A Wavelet based tool for the analysis of long range dependence is introduced and a related semiparametric estimator of the Hurst parameter. The estimator is shown to be unbiased under very general conditions, and efficient under Gaussian assumptions. It can be implemented very efficiently allowing the direct analysis of very large data sets, and is highly robust against the presence of deterministic trends, as well as allowing their detection and identification. Statistical, computational and numerical comparisons are made against traditional estimators including that of Whittle. The estimator is used to perform a thorough analysis of the long range dependence in Ethernet traffic traces. New features are found with important implications for the choice of valid models for performance evaluation. A study of mono vs multi-fractality is also performed, and a preliminary study of the stationarity with respect to the Hurst parameter and deterministic trends.

This paper presents a personal view of work to date on effective bandwidths, emphasising the unifying role of the concept: as a summary of the statistical characteristics of sources over different time and space scales; in bounds, limits and approximations for various models of multiplexing under quality of service constraints; and as the basis for simple and robust tariffing and connection acceptance control mechanisms for poorly characterized traffic. The framework assumes only stationarity of sources, and illustrative examples include periodic streams, fractional Brownian input, policed and shaped sources, and deterministic multiplexing.

There has been a growing concern about the potential impact of long-term correlations (second-order statistic) in variable-bit-rate (VBR) video traffic on ATM buffer dimensioning. Previous studies have shown that video traffic exhibits long-range dependence (LRD) (Hurst parameter large than 0.5). We investigate the practical implications of LRD in the context of realistic ATM traffic engineering by studying ATM multiplexers of VBR video sources over a range of desirable cell loss rates and buffer sizes (maximum delays). Using results based on large deviations theory, we introduce the notion of Critical Time Scale (CTS). For a given buffer size, link capacity, and the marginal distribution of frame size, the CTS of a VBR video source is defined as the number of frame correlations that contribute to the cell loss rate. In other words, second-order behavior at the time scale beyond the CTS does not significantly affect the network performance. We show that whether the video source model i...

A wavelet-based tool for the analysis of long-range dependence and a related semi-parametric estimator of the Hurst parameter is introduced. The estimator is shown to be unbiased under very general conditions, and efficient under Gaussian assumptions. It can be implemented very efficiently allowing the direct analysis of very large data sets, and is highly robust against the presence of deterministic trends, as well as allowing their detection and identification. Statistical, computational, and numerical comparisons are made against traditional estimators including that of Whittle. The estimator is used to perform a thorough analysis of the long-range dependence in Ethernet traffic traces. New features are found with important implications for the choice of valid models for performance evaluation. A study of mono versus multifractality is also performed, and a preliminary study of the stationarity with respect to the Hurst parameter and deterministic trends.

Over the last few years, a substantial number of call admission control (CAC) schemes have been proposed for ATM networks. In this article, we review the salient features of some of these algorithms. Also, we quantitatively compare the performance of three of these schemes.

Since the identification of long-range dependence in network traffic ten years ago, its consistent appearance across numerous measurement studies has largely discredited Poissonbased models. However, since that original data set was collected, both link speeds and the number of Internet-connected hosts have increased by more than three orders of magnitude. Thus, we now revisit the Poisson assumption, by studying a combination of historical traces and new measurements obtained from a major backbone link belonging to a Tier 1 ISP. We show that unlike the older data sets, current network traffic can be well represented by the Poisson model for sub-second time scales. At multi-second scales, we find a distinctive piecewise-linear non-stationarity, together with evidence of long-range dependence. Combining our observations across both time scales leads to a time-dependent Poisson characterization of network traffic that, when viewed across very long time scales, exhibits the observed long-range dependence. This traffic characterization reconciliates the seemingly contradicting observations of Poisson and long-memory traffic characteristics. It also seems to be in general agreement with recent theoretical models for large-scale traffic aggregation.

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Self-similar processes based on fractal point processes (FPPs) provide natural and attractive network tra#c models. We show that the point process formulation yields a wide range of FPPs which in turn yield a diversity of parsimonious, computationally e#cient, and highly practical asymptotic second-order self-similar processes. Using this framework, we show that the relevant second-order fractal characteristics such as long-range dependence (LRD), slowly-decaying variance, and 1/f noise are completely characterized by three fundamental quantities: mean arrival rate, Hurst parameter, and fractal onset time. Four models are proposed, and the relationship between their model parameters and the three fundamental quantities are analyzed. By successfully applying the proposed models to Bellcore's Ethernet traces, we show that the FPP models prove useful in evaluating and predicting the queueing performance of various types of fractal tra#c sources. Keywords: point process, fractal, self-similarity, long-range dependence, tra#c modeling 1 Throughout this paper, self-similarity refers to asymptotic second-order self-similarity [4], [13] unless otherwise defined. 1

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This paper studies the effective bandwidth required when multiple self-similar (i.e., long range dependent) traffic sources are multiplexed together in a network. In particular, an ATM network simulation tool is used to assess the accuracy of a theoretical effective bandwidth formula developed by Ilkka Norros for self-similar traffic. Synthetic traffic models with controllable workload parameters are used in the study, using a one-factor-at-a-time experimental design. In general, the simulation results show good qualitative and quantitative agreement between the effective bandwidths predicted by the formula and by the ATM network simulator, provided that the number of multiplexed sources and the switch buffer size are not too small. Where the results are in good agreement, the formula tends to err on the "safe side", thus making the theoretical formula useful for call admission control and network dimensioning in an ATM network. Keywords: Computer networks, telecommunication systems, ...