Self-similar Processes in Telecommunications

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  • Format: Hardcover
  • Copyright: 2007-04-09
  • Publisher: WILEY

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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

Forewordp. xi
About the authorsp. xv
Acknowledgementsp. xix
Principal Concepts of Fractal Theory and Self-Similar Processesp. 1
Fractals and Multifractalsp. 1
Fractal Dimension of a Setp. 2
Multifractalsp. 3
Fractal Dimension D[subscript o] and Informational Dimension D[subscript i]p. 5
Legendre Transformp. 7
Self-Similar Processesp. 8
Definitions and Properties of Self-Similar Processesp. 8
Multifractal Processesp. 12
Long-Range and Short-Range Dependencep. 13
Slowly Decaying Variancep. 14
'Heavy Tails'p. 15
Distribution with 'Heavy Tails' (DHT)p. 15
'Heavy Tails' Estimationp. 17
Hurst Exponent Estimationp. 18
Time Domain Methods of Hurst Exponent Estimationp. 19
Frequency Domain Methods of Hurst Exponent Estimationp. 26
Hurst Exponent Estimation Problemsp. 29
Estimation Problemsp. 29
Nonstationarity Problemsp. 31
Computational Problemsp. 36
Self-Similarity Origins in Telecommunication Trafficp. 39
User's Behaviourp. 39
Data Generation, Data Structure and its Searchp. 39
Traffic Aggregationp. 40
Means of Network Controlp. 40
Control Mechanisms based on Feedbackp. 41
Network Developmentp. 41
Referencesp. 41
Simulation Methods for Fractal Processesp. 49
Fractional Brownian Motionp. 49
RMD Algorithm for FBM Generationp. 51
SRA Algorithm for FBM Generationp. 53
Fractional Gaussian Noisep. 54
FFT Algorithm for FGN Synthesisp. 55
Advantages and Shortcomings of FBM/FGN Models in Network Applicationsp. 65
Regression Models of Trafficp. 66
Linear Autoregressive (AR) Processesp. 67
Processes of Moving Average (MA)p. 68
Autoregressive Models of Moving Average, ARMA(p,q)p. 68
Fractional Autoregressive Integrated Moving Average (FARIMA) Processp. 71
Parametric Estimation Methodsp. 75
FARIMA(p,d,q) Process Synthesisp. 79
Fractal Point Processp. 80
Statistical Characteristics of the Point Processp. 82
Fractal Structure of FPPp. 83
Methods of FPP Formationp. 85
Fractal Renewal Process (FRP)p. 86
FRP Superpositionp. 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
Resumep. 99
Fractional Levy Motion and its Application to Network Traffic Modellingp. 99
Fractional Levy Motion and its Propertiesp. 100
Algorithm of Fractional Levy Motion Modellingp. 102
Fractal Traffic Formation Based on FLMp. 103
Models of Multifractal Network Trafficp. 108
Multiplicative Cascadesp. 110
Modified Estimation Method of Multifractal Functionsp. 112
Generation of the Traffic Multifractal Modelp. 112
LRD Traffic Modelling with the Help of Waveletsp. 116
M/G/[infinity] Modelp. 117
M/G/[infinity] Model and Pareto Distributionp. 118
M/G/[infinity] Model and Log-Normal Distributionp. 118
Referencesp. 119
Self-Similarity of Real Time Trafficp. 123
Self-Similarity of Real Time Traffic Preliminariesp. 123
Statistical Characteristics of Telecommunication Real Time Trafficp. 124
Measurement Organizationp. 124
Pattern of TN Trafficp. 126
Voice Traffic Characteristicsp. 130
Voice Traffic Characteristics at the Call Layerp. 130
Voice Traffic Characteristics at the Packet Layerp. 133
Multifractal Analysis of Voice Trafficp. 135
Basicsp. 135
Algorithm for the Partition Function S[subscript m](q) Calculationp. 139
Multifractal Properties of Multiplexed Voice Trafficp. 140
Multifractal Properties of Two-Component Voice Trafficp. 142
Mathematical Models of VoIP Trafficp. 142
Problem Statementp. 142
Voice Traffic Models at the Call Layerp. 145
Estimation of Semi-Markovian Model Parameters and the Modelling Results of the Voice Traffic at the Call Layerp. 147
Mathematical Models of Voice Traffic at the Packets Layerp. 148
