian analysis. To achieve the required analyzability with this added model complexity we propose a simplified kind of analysis. In particular we avoid the customary queueing detail and its focus on buffer content and .

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