Wiley Self-Similar Processes in Telecommunications

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. Review Foreword. About the authors. Acknowledgements. 1 Principal Concepts of Fractal Theory and Self--Similar Processes. 1.1 Fractals and Multifractals. 1.1.1 Fractal Dimension of a Set. 1.1.2 Multifractals. 1.1.3 Fractal Dimension D0 and Informational Dimension D1. 1.1.4 Legendre Transform. 1.2 Self--Similar Processes. 1.2.1 Definitions and Properties of Self--Similar Processes. 1.2.2 Multifractal Processes. 1.2.3 Long--Range and Short--Range Dependence. 1.2.4 Slowly Decaying Variance. 1.3 'Heavy Tails'. 1.3.1 Distribution with 'Heavy Tails' (DHT). 1.3.2 'Heavy Tails' Estimation. 1.4 Hurst Exponent Estimation. 1.4.1 Time Domain Methods of Hurst Exponent Estimation. 1.4.2 Frequency Domain Methods of Hurst Exponent. Estimation. 1.5 Hurst Exponent Estimation Problems. 1.5.1 Estimation Problems. 1.5.2 Nonstationarity Problems. 1.5.3 Computational Problems. 1.6 Self--Similarity Origins in Telecommunication Traffic. 1.6.1 User's Behaviour. 1.6.2 Data Generation Data Structure and Its Search. 1.6.3 Traffic Aggregation. 1.6.4 Means of Network Control. 1.6.5 Control Mechanisms based on Feedback. 1.6.6 Network Development. References. 2 Simulation Methods for Fractal Processes. 2.1 Fractional Brownian Motion. 2.1.1 RMD Algorithm for FBM Generation. 2.1.2 SRA Algorithm for FBM Generation. 2.2 Fractional Gaussian Noise. 2.2.1 FFT Algorithm for FGN Synthesis. 2.2.2 Advantages and Shortcomings of FBM/FGN Models. in Network Applications. 2.3 Regression Models of Traffic. 2.3.1 Linear Autoregressive (AR) Processes. 2.3.2 Processes of Moving Average (MA). 2.3.3 Autoregressive Models of Moving Average, ARMAethp; qT. 2.3.4 Fractional Autoregressive Integra