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...

MPEG video traffic is expected to cause several problems in ATM networks, both from performance and from architectural viewpoint. For the solution of these difficulties, appropriate video traffic models are needed. A detailed statistical analysis of newly generated long MPEG encoded video sequences is presented and the results are compared to those of existing data sets. Based on the results of the analysis, a layered modeling scheme for MPEG video traffic is suggested which will simplify the finding of appropriate models for a lot performance analysis techniques.

Recent studies have suggested that stock markets' volatility has a type of long-range dependence that is not appropriately described by the usual Generalized Autoregressive Conditional Heteroskedastic (GARCH) and Exponential GARCH (EGARCH) models. In this paper, different models for describing this long-range dependence are examined and the properties of a Long-Memory Stochastic Volatility (LMSV) model, constructed by incorporating an Autoregressive Fractionally Integrated Moving Average (ARFIMA) process in a stochastic volatility scheme, are discussed. Strongly consistent estimators for the parameters of this LMSV model are obtained by maximizing the spectral likelihood. The distribution of the estimators is analyzed by means of a Monte Carlo study. The LMSV is applied to daily stock market returns providing an improved description of the volatility behavior. In order to assess the empirical relevance of this approach, tests for long-memory volatility are described and applied to an e...

Various methods for estimating the self-similarity parameter and/or the intensity of long-range dependence in a time series are available. Some are more reliable than others. To discover the ones that work best, we apply the different methods to simulated sequences of fractional Gaussian noise and fractional ARIMA(0, d, 0). We also provide here a theoretical justification for the method of residuals of regression.

this paper, we focus on the problem of making short and medium term forecasts of CPU availability on time-shared Unix systems. We evaluate the accuracy with which availability can be measured using Unix load average, the Unix utility vmstat, and the Network Weather Service CPU sensor that uses both. We also examine the autocorrelation between successive CPU measurements to determine their degree of self-similarity. While our observations show a long-range autocorrelation dependence, we demonstrate how this dependence manifests itself in the short and medium term predictability of the CPU resources in our study.

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...

After measurements on a lan at Bellcore, it is known that data traffic is extremely variable on time scales ranging from milliseconds to days. The traffic behaves quite differently to what has been assumed until now; traffic sources were generally characterized by short term dependences but characteristics of the measured traffic have shown that it is long term dependent. Therefore, new models (such as Fractional Brownian motion, arima processes and Chaotic maps) have been applied. Although they are not easily tractable, one big advantage of these models is that they give a good description of the traffic using few parameters. In this paper, we describe a Markov chain emulating self-similarity which is quite easy to manipulate and depends only on two parameters (plus the number of states in the Markov chain). An advantage of using it is that it is possible to re-use the well-known analytical queuing theory techniques developed in the past in order to evaluate network performance. The t...

Optical Burst Switching (OBS) is considered as a promising switching technique for building the next generation optical Internet. In OBS networks, one important issue is how the performance will be affected by bursts assembled from packets, which is the basic transmission unit in OBS. In this paper, we study the fundamental statistic properties such as the burst length distribution, inter-arrival time distribution, as well as correlation structure of assembled burst traffic from burst assembly algorithms. From both theoretical and empirical results, it is demonstrated that after the assembly, the traffic will in general approach the Gaussian distribution. In particular, the variance of assembled traffic decreases with the increase in the assembly window size and the traffic load. However, the long range dependence in the input traffic will not change after assembly.

This is an overview of a relatively recent application of long-range dependence (LRD) to the area of communication networks, in particular to problems concerned with the dynamic nature of packet flows in high-speed data networks such as the Internet. We demonstrate that this new application area offers unique opportunities for significantly advancing our understanding of LRD and related phenomena. These advances are made possible by moving beyond the conventional approaches associated with the wide-spread "black-box" perspective of traditional time series analysis and exploiting instead the physical mechanisms that exist in the networking context and that are intimately tied to the observed characteristics of measured network traffic. In order to describe this complexity we provide a basic understanding of the design, architecture and operations of data networks, including a description of the TCP/IP protocols used in today's Internet. LRD is observed in the large scale behavior of the data traffic and we provide a physical explanation for its presence. LRD tends to be caused by user and application characteristics and has little to do with the network itself. The network affects mostly small time scales, and this is why a rudimentary understanding of the main protocols is important. We illustrate why multifractals may be relevant for describing some aspects of the highly irregular traffic behavior over small time scales. We distinguish between a time-domain and wavelet-domain approach to analyzing the small time scale dynamics and discuss why the wavelet-domain approach appears to be better suited than the time-domain approach for identifying features in measured traffic (e.g., relatively regular traffic patterns over certain time scales) that have a direct networking interpretation (e....

We show that a class of microeconomic behavioral models with interacting agents, derived from Kirman (1991, 1993), can replicate the empirical long-memory properties of the two first conditional moments of financial time series. The essence of these models is that the forecasts and thus the desired trades of the individuals in the markets are influenced, directly, or indirectly by those of the other participants. These "field effects" generate "herding" behaviour which affects the structure of the asset price dynamics. The series of returns generated by these models display the same empirical properties as financial returns: returns are I(0), the series of absolute and squared returns display strong dependence, while the series of absolute returns do not display a trend. Furthermore, this class of models is able to replicate the common long-memory properties in the volatility and co-volatility of financial time series, revealed by Teyssière (1997, 1998a). These properties are investigated by using various model independent tests and estimators, i.e., semiparametric and nonparametric, introduced by Lo (1991), Kwiatkowski, Phillips, Schmidt and Shin (1992), Robinson (1995), Lobato and Robinson (1998), Giraitis, Kokoszka Leipus and Teyssière (2000, 2001). The relative performance of these tests and estimators for long-memory in a non-standard data generating process is then assessed.