Introduction

For reasons of tractibility, classical queuing theory assumes that the properties of network traffic (arrival rates, service times) include the Markovian property. While the Markovian assumption is valid for telephony networks, it has been widely reported that, for data networks, traffic is fractal in nature [6, 13, 16, 37]. One way to represent a traffic flow is as a stochastic process. Modelling traffic as Markovian stochastic processes is attractive because flows can be characterised by only a small number of parameters. Models of non-Markovian processes, however, are more complex and analytical results are difficult to derive. Markovian traffic can be clearly distinguished from Internet traffic patterns which exhibit properties of long-range dependence and self-similarity. That is, traffic is bursty over a wide range of time scales. Backlog and delay predictions are frequently underestimated if the Markovian property is assumed when traffic is actually long-range dependent (and self-similar) [16, 28].

A number of methods for generating fractal-like traffic processes have been put forward. Examples include Fractional ARIMA processes, Fractional Brownian motion, chaotic maps and the superposition of heavy-tailed on/off sources. Network performance can then be investigated using simulation techniques. Some of these fractal traffic generating techniques are described in this book.We use J to simulate network systems and analyse their performance under certain traffic conditions.