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Analysis of variations for self-similar processes : a stochastic calculus approach / / Ciprian A. Tudor
| Analysis of variations for self-similar processes : a stochastic calculus approach / / Ciprian A. Tudor |
| Autore | Tudor Ciprian A |
| Edizione | [1st ed. 2013.] |
| Pubbl/distr/stampa | Heidelberg ; ; New York, : Springer, c2013 |
| Descrizione fisica | 1 online resource (xi, 268 pages) |
| Disciplina | 519.23 |
| Collana | Probability and Its Applications |
| Soggetto topico |
Self-similar processes
Stochastic processes |
| ISBN | 3-319-00936-2 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Preface -- Introduction -- Part I Examples of Self-Similar Processes -- 1.Fractional Brownian Motion and Related Processes -- 2.Solutions to the Linear Stochastic Heat and Wave Equation -- 3.Non Gaussian Self-Similar Processes -- 4.Multiparameter Gaussian Processes -- Part II Variations of Self-Similar Process: Central and Non-Central Limit Theorems -- 5.First and Second Order Quadratic Variations. Wavelet-Type Variations -- 6.Hermite Variations for Self-Similar Processes -- Appendices: A.Self-Similar Processes with Stationary Increments: Basic Properties -- B.Kolmogorov Continuity Theorem -- C.Multiple Wiener Integrals and Malliavin Derivatives -- References -- Index. |
| Record Nr. | UNINA-9910735798603321 |
Tudor Ciprian A
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| Heidelberg ; ; New York, : Springer, c2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Scale invariance : self-similarity of the physical world / / Richard N. Henriksen
| Scale invariance : self-similarity of the physical world / / Richard N. Henriksen |
| Autore | Henriksen R. N. |
| Pubbl/distr/stampa | Weinheim, Germany : , : Wiley-VCH, , 2015 |
| Descrizione fisica | 1 online resource (301 p.) |
| Disciplina | 530.1595 |
| Soggetto topico |
Scaling laws (Statistical physics)
Self-similar processes Statistical mechanics |
| ISBN |
3-527-68735-1
3-527-68734-3 3-527-68733-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Cover ""; ""Contents ""; ""Preface ""; ""Acknowledgments ""; ""Introduction ""; ""Chapter 1 Arbitrary Measures of the Physical World ""; ""1.1 Similarity ""; ""1.2 Dimensional Similarity ""; ""1.3 Physical Equations and the 'Pi' Theorem ""; ""1.4 Applications of the Pi Theorem ""
""1.4.1 Plane Pendulum """"1.4.2 Pipe Flow of a Fluid ""; ""1.4.3 Steady Motion of a Rigid Object in Viscous 'Fluid' ""; ""1.4.4 Diffusion and Self-Similarity ""; ""1.4.5 Ship Wave Drag ""; ""1.4.6 Adiabatic Gas Flow ""; ""1.4.7 Time-Dependent Adiabatic Flow "" ""1.4.8 Point Explosion in a Gaseous Medium """"1.4.9 Applications in Fundamental Physics ""; ""1.4.10 Drag on a Flexible Object in Steady Motion ""; ""1.4.11 Dimensional Analysis of Mammals ""; ""1.4.12 Trees ""; ""References ""; ""Chapter 2 Lie Groups and Scaling Symmetry "" ""2.1 The Rescaling Group """"2.1.1 Rescaling Physical Objects ""; ""2.1.2 Reconciliation with the Buckingham Pi Theorem ""; ""2.1.3 Rescaling and Self-Similarity as a Lie Algebra ""; ""2.1.4 Practical Lie Self-Similarity ""; ""2.2 Familiar Physical Examples "" ""3.2.1 Self-Similar Lorentz Boost "" |
| Record Nr. | UNINA-9910131305903321 |
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Henriksen R. N.
