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...

This paper reviews and discusses briefly the known definitions and properties of second-order self-similar discrete-time processes and supplements them with some more general conditions of selfsimilarity. A model for ATM cell traffic is presented and self-similarity conditions of this model are found. 1. INTRODUCTION

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

A simple construction that will be referred to as an error duration model is shown to generate fractional integration and long memory. An error duration representation also exists for many familiar ARMA models, making error duration an alternative to autoregression for explaining dynamic persistence in economic variables. The results lead to a straightforward procedure for simulating fractional integration and establish a connection between fractional integration and common notions of structural change. Two examples show how the error duration model could account for fractional integration in aggregate employment and in asset price volatility.

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....

This paper studies tails of the duration distribution of internet data flows, and their "heaviness". Data analysis

We study the superposition process of a class of independent renewal processes with long-range dependence. It is known that under two different scalings in time and space either fractional Brownian motion or a stable Levy process may arise in the rescaling asymptotic limit. It is shown here that in a third, intermediate scaling regime a new limit process appears, which is neither Gaussian nor stable. The new limit process is characterized by its cumulant generating function and some of its properties are discussed.

Thispaperpresentsadiscussionofsimulation-related issuesarisinginthestudyofself-similarnetwork tra#cwithrespecttoitse#ectandcontrol.Selfsimilartra #chasbeenshowntobeanubiquitous phenomenonarisingindiversenetworkingcontexts withpotentiallyadversee#ectsonnetworkperformance. Inmanyinstances,anexperimentalorempirical approachneedstobetakentoe#ectivelyevaluate theperformanceimpactofsophisticatedcontrolalgorithmsactingatvariouslayersintheprotocolstack underself-similartra#cconditions.Simulatingorexperimentallyimplementingsuchenvironmentsisnon - trivialduetothefactthat,ingeneral,thecharacteristicsoftheobservedtra #cisitselfinfluencedbythe actionsofthecontrolalgorithmsunderstudy.To whatdegreeself-similaritymanifestsitselfinnetwork tra#cmaydependonthepropertiesoftheprotocols employed,andtrace-basedsimulationsthatrelyon tra#cmeasurementstodrivesimulationsfailtocapturethisdynamicaspect. Wediscussanapproachtoevaluatingcontrolprotocolsunderself -similartra#cconditionsbasedon asimple,robustapplication-levelcausalmechanism oftra#cself-similaritywhichisgroundedinboth empiricalUNIXfilesystemresearchandanalytic tra#cmodelsinvolvingcertainrenewalprocesses. Wepresentahigh-leveldiscussionconcentratingon simulation-relatedissues,withspecificresearchresultssummarizedorpointedtointhereferences. 1

One of the most significant findings... This paper reviews what is currently known about network traffic self-similarity and its significance. We then consider a matter of current research, namely, the manner in which network dynamics (specifically, the dynamics of transmission control protocol (TCP), the predominant transport protocol used in today's Internet) can affect the observed self-similarity. To this end, we first discuss some of the pitfalls associated with applying traditional performance evaluation techniques to highly-interacting, large-scale networks such as the Internet. We then present one promising approach based on chaotic maps to capture and model the dynamics of TCP-type feedback control in such networks. Not only can appropriately chosen chaotic map models capture a range of realistic source characteristics, but by coupling these to network state equations, one can study the effects of network dynamics on the observed scaling behavior. We consider several aspects of TCP feedback, and illustrate by examples that while TCP-type feedback can modify the self-similar scaling behavior of network traffic, it neither generates it nor eliminates it.

Several types of network trafic have been shown to exhibit long-range dependence (LRD). In this work, we show that the busy period of an ATM system driven by a long-range dependent process can be very large. We introduce a new trafjic model based on a fractional Brownian motion envelope process. We show that this characterization can be used to predict queueing dy-namics. Furthermore, we derive a new framework for computing delay bounds in ATM networks based on this trafic model. We show that it agrees with results given by large deviation theory with less computational complexity. 1