A number of recent empirical studies of traffic measurements from a variety of working packet networks have convincingly demonstrated that actual network traffic is self-similar or long-range dependent in nature (i.e., bursty over a wide range of time scales) -- in sharp contrast to commonly made traffic modeling assumptions. In this paper, we provide a plausible physical explanation for the occurrence of self-similarity in LAN traffic. Our explanation is based on new convergence results for processes that exhibit high variability (i.e., infinite variance) and is supported by detailed statistical analyses of real-time traffic measurements from Ethernet LAN's at the level of individual sources. This paper is an extended version of [53] and differs from it in significant ways. In particular, we develop here the mathematical results concerning the superposition of strictly alternating ON/OFF sources. Our key mathematical result states that the superposition of many ON/OFF sources (also k...

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...

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...

It has been known for several years now that variable-bit-rate video sources are strongly auto-correlated. Recently, several studies have indicated that the resulting stochastic processes exhibit long-range dependence properties. This implies that large buffers at intermediate switching points may not provide adequate delay performance for such classes of traffic in Broadband packet-switched networks (such as ATM). In this paper, we study the effect of long-memory processes on queue length statistics of a single queue system through a controlled fractionally differenced ARIMA(1; d; 0) input process. This process has two parameters OE 1 (0 OE 1 1) and d (0 d ! 1=2) representing an auto-regressive component and a long-range dependent component, respectively. Results show that the queue length statistics studied (mean, variance and the 0:999 quantile) are proportional to e c1 OE 1 e c2 d ; where (c 1 ; c 2 ) are positive constants, and c 2 ? c 1 : The effect of the auto-correlation...

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...

Background noise is the irregular variation across repeated measurements of human performance. Background noise remains after task and treatment effects are minimized. Background noise refers to intrinsic sources of variability, the intrinsic dynamics of mind and body, and the internal workings of a living being. Two experiments demonstrate 1/f scaling (pink noise) in simple reaction times and speeded word naming times, which round out a catalog of laboratory task demonstrations that background noise is pink noise. Ubiquitous pink noise suggests processes of mind and body that change each other’s dynamics. Such interaction-dominant dynamics are found in systems that self-organize their behavior. Self-organization provides an unconventional perspective on cognition, but this perspective closely parallels a contemporary interdisciplinary view of living systems. Psychological science usually ignores the background noise in behavioral data. Background noise is what is left over when task demands, experimental manipulations, and other external sources of variability have been eliminated or minimized. What we call background noise is treated as random variability in most research, the nuisance factor in factorial experiments. We argue, to the

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 use a Monte-Carlo approach to investigate the performance of five different time-series estimators of the exponent ff in 1=f ff noise. We find that a maximumlikelihood estimator is markedly superior to Fourier regression methods and Hurst exponent methods. The results indicate that useful estimates of ff can be made from time series that are much shorter than generally presumed. PACS codes: 72:70:+m, 73:50:Td, 74:40:+k Keywords: noise, noise parameter estimation, noise generation 1 Introduction Long-term correlations have been observed in many types of time series from physical, biological, physiological, economic, technological and sociological systems. Examples include geophysical data [1, 2, 3] such as rainfall, temperature measurements, sun-spot numbers, earthquake frequencies, and river flows, frequency fluctuations in electrical oscillators [4], rate of traffic flow [1], voltage or current fluctuations in metal films and semiconductor devices [4], loudness fluctuations i...

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...

There has been interest recently in the statistical property known as self-similarity, which has been observed experimentally in LAN traffic for instance. We define here a simple deterministic model of data transfer between remote sites and examine some of its properties. We show that waveforms which describe the network behaviour are aperiodic, despite the deterministic nature of our system, and also self-similar, with a Hurst parameter approaching unity, over a wide range of operating conditions. 1. Introduction Recently, there has been some interest in experimentally observed self-similar, or long range dependent, behaviour in for instance local area network (LAN) traffic [Leland 1994] and VBR video traffic [Garrett 1994]. The cause of self-similarity in traffic statistics in real networks is an open question at present. We approach this problem in the belief that many traffic flow control protocols are intrinsically capable of generating chaotic [Ott 1993] behaviour, which ...