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| Weinheim, Germany : , : Wiley-VCH, , 2015 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Scale invariance : self-similarity of the physical world / / Richard N. Henriksen
| Scale invariance : self-similarity of the physical world / / Richard N. Henriksen |
| Autore | Henriksen R. N. |
| Pubbl/distr/stampa | Weinheim, Germany : , : Wiley-VCH, , 2015 |
| Descrizione fisica | 1 online resource (301 p.) |
| Disciplina | 530.1595 |
| Soggetto topico |
Scaling laws (Statistical physics)
Self-similar processes Statistical mechanics |
| ISBN |
3-527-68735-1
3-527-68734-3 3-527-68733-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Cover ""; ""Contents ""; ""Preface ""; ""Acknowledgments ""; ""Introduction ""; ""Chapter 1 Arbitrary Measures of the Physical World ""; ""1.1 Similarity ""; ""1.2 Dimensional Similarity ""; ""1.3 Physical Equations and the 'Pi' Theorem ""; ""1.4 Applications of the Pi Theorem ""
""1.4.1 Plane Pendulum """"1.4.2 Pipe Flow of a Fluid ""; ""1.4.3 Steady Motion of a Rigid Object in Viscous 'Fluid' ""; ""1.4.4 Diffusion and Self-Similarity ""; ""1.4.5 Ship Wave Drag ""; ""1.4.6 Adiabatic Gas Flow ""; ""1.4.7 Time-Dependent Adiabatic Flow "" ""1.4.8 Point Explosion in a Gaseous Medium """"1.4.9 Applications in Fundamental Physics ""; ""1.4.10 Drag on a Flexible Object in Steady Motion ""; ""1.4.11 Dimensional Analysis of Mammals ""; ""1.4.12 Trees ""; ""References ""; ""Chapter 2 Lie Groups and Scaling Symmetry "" ""2.1 The Rescaling Group """"2.1.1 Rescaling Physical Objects ""; ""2.1.2 Reconciliation with the Buckingham Pi Theorem ""; ""2.1.3 Rescaling and Self-Similarity as a Lie Algebra ""; ""2.1.4 Practical Lie Self-Similarity ""; ""2.2 Familiar Physical Examples "" ""3.2.1 Self-Similar Lorentz Boost "" |
| Record Nr. | UNINA-9910828806903321 |
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Henriksen R. N.
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| Weinheim, Germany : , : Wiley-VCH, , 2015 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Self-similar groups / Volodymyr Nekrashevych
| Self-similar groups / Volodymyr Nekrashevych |
| Autore | Nekrashevych, Volodymyr |
| Pubbl/distr/stampa | Providence, R. I. : American Mathematical Society, c2005 |
| Descrizione fisica | xi, 231 p. : ill. ; 27 cm |
| Disciplina | 512.2 |
| Collana | Mathematical surveys and monographs, 0076-5376 ; 117 |
| Soggetto topico |
Geometric group theory
Symbolic dynamics Self-similar processes |
| ISBN | 0821838318 |
| Classificazione |
AMS 20F65
AMS 37B10 LC QA183.N45 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991001298509707536 |
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Nekrashevych, Volodymyr
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| Providence, R. I. : American Mathematical Society, c2005 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
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Self-similar processes in telecommunications / / Oleg I. Sheluhin, Sergey M. Smolskiy, Andrey V. Osin
| Self-similar processes in telecommunications / / Oleg I. Sheluhin, Sergey M. Smolskiy, Andrey V. Osin |
| Autore | Sheluhin Oleg I. |
| Pubbl/distr/stampa | Chichester, England ; , : Wiley, , c2007 |
| Descrizione fisica | 1 online resource (336 p.) |
| Disciplina |
621.382
621.382150151922 |
| Altri autori (Persone) |
SmolskiySergey M
OsinAndrey V |
| Soggetto topico |
Telecommunication systems - Mathematical models
Internetworking (Telecommunication) Self-similar processes |
| ISBN |
1-282-34615-6
9786612346156 0-470-06209-6 0-470-06210-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
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, ARMA#p; q -- 2.3.4 Fractional Autoregressive Integrated Moving Average -- (FARIMA) Process -- 2.3.5 Parametric Estimation Methods -- 2.3.6 FARIMA#p,d,q Process Synthesis -- 2.4 Fractal Point Process -- 2.4.1 Statistical Characteristics of the Point Process -- 2.4.2 Fractal Structure of FPP -- 2.4.3 Methods of FPP Formation.
