As the World Wide Web (Web) is increasingly adopted as the infrastructure for large-scale distributed information systems, issues of performance modeling become ever more critical. In particular, locality of reference is an important property in the performance modeling of distributed information systems. In the case of the Web, understanding the nature of reference locality will help improve the design of middleware, such as caching, prefetching, and document dissemination systems. For example, good measurements of reference locality would allow us to generate synthetic reference streams with accurate performance characteristics, would allow us to compare empirically measured streams to explain differences, and would allow us to predict expected performance for system design and capacity planning. In this paper we propose models for both temporal and spatial locality of reference in streams of requests arriving at Web servers. We show that simple models based only on document popularity (likelihood of reference) are insufficient for capturing either temporal or spatial locality. Instead, we rely on an equivalent, but numerical, representation of a reference stream: a stack distance trace. We show that temporal locality can be characterized by

Recent evidence suggests that some characteristics of computer and telecommunications systems may be well described using heavy tailed distributions — distributions whose tail declines like a power law, which means that the probability of extremely large observations is non-negligible. For example, such distributions have been found to describe the lengths of bursts in network traffic and the sizes of files in some systems. As a result, system designers are increasingly interested in employing heavy-tailed distributions in simulation workloads. Unfortunately, these distributions have properties considerably different from the kinds of distributions more commonly used in simulations; these properties make simulation stability hard to achieve. In this paper we explore the difficulty of achieving stability in such simulations, using tools from the theory of stable distributions. We show that such simulations exhibit two characteristics related to stability: slow convergence to steady state, and high variability at steady state. As a result, we argue that such simulations must be treated as effectively always in a transient condition. One way to address this problem is to introduce the notion of time scale as a parameter of the simulation, and we discuss methods for simulating such systems while explicitly incorporating time scale as a parameter. 1

We demonstrate that high-level file system events exhibit self-similar behaviour, but only for short-term time scales of approximately under a day. We do so through the analysis of four sets of traces that span time scales of milliseconds through months, and that differ in the trace collection method, the file systems being traced, and the chronological times of the tracing. Two sets of detailed, short-term file system trace data are analyzed; both are shown to have self-similar like behaviour, with consistent Hurst parameters (a measure of self-similarity) for all file system traffic as well as individual classes of file system events. Long-term file system trace data is then analyzed, and we discover that the traces' high variability and self-similar behaviour does not persist across time scales of days, weeks, and months. Using the short-term trace data, weshow that sources of file system traffic exhibit ON/OFF source behaviour, which is characterized by highly variably lengthed bursts of activity, followed by similarly variably lengthed periods of inactivity. This ON/OFF behaviour is used to motivate a simple technique for synthesizing a stream of events that exhibit the same self-similar short-term behaviour as was observed in the file system traces.

INTRODUCTION In the last decade a number of extensive studies of high resolution traffic measurements from a wide range of packet traffic networks have been reported [1,6,7,10,11,14,22]. The most important finding of these studies is the identified fractal-like behaviour implying the so called long-range dependence and self-similarity properties. As a result of intensive research at Bellcore a series of papers reported these findings in Ethernet LAN [7,9,11,12]. The comprehensive study of Leland's group with the conclusion that this traffic is self-similar was published in detail in [11]. The study of Duffy et al. [6] revealed the self-similarity traffic property in common-channel signalling network. Meier-Hellstern et al. [14] found that the Pareto distribution with infinite variance is applicable for characterizing the D-channel traffic in N-ISDN. Paxson et al. [20,22] reported the self-similar features of TCP traffic. The fractal properties also

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.

A significant discovery from this work is that although video traffic has complicated short- and longrange dependence in the time domain, the corresponding wavelet coefficients are no longer long-range dependent in the wavelet domain. Therefore, a "short-range" dependent process can be used to model video traffic in the wavelet domain. In this work, we develop such wavelet models for VBR video traffic. The strength of the developed wavelet models includes (1) it provides a unified approach to model both long-range and short-range dependence in video traffic simultaneously, (2) it has the ability to reduce the temporal dependence so significantly that the wavelet coefficients can be modeled by either independent or Markov models, and (3) the model results in a computationally efficient method on generating high quality video traffic. Key words: wavelet, long-range dependence, short-range dependence, traffic modeling, VBR video traffic. Topics: video networking, B-ISDN and ATM, admission control. I.

Following our work described in Part I of this paper that modeled various correlation structures of Gaussian traffic in wavelet domain, we extend our previous models to heterogeneous network traffic with either a non-Gaussian distribution or a periodic structure. To include a non-Gaussian distribution, we first investigate what higher-order statistics are pertinent by exploring a relationship between time-scale analysis of wavelets and cumulative traffic. We then develop a novel algorithm in the wavelet domain to capture the important statistics. By utilizing local properties of wavelet basis in both space and time, we further extend such wavelet models to periodic MPEG traffic. As wavelets provide a natural fit to higher-order statistics as well as localized spatial and temporal dependence of periodic traffic at different time scales, the resulting wavelet models for both non-Gaussian and periodic traffic are simple and accurate with the lowest computational complexity attainable. 1 I...

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...

The concepts of self-similarity, fractals, and long-range dependence (LRD) have revolutionized network modeling during the last decade. However, despite all the attention these concepts have received, they remain di#cult to use by non-experts. This di#- culty can be attributed to a relative complexity of the mathematical basis, the absence of a systematic approach to their application and the absence of publicly available software. In this paper, we introduce SELFIS, a comprehensive tool, to facilitate the evaluation of LRD by practitioners. Our goal is to create a stand-alone public tool that can become a reference point for the community. Our tool integrates most of the required functionality for an in-depth LRD analysis, including several LRD estimators. In addition, SELFIS includes a powerful approach to stress-test the existence of LRD. Using our tool, evidence are presented that the widely-used LRD estimators can provide misleading results. It is worth mentioning that 25 researchers have acquired SELFIS within a month of its release, which clearly demonstrates the need for such a tool.

Recently, statistical analysis of high-resolution measurements of several types of network traffic has shown that many type of network traffic are self-similar or fractal in nature. This report gives an overview of self-similarity and examines the effect of self-similar inputs on the performance of asynchronous transfer mode (ATM) switches. This is done through the use of trace based simulation using actual Ethernet traffic traces. The results of these simulations suggest that self-similarity has an adverse effect on the performance of ATM switches and that certain suggested bandwidth allocation policies for ATM switches will significantly outperform others in the presence of self-similarity. ii Acknowledgements I would like to acknowledge several people who have helped with this project: Mike Devetsikiotis for providing me with numerous papers addressing the topic of selfsimilarity and for introducing me to several members of the Bellcore research team, Rob Tyson for providing me wi...