IP-Traffic Theory and Performance (eBook)

Professor Dr.- Ing. Christian Grimm has been working for more than ten years with measuring and modelling of data traffic in packet switched networks. In his PhD thesis he investigated complex methods for the traffic modelling in the World Wide Web. At present he is head of the division for research and development and new network services at the regional computing centre for lower saxony. Since 2003 he has an assistant professorship (Juniorprofessur) in computer networks at the faculty of electrical engineering and computer sciences at the university of Hannover. Professor Dr. rer.nat. Georg Schlüchtermann finished his study in Mathematics in 1984. He habilitated 1994 at the Ludwig-Maximilians-Universität in functional analysis. Since 2001 he is apl. professor at the faculty for mathematics, computer sciences and statistics at the university of Munich. He is lecturing in the fields of traffic theory, mathematical modelling in mobile communication and finance mathematics.

Preface 7
Contents 11
1 Introduction to IP Traffic 15
1.1 TCP/IP Architecture Model 15
1.2 Aspects of IP Modeling 23
1.3 Quality of Service 33
1.4 Why Traditional Models Fail 36
2 Classical Traffic Theory 43
2.1 Introduction to Traffic Theory 43
2.2 Kolmogorov Equation 48
2.3 Transition Processes 52
2.4 Pure Markov Systems M/M/n 54
2.5 Special Traffic Models 72
2.6 Renewal Processes 74
2.7 General Poisson Arrival and Serving SystemsM/G/n 87
2.8 General Serving Systems GI/G/n 121
2.9 Network Models 136
2.10 Matrix-Analytical Methods 162
Further Literature 193
3 Mathematical Modeling of IP-based Traffic 194
3.1 Scalefree Traffic Observation 194
3.2 Self-Similar Processes 197
3.3 Long-Range Dependence 215
3.4 Influence of Heavy-Tail Distributions on Long-Range Dependence 239
3.5 Models for Time Sensitive Traffic 258
3.6 Fractional L´evy Motion in IP-based Network Traffic 272
3.7 Fractional Ornstein-Uhlenbeck Processes and Telecom Processes 274
3.8 Multifractal Models and the Influence of Small Scales 280
3.9 Summary of Models for IP Traffic 329
Further Literature 330
4 Statistical Estimators 333
4.1 Parameter Estimation 333
4.2 Estimators of Hurst Exponent in IP Traffic 361
Further Literature 394
5 Performance of IP: Waiting Queues and Optimization 395
5.1 Queueing of IP Traffic for Perturbation with Long- Range Dependence Processes 395
5.2 Queueing in Multifractal Traffic 423
5.3 Traffic Optimization 435
Further Literature 475
References 476
Index 490