Performance Evaluation 58 (2004) 261–284 Variable heavy tails in Internet traffic F´ elix Hern´ andez-Campos a, ∗ , J.S. Marron b,c , Gennady Samorodnitsky d , F.D. Smith a a Department of Computer Science, University of North Carolina at Chapel Hill, NC 27599-3175, USA b Department of Statistics, University of North Carolina at Chapel Hill, NC 27599-3260, USA c Department of Statistical Science, Cornell University, Ithaca, NY 14853, USA d School of Operations Research and Industrial Engineering, Cornell University, Ithaca, NY 14853, USA Available online 11 September 2004 Abstract This paper studies tails of the size distribution of Internet data flows and their “heaviness”. Data analysis motivates the concepts of moderate, far and extreme tails for understanding the richness of information available in the data. The data analysis also motivates a notion of “variable tail index”, which leads to a generalization of existing theory for heavy-tail durations leading to long-range dependence. © 2004 Elsevier B.V. All rights reserved. Keywords: Heavy-tailed distributions; Long-range dependence; Extreme value theory; World Wide Web 1. Introduction Mathematical and simulation modelling of Internet traffic, even at a single location, has proven to be a surprisingly complex task and has been surrounded by substantial controversy. A simple view of Internet traffic on any given link is that it is an aggregation of flows where each flow is a set of packets with the same source and destination Internet Protocol (IP) addresses. The first models for aggregated Internet traffic were based on standard queueing theory ideas, using the exponential distribution to model flow durations. These models have the advantage of being tractable ∗ Corresponding author. E-mail addresses: fhernand@cs.unc.edu (F. Hern´ andez-Campos), marron@stat.unc.edu (J.S. Marron), gennady@orie.cornell.edu (G. Samorodnitsky), smithfd@cs.unc.edu (F.D. Smith) 0166-5316/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.peva.2004.07.008