2.5 Fractional Levy Motion and its Application to Network -- Traffic Modelling -- 2.5.1 Fractional Levy Motion and Its Properties -- 2.5.2 Algorithm of Fractional Levy Motion Modelling -- 2.5.3 Fractal Traffic Formation Based on FLM -- 2.6 Models of Multifractal Network Traffic -- 2.6.1 Multiplicative Cascades -- 2.6.2 Modified Estimation Method of Multifractal Functions -- 2.6.3 Generation of Traffic the Multifractal Model -- 2.7 LRD Traffic Modelling with the Help of Wavelets -- 2.8 M/G/1Model -- 2.8.1 M/G/1Model and Pareto Distribution -- 2.8.2 M/G/1Model and Log-Normal Distribution -- References -- 3 Self-Similarity of Real Time Traffic -- 3.1 Self-Similarity of Real Time Traffic Preliminaries -- 3.2 Statistical Characteristics of Telecommunication Real Time Traffic -- 3.2.1 Measurement Organization -- 3.2.2 Pattern of TN Traffic -- 3.3 Voice Traffic Characteristics -- 3.3.1 Voice Traffic Characteristics at the Call Layer -- 3.3.2 Voice Traffic Characteristics at the Packet Layer -- 3.4 Multifractal Analysis of Voice Traffic -- 3.4.1 Basics -- 3.4.2 Algorithm for the Partition Function Sm#q Calculation -- 3.4.3 Multifractal Properties of Multiplexed Voice Traffic -- 3.4.4 Multifractal Properties of Two-Component Voice Traffic -- 3.5 Mathematical Models of VoIP Traffic -- 3.5.1 Problem Statement -- 3.5.2 Voice Traffic Models at the Call Layer -- 3.5.3 Estimation of Semi-Markovian Model Parameters and the Modelling -- Results of the Voice Traffic at the Call Layer -- 3.5.4 Mathematical Models of Voice Traffic at the Packets Layer -- 3.6 Simulation of the Voice Traffic -- 3.6.1 Simulation Structure -- 3.6.2 Parameters Choice of Pareto Distributions for Voice -- Traffic Source in ns2 -- 3.6.3 Results of Separate Sources Modelling -- 3.6.4 Results of Traffic Multiplexing for the Separate -- ON/OFF Sources -- 3.7 Long-Range Dependence for the VBR-Video -- 3.7.1 Distinguished Characteristics of Video Traffic -- 3.7.2 Video Conferences -- 3.7.3 Video Broadcasting -- 3.7.4 MPEG Video Traffic. 3.7.5 Nonstationarity of VBR Video Traffic -- 3.8 Self-Similarity Analysis of Video Traffic -- 3.8.1 Video Broadcasting Wavelet Analysis -- 3.8.2 Numerical Results -- 3.8.3 Multifractal Analysis -- 3.9 Models and Modelling of Video Sequences -- 3.9.1 Nonstationarity Types for VBR Video Traffic -- 3.9.2 Model of the Video Traffic Scene Changing Based on the -- Shifting Level Process -- 3.9.3 Video Traffic Models in the Limits of the Separate Scene -- 3.9.4 Fractal Autoregressive Models of p-Order -- 3.9.5 MPEG Data Modelling Using I, P and B Frames Statistics -- 3.9.6 ON/OFF Model of the Video Sequences -- 3.9.7 Self-Similar Norros Model -- 3.9.8 Hurst Exponent Dependence on N -- References -- 4 Self-Similarity of Telecommunication