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Large teletraf®c data sets exhibiting nonstandard features incompatible with classical assumptions of short-range dependence and exponentially decreasing tails can now be explored, for instance, at the ITA Web site . These data sets exhibit the phenomena of heavy-tailed marginal distributions and long-range dependence. Tails can be so heavy that only in®nite variance models are possible (., see Willinger et al. [49]), and sometimes, as in ®le size data, even ®rst moments are in®nite [1]. | 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 7 FLUID QUEUES ON OFF PROCESSES AND TELETRAFFIC MODELING WITH HIGHLY VARIABLE AND CORRELATED INPUTS Sidney Resnick and Gennady Samorodnitsky Cornell University School of Operations Research and Industrial Engineering Ithaca NY 14853 INTRODUCTION Large teletraffic data sets exhibiting nonstandard features incompatible with classical assumptions of short-range dependence and exponentially decreasing tails can now be explored for instance at the ITA Web site sigcomm ITA . These data sets exhibit the phenomena of heavy-tailed marginal distributions and long-range dependence. Tails can be so heavy that only infinite variance models are possible . see Willinger et al. 49 and sometimes as in file size data even first moments are infinite 1 . See also Beran et al. 3 Crovella and Bestavros 12-14 Leland et al. 33 Resnick 38 Taqqu et al. 48 and Willinger et al. 49 . Other areas where heavy tails and long-range dependence are crucial properties are finance insurance and hydrology 4-7 16 17 24-26 35 37 . New features in the teletraffic data discussed in recent studies suggest several issues for study and discussion. Statistical. How can statistical models be fit to such data Unite variance black box time series modeling has traditionally been dominated by ARMA or Box-Jenkins models. These models can be adapted to heavy-tailed data and work very well on simulated data. However for real nonsimulated data exhibiting 171 172 FLUID QUEUES ON OFF PROCESSES AND TELETRAFFIC MODELING dependencies such ARMA models provide unacceptable fits and do not capture the correct dependence structure. For discussion see Davis and Resnick 15 Resnick 38 39 Resnick et al. 42 and Resnick and van den Berg 43 . Probabilistic. What probability models explain observed features in the data such as

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