Simulation of the Voice Trafficp. 151
Simulation Structurep. 151
Parameters Choice of Pareto Distributions for Voice Traffic Source in ns2p. 155
Results of Separate Sources Modellingp. 157
Results of Traffic Multiplexing for the Separate ON/OFF Sourcesp. 157
Long-Range Dependence for the VBR-Videop. 162
Distinguished Characteristics of Video Trafficp. 162
Video Conferencesp. 163
Video Broadcastingp. 163
MPEG Video Trafficp. 167
Nonstationarity of VBR Video Trafficp. 175
Self-Similarity Analysis of Video Trafficp. 177
Video Broadcasting Wavelet Analysisp. 177
Numerical Resultsp. 180
Multifractal Analysisp. 185
Models and Modelling of Video Sequencesp. 192
Nonstationarity Types for VBR Video Trafficp. 192
Model of the Video Traffic Scene Changing Based on the Shiffing Level Processp. 197
Video Traffic Models in the Limits of the Separate Scenep. 200
Fractal Autoregressive Models of p-Orderp. 203
MPEG Data Modelling Using I, P and B Frames Statisticsp. 206
ON/OFF Model of the Video Sequencesp. 207
Self-Similar Norros Modelp. 207
Hurst Exponent Dependence on Np. 207
Referencesp. 208
Self-Similarity of Telecommunication Networks Trafficp. 211
Problem Statementp. 211
Self-Similarity and 'Heavy Tails' in LAN Trafficp. 212
Experimental Investigations of the Ethernet Traffic Self-Similar Structurep. 213
Estimation of Testing Resultsp. 213
Self-Similarity of WAN Trafficp. 218
WAN Traffic at the Application Levelp. 218
Some Limiting Results for Aggregated WAN Trafficp. 219
The Statistical Analysis of WAN Traffic at the Application Levelp. 221
Multifractal Analysis of WAN Trafficp. 222
Self-Similarity of Internet Trafficp. 222
Results of Experimental Studiesp. 223
Stationarity Analysis of IP Trafficp. 223
Nonstationarity of Internet Trafficp. 230
Scaling Analysisp. 232
Multilevel ON/OFF Model of Internet Trafficp. 236
Problem Statementp. 236
Estimation of Parameters and Model Parameterizationp. 237
Parallel Buffer Structure for Active Queue Controlp. 240
Referencesp. 243
Queuing and Performance Evaluation of Telecommunication Networks under Traffic Self-Similarity Conditionsp. 247
Traffic Fractality Influence Estimate on Telecommunication Network Queuingp. 247
Monofractal Trafficp. 248
Communication System Model and the Packet Loss Probability Estimate for the Asymptotic Self-Similar Traffic Described by Pareto Distributionp. 251
Queuing Model with fractional Levy Motionp. 253
Estimate of the Effect of Traffic Multifractality Effect on Queuingp. 257
Estimate of Voice Traffic Self-Similarity Effects on the IP Networks Input Parameter Optimizationp. 261
Problem Statementp. 261
Simulation Structurep. 261
Estimate of the Traffic Self Similarity Influence on QoSp. 263
TN Input Parameter Optimization for Given QoS Characteristicsp. 266
Conclusionsp. 269
Telecommunication Network Parameters Optimization Using the Tikhonov Regularization Approachp. 269
Problem Statementp. 269
Telecommunication Network Parameter Optimization on the Basis of the Minimization of the Discrepancy Functional of QoS Characteristicsp. 271
Optimization Resultsp. 272
TN Parameter Optimization on the Basis of Tikhonov Functional Minimizationp. 274
Regularization Resultsp. 276
Conclusionsp. 281
Estimation of the Voice Traffic Self-Similarity Influence on QoS with Frame Relay Networksp. 282
Packet Delay at Transmission through the Frame Relay Networkp. 283
Frame Relay Router Modellingp. 283
Simulation Resultsp. 287
Bandwidth Prediction in Telecommunication Networksp. 291
Congestion Control of Self-Similar Trafficp. 295
Unimodal Ratio Loading/Productivityp. 297
Selecting Aggressiveness Control (SAC) Schemep. 297
Referencesp. 298
List of Symbolsp. 301
List of Acronymsp. 305
Indexp. 307
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