Self-similar Processes in Telecommunications

by Sheluhin, Oleg; Smolskiy, Sergey; Osin, Andrew

• ISBN13: 9780470014868
• ISBN10: 0470014865
• Edition: 1st
• Format: Hardcover
• Copyright: 2007-04-09
• Publisher: WILEY

Summary

For the first time the problems of voice services self-similarity are discussed systematically and in detail with specific examples and illustrations.Self-Similar Processes in Telecommunications considers the self-similar (fractal and multifractal) models of telecommunication traffic and efficiency based on the assumption that its traffic has fractal or multifractal properties (is self-similar). The theoretical aspects of the most well-known traffic models demonstrating self-similar properties are discussed in detail and the comparative analysis of the different models' efficiency for self-similar traffic is presented.This book demonstrates how to use self-similar processes for designing new telecommunications systems and optimizing existing networks so as to achieve maximum efficiency and serviceability. The approach is rooted in theory, describing the algorithms (the logical arithmetical or computational procedures that define how a task is performed) for modeling these self-similar processes. However, the language and ideas are essentially accessible for those who have a general knowledge of the subject area and the advice is highly practical: all models, problems and solutions are illustrated throughout using numerous real-world examples.Adopts a detailed, theoretical, yet broad-based and practical mathematical approach for designing and operating numerous types of telecommunications systems and networks so as to achieve maximum efficiencyPlaces the subject in context, describing the current algorithms that make up the fractal or self-similar processes while pointing to the future development of the technologyOffers a comparative analysis of the different types of self-similar process usage within the context of local area networks, wide area networks and in the modeling of video traffic and mobile communications networksDescribes how mathematical models are used as a basis for building numerous types of network, including voice, audio, data, video, multimedia services and IP (Internet Protocol) telephonyThe book will appeal to the wide range of specialists dealing with the design and exploitation of telecommunication systems. It will be useful for the post-graduate students, lecturers and researchers connected with communication networks disciplines.

Author Biography

Oleg I. Sheluhin is Head of Department of the Radio Engineering and Systems department of Moscow State Technical University of Service (MSTUS). He specializes in the areas of statistical radio engineering, radio systems theory and information systems simulation.

Sergey M. Smolskiy is Head of the Department of Radio Receivers  in the Moscow Power Engineering Institute (MPEI). He has extensive experience in the field of telecommunications and is an active member of IEEE. His recent research topics include low distance radar systems and radio measuring systems.

Andrey V. Osin is currently Assistant Professor in the Department of Radio Engineering and Radio Systems at MSTUC. His PhD thesis focused on imitation modeling of self-similar processes in telecommunications and he has since published widely on the subject in numerous articles and conference journals.

