THE SCALING PHENOMENA Scaling Issues in Traf®c The presence of scaling behavior in telecommunications traf®c is striking not only in its ubiquity, appearing in almost every kind of packet data, but also in the wide range of scales over which the scaling holds (., see Beran et al. [18], Leland et al. [43], and Willinger et al. [78]). It is rare indeed that a physical phenomenon obeys a consistent law over so | 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 2 WAVELETS FOR THE ANALYSIS ESTIMATION AND SYNTHESIS OF SCALING DATA P. Abry and P. Flandrin CNRS UMR 5672 Ecole Normale Supérieure de Lyon Laboratoire de Physique 69 364 Lyon Cedex 07 France M. S. Taqqu Department of Mathematics Boston University Boston MA 02215-2411 D. Veitch Software Engineering Research Centre Carlton Victoria 3053 Australia THE SCALING PHENOMENA Scaling Issues in Traffic The presence of scaling behavior in telecommunications traffic is striking not only in its ubiquity appearing in almost every kind of packet data but also in the wide range of scales over which the scaling holds . see Beran et al. 18 Leland et al. 43 and Willinger et al. 78 . It is rare indeed that a physical phenomenon obeys a consistent law over so many orders of magnitude. This may well extend further as increases in network bandwidth over time progressively reveal higher scales. While the presence of scaling is now well established its impact on teletraffic issues and network performance is still the subject of some confusion and uncertainty. Why is scaling in traffic important for networking It is clear as far as modeling of the traffic itself is concerned that a feature as prominent as scaling 39 40 WAVELETS FOR THE ANALYSIS ESTIMATION AND SYNTHESIS OF SCALING DATA should be built into models at a fundamental level if these are to be both accurate and parsimonious. Scaling therefore has immediate implications for the choice of classes of traffic models and consequently on the choice and subsequent estimation of model parameters. Such estimation is required for initial model verification for fitting purposes as well as for traffic monitoring. Traffic modeling however does not occur in isolation but in the context of performance issues. Depending on the performance .
