We present a detailed statistical analysis of a 2-hour long empirical sample of VBR video. The sample was obtained by applying a simple intraframe video compression code to an action movie. The main findings of our analysis are (1) the tail behavior of the marginal bandwidth distribution can be accurately described using "heavy-tailed" distributions (e.g., Pareto); (2) the autocorrelation of the VBR video sequence decays hyperbolically (equivalent to long-range dependence) and can be modeled using self-similar processes. We combine our findings in a new (non-Markovian) source model for VBR video and present an algorithm for generating synthetic traffic. Trace-driven simulations show that statistical multiplexing results in significant bandwidth efficiency even when long-range dependence is present. Simulations of our source model show long-range dependence and heavy-tailed marginals to be important components which are not accounted for in currently used VBR video traffic models. 1 I...

Many designs for integrated service networks offer a bounded delay packet delivery service to support real-time applications. To provide bounded delay service, networks must use admission control to regulate their load. Previous work on admission control mainly focused on algorithms that compute the worst case theoretical queueing delay to guarantee an absolute delay bound for all packets. In this paper we describe a measurement-based admission control algorithm for predictive service, which allows occasional delay violations. We have tested our algorithm through simulations on a wide variety of network topologies and driven with various source models, including some that exhibit long-range dependence, both in themselves and in their aggregation. Our simulation results suggest that, at least for the scenarios studied here, the measurement-based approach combined with the relaxed service commitment of predictive service enables us to achieve a high

Traffic models are at the heart of any performance evaluation of telecommunications networks. An accurate estimation of network performance is critical for the success of broadband networks. Such networks need to guarantee an acceptable quality of service (QoS) level to the users. Therefore, traffic models need to be accurate and able to capture the statistical characteristics of the actual traffic. In this article we survey and examine traffic models that are currently used in the literature. Traditional short-range and non-traditional long-range dependent traffic models are presented. Number of parameters needed, parameter estimation, analytical tractability, and ability of traffic models to capture marginal distribution and auto-correlation structure of actual traffic are discussed. n Figure 1. Finite state model for voice. This research was supported in part by the National Science Foundation under grant NCR-9396299. This article is based on Georgia Tech technical report G...

Traffic variables on an uncongested Internet wire exhibit a pervasive nonstationarity. As the rate of new TCP connections increases, arrival processes (packet and connection) tend locally toward Poisson, and time series variables (packet sizes, transferred file sizes, and connection round-trip times) tend locally toward independent. The cause of the nonstationarity is superposition: the intermingling of sequences of connections between different source-destination pairs, and the intermingling of sequences of packets from different connections. We show this empirically by extensive study of packet traces for nine links coming from four packet header databases. We show it theoretically by invoking the mathematical theory of point processes and time series. If the connection rate on a link gets sufficiently high, the variables can be quite close to Poisson and independent; if major congestion occurs on the wire before the rate gets sufficiently high, then the progression toward Poisson and independent can be arrested for some variables.

[1] The ‘‘hockey stick’ ’ shaped temperature reconstruction of Mann et al. (1998, 1999) has been widely applied. However it has not been previously noted in print that, prior to their principal components (PCs) analysis on tree ring networks, they carried out an unusual data transformation which strongly affects the resulting PCs. Their method, when tested on persistent red noise, nearly always produces a hockey stick shaped first principal component (PC1) and overstates the first eigenvalue. In the controversial 15th century period, the MBH98 method effectively selects only one species (bristlecone pine) into the critical North American PC1, making it implausible to describe it as the ‘‘dominant pattern of variance’’. Through Monte Carlo analysis, we show that MBH98 benchmarks for significance of the Reduction of Error (RE) statistic are substantially under-stated and, using a range of cross-validation statistics, we show that the MBH98 15th century reconstruction lacks statistical significance. Citation: McIntyre, S., and R. McKitrick (2005), Hockey sticks, principal components, and

This paper is a condensed introduction to self-similarity, self-similar processes, and the estimation of the Hurst parameter in the context of time series analysis. It gives an overview of the literature on this subject and provides some assistance in implementing Hurst parameter estimators and carrying out experiments with empirical time series. 1 Introduction The subject of self-similarity and the estimation of statistical parameters of time series in the presence of long-range dependence are becoming more and more common in several fields of science. Up to now there are only a few text books available, e.g. in [2], which give a comprehensive overview of the techniques and estimators. The intention of this paper is not to close this gap but to provide some basic information about self-similarity, self-similar processes, and estimators of the so-called Hurst parameter H. It gives a rather condensed introduction to self-similarity and contains a number of referenced papers which can ...

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Designing and planning networks is often done by simulating the inuence of various traffic types. This simulation approach depends on reliable and realistic traffic models that are capable of covering first- and second-order statistics of the observed network traffic. In this report, an overview over state-of-the-art models for the simulation of network traffic will be given.

We analyze 12 traces of round-trip Internet packet delay. We find that these traces, when viewed as time series data, often exhibit Hurst parameter (H) estimates greater than 0.5, indicating long-range dependence. Several traces, however, are not well-modeled with a constant H . We discuss in detail our analytical methods and the robustness of empirical estimators of H under conditions of non-negligible packet loss. Our results indicate that Internet delay is bursty across multiple time scales, which implies that end-user quality of service in the Internet is likely to be impacted by long periods of very large and/or highly variable delays. 1 Introduction It is now widely accepted that network traffic exhibits longrange dependence (LRD). While the practical implications of this discovery are not yet completely understood, it is known that traditional Poisson models of network traffic cannot capture the behavior of LRD traffic. Often LRD data is also selfsimilar, indicating that it pos...

Abstract—Statistically self-similar (SSS) processes can be used to describe a variety of physical phenomena, yet modeling these phenomena has proved challenging. Most of the proposed models for SSS and approximately SSS processes have power spectra that behave as 1=f, such as fractional Brownian motion (fBm), fractionally differenced noise, and wavelet-based syntheses. The most flexible framework is perhaps that based on wavelets, which provides a powerful tool for the synthesis and estimation of 1=f processes, but assumes a particular distribution of the measurements. An alternative framework is the class of multiresolution processes proposed by Chou et al. [1994], which has already been shown to be useful for the identification of the parameters of fBm. These multiresolution processes are defined by an autoregression in scale that makes them naturally suited to the representation of SSS (and approximately SSS) phenomena, both stationary and nonstationary. Also, this multiresolution framework is accompanied by an efficient estimator, likelihood calculator, and conditional simulator that make no assumptions about the distribution of the measurements. In this paper, we show how to use the multiscale framework to represent SSS (or approximately SSS) processes such as fBm and fractionally differenced Gaussian noise. The multiscale models are realized by using canonical correlations (CC) and by exploiting the selfsimilarity and possible stationarity or stationary increments of the desired process. A number of examples are provided to demonstrate the utility of the multiscale framework in simulating and estimating SSS processes. Index Terms—Canonical correlations, fractional Brownian motion, multiscale, self-similarity. I.