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dependence of mean queue length on self-similarity is consistent with previous works [2, 15, 16] showing that queue length distribution decays more slowly for long-range dependent (LRD) sources than for short-range dependent (SRD) sources. The aforementioned traf c-shaping effect of ow-controlled, reliable transport transforming a large le transfer into an on-average ``thin'' packet train (stretching-in-time effect) suggests, in part, why the on=off model has been so successful despite its limitations a principal effect of interaction among traf c sources in an internetworked environment lies in the generation of long packet trains wherein the correlation structure inherent in heavy-tailed le size distributions is suf ciently preserved. The rest of the chapter is organized as follows. In the next two sections, we discuss related work, the network model, and the simulation setup. This is followed by the main section, which explores the effect of le size distribution on traf c selfsimilarity, including the role of the protocol stack, heavy-tailed versus non-heavytailed interarrival time distribution, resource variations, and traf c mixing. We conclude with a discussion of the effect of traf c self-similarity from a performance evaluation perspective, showing its quantitative and qualitative effects with respect to performance measures when both the degree of self-similarity and network resources are varied.

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Since the seminal study of Leland et al. [14], which set the groundwork for considering self-similar network traf c as an important modeling and performance evaluation problem, a string of work has appeared dealing with various aspects of traf c self-similarity [1, 2, 7, 11, 12, 15, 16, 22, 28]. In measurement based work [7, 11, 12, 14, 22, 28], traf c traces from physical network measurements are employed to identify the presence of scale-invariant burstiness, and models are constructed capable of generating synthetic traf c with matching characteristics. These works show that long-range dependence is an ubiquitous phenomenon encompassing both local-area and wide-area network traf c. In the performance evaluation category are works that have evaluated the effect of self-similar traf c on idealized or simpi ed networks [1, 2, 15, 16]. They show that long-range dependent traf c is likely to degrade performance, and a principal result is the observation that queue length distribution under self-similar traf c decays much more slowly than with short-range-dependent sources (e.g., Poisson). We refer the reader to 1 for a comprehensive survey of related works. Our work is an extension of the line of research in the rst category, where we investigate causal mechanisms that may be at play in real networks responsible for generating the self-similarity phenomena observed in diverse networking contexts.

1 H-estimates and performance results when an open-loop ow control is active can be found in Park et al. [17].

... Preface -- 1 -- 2 -- 3 -- 4 -- 5 -- 6 -- 7 -- 8 -- 9 -- A -- B -- C -- Refs Front -- Contents -- Help

The relationship between le sizes and self-similar traf c was explored in Park et al. [18], and is also indicated by the work described in Crovella and Bestavros [7], which showed that self-similarity in World Wide Web traf c might arise due to the heavy-tailed distribution of le sizes present on the Web. An important question is whether le size distributions in practice are in fact typically heavy-tailed, and whether le size access patterns can be modeled as randomly sampling from such distributions. Previous measurement-based studies of le systems have recognized that le size distributions possess long tails, but they have not explicitly examined the tails for power-law behavior [4, 17, 23 25]. Crovella and Bestavros [7] showed that the size distribution of les found in the World Wide Web appears to be heavy-tailed with a approximately equal to 1, which stands in general agreement with measurements reported by Arlitt and Williamson [3]. Bodnarchuk and Bunt [6] show that the sizes of reads and writes to an NFS server appear to show power-law behavior. Paxson and Floyd [22] found that the upper tail of the distribution of data bytes in FTP bursts was well t to a Pareto distribution with 0:9 a 1:1. A general study of UNIX le systems has found distributions that appear to be approximately power law [13].

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14.3 14.3.1

Fig. 2.3 LRD and H-sssi behavior in Ethernet traf c data. Left: Logscale diagram for the discrete series of successive interarrival times, showing a range of alignments and an a estimate consistent with long-range dependence. Right: Logscale diagram for the cumulative work process (bytes up to time t), consistent with an asymptotically self-similar (close to exactly self-similar) process with stationary increments.

Copyright 1999 Gary McGraw and Edward Felten. All rights reserved. Published by John Wiley & Sons, Inc.

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