Multifractal Based Network Traffic Modeling

1. Introduction.- 1 Complexity of Broadband Network Traffic.- 2 Teletraffic Modeling: Historical Perspective.- 3 Motivation for the Problem.- 4 Contributions of the Monograph.- 5 Organization of the Monograph.- 2. Mathematical Preliminaries.- 1 Random Processes.- 2 Bernoulli (Counting) Process.- 3 Poisson Process.- 3.1 Applications to Queuing Theory.- 4 Markov Process.- 5 Independent Increment Processes.- 6 Self Similar Processes.- 7 Fractional Brownian Motion.- 8 Heavy Tailed Processes.- 9 Analysis and Estimation Techniques for Self Similar Processes.- 10 Wavelet Based Analysis of Self Similar Process.- 11 The Need for Multifractal Processes.- 12 Salient points from the chapter.- 3. Broadband Network Traffic Modeling.- 1 Broadband Network Traffic Characteristics.- 2 Network Traffic Modeling Methodology.- 3 State-of-the-Art in Teletraffic Modeling.- 4 Video Traffic Modeling.- 5 Summary of Broadband Traffic Models.- 4. Multiplicative Cascades.- 1 Binomial Multiplicative Cascade.- 2 Characterizing Multifractals through Multifractal Spectrum.- 3 Methods to Estimate Multifractal Spectrum.- 4 Interpreting the Multifractal Spectrum.- 5 Generalized Dimensions.- 6 Summary of the Chapter.- 5. V.V.G.M Multifractal Model.- 1 Development of V.V.G.M Multifractal Model.- 2 Statistical Comparison Tests.- 3 Test for Robustness of the Parametric Model.- 4 Performance and Queuing Tests.- 5 Inter Departure Process.- 6 V.V.G.M and MWM : A Comparison.- 7 Salient Points of the V.V.G.M Model.- 6. Analysis of the Multiplexing of Traffic.- 1 Analysis of Multiplexing using V.V.G.M Model.- 2 Analysis of Multiplexing using Multifractal Spectrum.- 3 Analysis of the Multiplexing using Entropy.- 4 How Complex is Inter Arrival Data?.- 5 Salient points from the chapter.- 7. Modeling of VBR Video Traces.- 1 VBR Video Modeling Using Multifractals.- 2 Statistical Tests for Model Evaluation.- 3 Results of Queuing Simulations.- 4 Complexity of VBR Video Traces.- 5 Salient points from the Chapter.- 8. Qos Issues and Control of Broadband Traffic.- 1 Statistics of Multiplicative Cascade Processes.- 2 Queuing Theory for Cascade Processes.- 3 Effective Bandwidth Estimation for QoS.- 4 Estimation and Prediction of Burstiness.- 5 Salient points from the chapter.- 9. Conclusions.- 1 V.V.G.M Cascade Process for Broadband Network Traffic.- 2 Future Work.- Appendices.- A. Wavelet Transform.- B. Legendre Transform.- C. Large Deviation Theory.- D. Norros’s Queuing Model.- D.1 Parameterizing QoS Requirements.- D.1.1 Parameterizing Buffer Length.- D.1.2 Parameterizing Service Rate.- D.1.3 Parameterizing Queue Length Distribution.- E. Effective Bandwidth.- E.1 Properties.- E.2 Application in Queuing Systems.- F. Kaiman Filter.- G. Some Websites of Interest.- References.