Network arrivals are often modeled as Poisson processes for analytic simplicity, even though a number of traffic studies have shown that packet interarrivals are not exponentially distributed. We evaluate 24 wide-area traces, investigating a number of wide-area TCP arrival processes (session and connection arrivals, FTP data connection arrivals within FTP sessions, and TELNET packet arrivals) to determine the error introduced by modeling them using Poisson processes. We find that user-initiated TCP session arrivals, such as remotelogin and file-transfer, are well-modeled as Poisson processes with fixed hourly rates, but that other connection arrivals deviate considerably from Poisson; that modeling TELNET packet interarrivals as exponential grievously underestimates the burstiness of TELNET traffic, but using the empirical Tcplib [Danzig et al, 1992] interarrivals preserves burstiness over many time scales; and that FTP data connection arrivals within FTP sessions come bunched into “connection bursts,” the largest of which are so large that they completely dominate FTP data traffic. Finally, we offer some results regarding how our findings relate to the possible self-similarity of widearea traffic.

There is much experimental evidence that network traffic processes exhibit ubiquitous properties of selfsimilarity and long range dependence (LRD), i.e., of correlations over a wide range of time scales. However, there is still considerable debate about how to model such processes and about their impact on network and application performance. In this paper, we argue that much recent modeling work has failed to consider the impact of two important parameters, namely the finite range of time scales of interest in performance evaluation and prediction problems, and the first-order statistics such as the marginal distribution of the process.

Recent network traffic studies argue that network arrival processes are much more faithfully modeled using statistically self-similar processes instead of traditional Poisson processes [LTWW94a, PF94]. One difficulty in dealing with selfsimilar models is how to efficiently synthesize traces (sample paths) corresponding to self-similar traffic. We present a fast Fourier transform method for synthesizing approximate selfsimilar sample paths and assess its performance and validity. We find that the method is as fast or faster than existing methods and appears to generate a closer approximation to true self-similar sample paths than the other known fast method (Random Midpoint Displacement). We then discuss issues in using such synthesized sample paths for simulating network traffic, and how an approximation used by our method can dramatically speed up evaluation of Whittle's estimator for H, the Hurst parameter giving the strength of long-range dependence present in a self-similar time s...

We present a set of stylized empirical facts emerging from the statistical analysis of price variations in various types of financial markets. We first discuss some general issues common to all statistical studies of financial time series. Various statistical properties of asset returns are then described: distributional properties, tail properties and extreme fluctuations, pathwise regularity, linear and nonlinear dependence of returns in time and across stocks. Our description emphasizes properties common to a wide variety of markets and instruments. We then show how these statistical properties invalidate many of the common statistical approaches used to study financial data sets and examine some of the statistical problems encountered in each case.

Recent network traffic studies argue that network arrival processes are much more faithfully modeled using statistically self-similar processes instead of traditional Poisson processes [LTWW94, PF95]. One difficulty in dealing with selfsimilar models is how to efficiently synthesize traces (sample paths) corresponding to self-similar traffic. We present a fast Fourier transform method for synthesizing approximate self-similar sample paths for one type of self-similar process, Fractional Gaussian Noise, and assess its performance and validity. We find that the method is as fast or faster than existing methods and appears to generate close approximations to true self-similar sample paths. We also discuss issues in using such synthesized sample paths for simulating network traffic, and how an approximation used by our method can dramatically speed up evaluation of Whittle's estimator for H, the Hurst parameter giving the strength of long-range dependence present in a self-similar time series.

This paper evaluates linear models for predicting the Digital Unix five-second host load average from 1 to 30 seconds into the future. A detailed statistical study of a large number of long, fine grain load traces from a variety of real machines leads to consideration of the Box-Jenkins models (AR, MA, ARMA, ARIMA), and the ARFIMA models (due to self-similarity.) We also consider a simple windowed-mean model. The computational requirements of these models span a wide range, making some more practical than others for incorporation into an online prediction system. We rigorously evaluate the predictive power of the models by running a large number of randomized testcases on the load traces and then data-mining their results. The main conclusions are that load is consistently predictable to a very useful degree, and that the simple, practical models such as AR are sufficient for host load prediction. We recommend AR(16) models or better for host load prediction. We implement an online host load prediction system around the AR(16) model and evaluate its overhead, finding that it uses miniscule amounts of CPU time and network bandwidth

Abstract—RPS is a publicly available toolkit that allows a practitioner to straightforwardly create flexible online and offline resource prediction systems in which resources are represented by independent, periodically sampled, scalar-valued measurement streams. The systems predict the future values of such streams from past values and are composed at runtime out of a large and extensible set of communicating components that are in turn constructed using RPS’s extensible sensor, prediction, wavelet, and communication libraries. This paper describes the design, implementation, and performance of RPS. We have used RPS extensively to evaluate predictive models and build online prediction systems for host load, Windows performance data, and network bandwidth. The computation and communication overheads involved in such systems are quite low. Index Terms—Distributed systems, performance of systems. æ 1

This paper evaluates linear models for predicting the Digital Unix five-second load average from 1 to 30 seconds into the future. A detailed statistical study of a large number of load traces leads to consideration of the Box-Jenkins models (AR, MA, ARMA, ARIMA), and the ARFIMA models (due to self-similarity.) These models, as well as a simple windowed-mean scheme, are evaluated by running a large number of randomized testcases on the load traces. The main conclusions are that load is consistently predictable to a useful degree, and that the simpler models such as AR are sufficient for doing this prediction.

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Modern telecommunications networks are being designed to accomodate a heterogenous mix of traffic classes ranging from traditional telephone calls to video and data services. Thus, traffic models are of crucial importance to the engineering and performance analysis of telecommunications system, notably congestion and overload controls and capacity estimation. This chapter surveys teletraffic models, addressing both theoretical and computational aspects. It first surveys the main classes of teletraffic models commonly used in teletraffic modeling, and then proceeds to survey traffic methods for computing statistics relevant to the engineering a teletraffic network. 1 INTRODUCTION Traffic is the driving force of telecommunications systems, representing customers making phone calls, transferring data files and other electronic information, or more recently, transmitting compressed video frames to a display device. The most common modeling context is queueing; traffic is offered to a qu...