ABSTRACT
Abstract .......................................................................................................................................... 150 6.1 Introduction .......................................................................................................................... 150
6.1.1 Fractal Modeling of Network Trafc........................................................................ 150 6.2 Monofractal Processes .......................................................................................................... 152
6.2.1 Self-Similar Stochastic Processes ............................................................................. 153 6.2.2 Second-Order Self-Similar Process .......................................................................... 154 6.2.3 Methods for Estimating the Hurst Parameter ........................................................... 156 6.2.4 Evaluating the Estimators ......................................................................................... 156
6.3 Multifractal Processes .......................................................................................................... 159 6.3.1 Multifractal Analysis ................................................................................................ 160
6.3.1.1 Holder Exponent and Network Trafc ....................................................... 161 6.3.1.2 Multifractal Spectrum................................................................................ 161 6.3.1.3 Multiscale Diagram ................................................................................... 161 6.3.1.4 Autocorrelation Function ........................................................................... 163
6.4 Trafc Characterization ........................................................................................................ 164 6.4.1 Single-Source Trafc ................................................................................................ 164 6.4.2 Aggregate Trafc ...................................................................................................... 164
6.4.2.1 Vertical Aggregation .................................................................................. 165 6.4.2.2 Horizontal Aggregation ............................................................................. 166
6.4.3 Parameters of Trafc Characterization .................................................................... 166 6.4.3.1 Average Rate .............................................................................................. 167 6.4.3.2 Peak Rate ................................................................................................... 167 6.4.3.3 Peak-to-Mean Ratio ................................................................................... 167 6.4.3.4 Coefcient of Variability ........................................................................... 167 6.4.3.5 Index of Dispersion of Counts ................................................................... 167 6.4.3.6 Maximum Burst Size ................................................................................. 167 6.4.3.7 Time Burst Mean ....................................................................................... 168 6.4.3.8 Number of Trafc Sources ......................................................................... 168 6.4.3.9 Self-Similarity Parameters......................................................................... 168 6.4.3.10 Hölder Exponent ........................................................................................ 168
6.4.4 Real Trafc Analysis ................................................................................................ 168 6.4.4.1 Trafc Parameters ...................................................................................... 169 6.4.4.2 Self-Similarity and Multifractal Analysis ................................................. 170
6.5 Future Research Direction .................................................................................................... 174 6.6 Conclusion ............................................................................................................................ 175 References ...................................................................................................................................... 176
For network engineering, simulation strategies have become indispensable for almost all network issues, especially in network design and performance analysis. Network trafc modeling and analysis are two essential topics for today’s multimedia and high-speed networks. Better understanding of trafc characteristics and behavior allows maximum benecial use of network capacities and therefore achieving better network performance. In this chapter, we focus our attention to fractaltheory-based trafc modeling and simulations procedures for this end. Initially, we introduce some main features of monofractal processes, emphasizing the characterization of the Hurst parameter. Then we extend our discussion to multifractal theory and processes, especially two functional parameters called the Hölder exponents and multifractal spectrum. In sequel, we compare the difference between monofractal and multifractal processes and how each one of these two process types inuences network performance. For trafc characterization, we list a set of statistical parameters extracted from different real network trafc data and evaluate their relevance for trafc modeling and network simulations, in the sense of how to create a more realistic scenario for simulation of a network. Finally, we conclude this chapter by suggesting some possible future research themes.