Table of Contents

Foreword	p. xi
About the authors	p. xv
Acknowledgements	p. xix
Principal Concepts of Fractal Theory and Self-Similar Processes	p. 1
Fractals and Multifractals	p. 1
Fractal Dimension of a Set	p. 2
Multifractals	p. 3
Fractal Dimension D[subscript o] and Informational Dimension D[subscript i]	p. 5
Legendre Transform	p. 7
Self-Similar Processes	p. 8
Definitions and Properties of Self-Similar Processes	p. 8
Multifractal Processes	p. 12
Long-Range and Short-Range Dependence	p. 13
Slowly Decaying Variance	p. 14
'Heavy Tails'	p. 15
Distribution with 'Heavy Tails' (DHT)	p. 15
'Heavy Tails' Estimation	p. 17
Hurst Exponent Estimation	p. 18
Time Domain Methods of Hurst Exponent Estimation	p. 19
Frequency Domain Methods of Hurst Exponent Estimation	p. 26
Hurst Exponent Estimation Problems	p. 29
Estimation Problems	p. 29
Nonstationarity Problems	p. 31
Computational Problems	p. 36
Self-Similarity Origins in Telecommunication Traffic	p. 39
User's Behaviour	p. 39
Data Generation, Data Structure and its Search	p. 39
Traffic Aggregation	p. 40
Means of Network Control	p. 40
Control Mechanisms based on Feedback	p. 41
Network Development	p. 41
References	p. 41
Simulation Methods for Fractal Processes	p. 49
Fractional Brownian Motion	p. 49
RMD Algorithm for FBM Generation	p. 51
SRA Algorithm for FBM Generation	p. 53
Fractional Gaussian Noise	p. 54
FFT Algorithm for FGN Synthesis	p. 55
Advantages and Shortcomings of FBM/FGN Models in Network Applications	p. 65
Regression Models of Traffic	p. 66
Linear Autoregressive (AR) Processes	p. 67
Processes of Moving Average (MA)	p. 68
Autoregressive Models of Moving Average, ARMA(p,q)	p. 68
Fractional Autoregressive Integrated Moving Average (FARIMA) Process	p. 71
Parametric Estimation Methods	p. 75
FARIMA(p,d,q) Process Synthesis	p. 79
Fractal Point Process	p. 80
Statistical Characteristics of the Point Process	p. 82
Fractal Structure of FPP	p. 83
Methods of FPP Formation	p. 85
Fractal Renewal Process (FRP)	p. 86
FRP Superposition	p. 87
Alternative Fractal Renewal Process (AFRP)	p. 90
Fractal Binomial Noise Driven Poisson Process (FBNDP)	p. 96
Fractal Shot Noise Driven Poisson Process (FSNDP)	p. 97
Resume	p. 99
Fractional Levy Motion and its Application to Network Traffic Modelling	p. 99
Fractional Levy Motion and its Properties	p. 100
Algorithm of Fractional Levy Motion Modelling	p. 102
Fractal Traffic Formation Based on FLM	p. 103
Models of Multifractal Network Traffic	p. 108
Multiplicative Cascades	p. 110
Modified Estimation Method of Multifractal Functions	p. 112
Generation of the Traffic Multifractal Model	p. 112
LRD Traffic Modelling with the Help of Wavelets	p. 116
M/G/[infinity] Model	p. 117
M/G/[infinity] Model and Pareto Distribution	p. 118
M/G/[infinity] Model and Log-Normal Distribution	p. 118
References	p. 119
Self-Similarity of Real Time Traffic	p. 123
Self-Similarity of Real Time Traffic Preliminaries	p. 123
Statistical Characteristics of Telecommunication Real Time Traffic	p. 124
Measurement Organization	p. 124
Pattern of TN Traffic	p. 126
Voice Traffic Characteristics	p. 130
Voice Traffic Characteristics at the Call Layer	p. 130
Voice Traffic Characteristics at the Packet Layer	p. 133
Multifractal Analysis of Voice Traffic	p. 135
Basics	p. 135
Algorithm for the Partition Function S[subscript m](q) Calculation	p. 139
Multifractal Properties of Multiplexed Voice Traffic	p. 140
Multifractal Properties of Two-Component Voice Traffic	p. 142
Mathematical Models of VoIP Traffic	p. 142
Problem Statement	p. 142
Voice Traffic Models at the Call Layer	p. 145
Estimation of Semi-Markovian Model Parameters and the Modelling Results of the Voice Traffic at the Call Layer	p. 147
Mathematical Models of Voice Traffic at the Packets Layer	p. 148
Simulation of the Voice Traffic	p. 151
Simulation Structure	p. 151
Parameters Choice of Pareto Distributions for Voice Traffic Source in ns2	p. 155
Results of Separate Sources Modelling	p. 157
Results of Traffic Multiplexing for the Separate ON/OFF Sources	p. 157
Long-Range Dependence for the VBR-Video	p. 162
Distinguished Characteristics of Video Traffic	p. 162
Video Conferences	p. 163
Video Broadcasting	p. 163
MPEG Video Traffic	p. 167
Nonstationarity of VBR Video Traffic	p. 175
Self-Similarity Analysis of Video Traffic	p. 177
Video Broadcasting Wavelet Analysis	p. 177
Numerical Results	p. 180
Multifractal Analysis	p. 185
Models and Modelling of Video Sequences	p. 192
Nonstationarity Types for VBR Video Traffic	p. 192
Model of the Video Traffic Scene Changing Based on the Shiffing Level Process	p. 197
Video Traffic Models in the Limits of the Separate Scene	p. 200
Fractal Autoregressive Models of p-Order	p. 203
MPEG Data Modelling Using I, P and B Frames Statistics	p. 206
ON/OFF Model of the Video Sequences	p. 207
Self-Similar Norros Model	p. 207
Hurst Exponent Dependence on N	p. 207
References	p. 208
Self-Similarity of Telecommunication Networks Traffic	p. 211
Problem Statement	p. 211
Self-Similarity and 'Heavy Tails' in LAN Traffic	p. 212
Experimental Investigations of the Ethernet Traffic Self-Similar Structure	p. 213
Estimation of Testing Results	p. 213
Self-Similarity of WAN Traffic	p. 218
WAN Traffic at the Application Level	p. 218
Some Limiting Results for Aggregated WAN Traffic	p. 219
The Statistical Analysis of WAN Traffic at the Application Level	p. 221
Multifractal Analysis of WAN Traffic	p. 222
Self-Similarity of Internet Traffic	p. 222
Results of Experimental Studies	p. 223
Stationarity Analysis of IP Traffic	p. 223
Nonstationarity of Internet Traffic	p. 230
Scaling Analysis	p. 232
Multilevel ON/OFF Model of Internet Traffic	p. 236
Problem Statement	p. 236
Estimation of Parameters and Model Parameterization	p. 237
Parallel Buffer Structure for Active Queue Control	p. 240
References	p. 243
Queuing and Performance Evaluation of Telecommunication Networks under Traffic Self-Similarity Conditions	p. 247
Traffic Fractality Influence Estimate on Telecommunication Network Queuing	p. 247
Monofractal Traffic	p. 248
Communication System Model and the Packet Loss Probability Estimate for the Asymptotic Self-Similar Traffic Described by Pareto Distribution	p. 251
Queuing Model with fractional Levy Motion	p. 253
Estimate of the Effect of Traffic Multifractality Effect on Queuing	p. 257
Estimate of Voice Traffic Self-Similarity Effects on the IP Networks Input Parameter Optimization	p. 261
Problem Statement	p. 261
Simulation Structure	p. 261
Estimate of the Traffic Self Similarity Influence on QoS	p. 263
TN Input Parameter Optimization for Given QoS Characteristics	p. 266
Conclusions	p. 269
Telecommunication Network Parameters Optimization Using the Tikhonov Regularization Approach	p. 269
Problem Statement	p. 269
Telecommunication Network Parameter Optimization on the Basis of the Minimization of the Discrepancy Functional of QoS Characteristics	p. 271
Optimization Results	p. 272
TN Parameter Optimization on the Basis of Tikhonov Functional Minimization	p. 274
Regularization Results	p. 276
Conclusions	p. 281
Estimation of the Voice Traffic Self-Similarity Influence on QoS with Frame Relay Networks	p. 282
Packet Delay at Transmission through the Frame Relay Network	p. 283
Frame Relay Router Modelling	p. 283
Simulation Results	p. 287
Bandwidth Prediction in Telecommunication Networks	p. 291
Congestion Control of Self-Similar Traffic	p. 295
Unimodal Ratio Loading/Productivity	p. 297
Selecting Aggressiveness Control (SAC) Scheme	p. 297
References	p. 298
List of Symbols	p. 301
List of Acronyms	p. 305
Index	p. 307
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