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Recently the phenomenon of network traf®c self-similarity has received signi®cant attention in the networking community [10]. Asymptotic self-similarity refers to the condition in which a time series's autocorrelation function declines like a power law, leading to positive correlations among widely separated observations. Thus the fact that network traf®c often shows self-similarity means that it shows noticeable bursts at a wide range of time scalesÐtypically at least four or ®ve orders of magnitude. . | 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 3 SIMULATIONS WITH HEAVY-TAILED WORKLOADS Mark E. Crovella Department of Computer Science Boston University Boston MA 02215 Lester Lipsky Department of Computer Science and Engineering University of Connecticut Storrs CT 06268 INTRODUCTION Recently the phenomenon of network traffic self-similarity has received sign ificant attention in the networking community 10 . Asymptotic self-similarity refers to the condition in which a time series s autocorrelation function declines like a power law leading to positive correlations among widely separated observations. Thus the fact that network traffic often shows self-similarity means that it shows noticeable bursts at a wide range of time scales typically at least four or five orders of magnitude. A related observation is that file sizes in some systems have been shown to be well described using distributions that are heavy-tailed distributions whose tails follow a power law meaning that file sizes also often span many orders of magnitude 3 . Heavy-tailed distributions behave quite differently from the distributions more commonly used to describe characteristics of computing systems such as the normal distribution and the exponential distribution which have tails that decline exponentially or faster . In contrast because their tails decline relatively slowly the proabability of very large observations occurring when sampling random variables that follow heavy-tailed distributions is nonnegligible. In fact the distributions we discuss in this chapter have infinite variance reflecting the extremely high variability that they capture. 89 90 SIMULATIONS WITH HEAVY-TAILED WORKLOADS As a result designers of computing and telecommunication systems are increasingly interested in employing heavy-tailed distributions to generate workloads

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