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High-quality traf®c measurements indicate that actual traf®c behavior over highspeed networks shows self-similar features. These include an analysis of hundreds of millions of observed packets on several Ethernet LANs [7, 8], and an analysis of a few million observed frame data by variable bit rate (VBR) video services [1]. In these studies, packet traf®c appears to be statistically self-similar [2, 11]. | 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 8 BOUNDS ON THE BUFFER OCCUPANCY PROBABILITY WITH SELF-SIMILAR INPUT TRAFFIC N. Likhanov Institute for Problems of Information Transmission Russian Academy of Science Moscow Russia INTRODUCTION High-quality traffic measurements indicate that actual traffic behavior over highspeed networks shows self-similar features. These include an analysis of hundreds of millions of observed packets on several Ethernet LANs 7 8 and an analysis of a few million observed frame data by variable bit rate VBR video services 1 . In these studies packet traffic appears to be statistically self-similar 2 11 . Self-similar traffic is characterized by burstiness across an extremely wide range of time scales 7 . This behavior of aggregate Ethernet traffic is very different from conventional traffic models . Poisson batch Poisson Markov modulated Poisson process 4 . A lot of studies have been made for the design control and performance of highspeed and cell-relay networks using traditional traffic models. It is likely that many of those results need major revision when self-similar traffic models are considered 18 . Self-similarity manifests itself in a variety of different ways a spectral density that diverges at the origin a nonsummable autocorrelation function indicating long-range dependence an index of dispersion of counts IDCs that increases monotonically with the sample time T and so on 7 . A key parameter characterizing selfsimilar processes is the so-called Hurst parameter H which is designed to capture the degree of self-similarity. 193 194 BOUNDS ON THE BUFFER OCCUPANCY PROBABILITY Self-similar process models can be derived in different ways. One way is to construct the self-similar process as a sum of independent sources with a special form of the autocorrelation function. If we put