Networks Traffic -- 4.1 Problem Statement -- 4.2 Self-Similarity and 'Heavy Tails' in Lan Traffic -- 4.2.1 Experimental Investigations of Ethernet Traffic Self-Similar -- Structure -- 4.2.2 Estimation of Testing Results -- 4.3 Self-Similarity of WAN Traffic -- 4.3.1 WAN Traffic at the Application Level -- 4.3.2 Some Limiting Results for Aggregated WAN Traffic -- 4.3.3 The Statistical Analysis of WAN Traffic at the -- Application Level -- 4.3.4 Multifractal Analysis of WAN Traffic -- 4.4 Self-Similarity of Internet Traffic -- 4.4.1 Results of Experimental Studies -- 4.4.2 Stationarity Analysis of IP Traffic -- 4.4.3 Nonstationarity of Internet Traffic -- 4.4.4 Scaling Analysis -- 4.5 Multilevel ON/OFF Model of Internet Traffic -- 4.5.1 Problem Statement -- 4.5.2 Estimation of Parameters and Model Parameterization -- 4.5.3 Parallel Buffer Structure for Active Queue Control -- References -- 5 Queuing and Performance Evaluation of Telecommunication -- Networks under Traffic Self-Similarity Conditions -- 5.1 Traffic Fractality Influence Estimate on Telecommunication -- Networks Queuing -- 5.1.1 Monofractal Traffic -- 5.1.2 Communication System Model and the Packet Loss Probability -- Estimate for the Asymptotic Self-Similar Traffic Described by. Pareto Distribution -- 5.1.3 Queuing Model with Fractal Levy Motion -- 5.1.4 Estimate of the Effect of Traffic Multifractality Effect on Queuing -- 5.2 Estimate of Voice Traffic Self-Similarity Effects on the iP Networks -- Input Parameter Optimization -- 5.2.1 Problem Statement -- 5.2.2 Simulation Structure -- 5.2.3 Estimate of the Traffic Self-Similarity Influence on QoS -- 5.2.4 TN input Parameter Optimization for Given QoS Characteristics -- 5.2.5 Conclusions -- 5.3 Telecomminication Network Parameters Optimization Using the Tikhonov -- Regularization Approach -- 5.3.1 Problem Statement -- 5.3.2 Telecommunication Network Parameter Optimization on the Basis of -- the Minimization of the Discrepancy Functional of QoS Parameters -- 5.3.3 Optimization Results -- 5.3.4 TN Parameter Optimization on the Basis of Tikhonov -- Functional Minimization -- 5.3.5 Regularization Results -- 5.3.6 Conclusions -- 5.4 Estimation of the Voice Traffic Self-Similarity Influence on QoS -- with Frame Relay Networks -- 5.4.1 Pocket Delay at Transmission through the Frame Relay Network -- 5.4.2 Frame Relay Router Modelling -- 5.4.3 Simulation Results -- 5.5 Bandwidth Prediction in Telecommunication Networks -- 5.6 Congestion Control of Self-Similar Traffic -- 5.6.1 Unimodal Ratio Loading/Productivity -- 5.6.2 Selecting Aggressiveness Control (SAC) Scheme -- References -- Appendix A List of Symbols -- Appendix B List of Acronyms -- Index. |
| Record Nr. | UNINA-9910143701603321 |
|
Sheluhin Oleg I.
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||
| Chichester, England ; , : Wiley, , c2007 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Self-similar processes in telecommunications / / Oleg I. Sheluhin, Sergey M. Smolskiy, Andrey V. Osin
| Self-similar processes in telecommunications / / Oleg I. Sheluhin, Sergey M. Smolskiy, Andrey V. Osin |
| Autore | Sheluhin Oleg I. |
| Pubbl/distr/stampa | Chichester, England ; , : Wiley, , c2007 |
| Descrizione fisica | 1 online resource (336 p.) |
| Disciplina |
621.382
621.382150151922 |
| Altri autori (Persone) |
SmolskiySergey M
OsinAndrey V |
| Soggetto topico |
Telecommunication systems - Mathematical models
Internetworking (Telecommunication) Self-similar processes |
| ISBN |
1-282-34615-6
9786612346156 0-470-06209-6 0-470-06210-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
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, ARMA#p; q -- 2.3.4 Fractional Autoregressive Integrated Moving Average -- (FARIMA) Process -- 2.3.5 Parametric Estimation Methods -- 2.3.6 FARIMA#p,d,q Process Synthesis -- 2.4 Fractal Point Process -- 2.4.1 Statistical Characteristics of the Point Process -- 2.4.2 Fractal Structure of FPP -- 2.4.3 Methods of FPP Formation.
2.5 Fractional Levy Motion and its Application to Network -- Traffic Modelling -- 2.5.1 Fractional Levy Motion and Its Properties -- 2.5.2 Algorithm of Fractional Levy Motion Modelling -- 2.5.3 Fractal Traffic Formation Based on FLM -- 2.6 Models of Multifractal Network Traffic -- 2.6.1 Multiplicative Cascades -- 2.6.2 Modified Estimation Method of Multifractal Functions -- 2.6.3 Generation of Traffic the Multifractal Model -- 2.7 LRD Traffic Modelling with the Help of Wavelets -- 2.8 M/G/1Model -- 2.8.1 M/G/1Model and Pareto Distribution -- 2.8.2 M/G/1Model and Log-Normal Distribution -- References -- 3 Self-Similarity of Real Time Traffic -- 3.1 Self-Similarity of Real Time Traffic Preliminaries -- 3.2 Statistical Characteristics of Telecommunication Real Time Traffic -- 3.2.1 Measurement Organization -- 3.2.2 Pattern of TN Traffic -- 3.3 Voice Traffic Characteristics -- 3.3.1 Voice Traffic Characteristics at the Call Layer -- 3.3.2 Voice Traffic Characteristics at the Packet Layer -- 3.4 Multifractal Analysis of Voice Traffic -- 3.4.1 Basics -- 3.4.2 Algorithm for the Partition Function Sm#q Calculation -- 3.4.3 Multifractal Properties of Multiplexed Voice Traffic -- 3.4.4 Multifractal Properties of Two-Component Voice Traffic -- 3.5 Mathematical Models of VoIP Traffic -- 3.5.1 Problem Statement -- 3.5.2 Voice Traffic Models at the Call Layer -- 3.5.3 Estimation of Semi-Markovian Model Parameters and the Modelling -- Results of the Voice Traffic at the Call Layer -- 3.5.4 Mathematical Models of Voice Traffic at the Packets Layer -- 3.6 Simulation of the Voice Traffic -- 3.6.1 Simulation Structure -- 3.6.2 Parameters Choice of Pareto Distributions for Voice -- Traffic Source in ns2 -- 3.6.3 Results of Separate Sources Modelling -- 3.6.4 Results of Traffic Multiplexing for the Separate -- ON/OFF Sources -- 3.7 Long-Range Dependence for the VBR-Video -- 3.7.1 Distinguished Characteristics of Video Traffic -- 3.7.2 Video Conferences -- 3.7.3 Video Broadcasting -- 3.7.4 MPEG Video Traffic. 3.7.5 Nonstationarity of VBR Video Traffic -- 3.8 Self-Similarity Analysis of Video Traffic -- 3.8.1 Video Broadcasting Wavelet Analysis -- 3.8.2 Numerical Results -- 3.8.3 Multifractal Analysis -- 3.9 Models and Modelling of Video Sequences -- 3.9.1 Nonstationarity Types for VBR Video Traffic -- 3.9.2 Model of the Video Traffic Scene Changing Based on the -- Shifting Level Process -- 3.9.3 Video Traffic Models in the Limits of the Separate Scene -- 3.9.4 Fractal Autoregressive Models of p-Order -- 3.9.5 MPEG Data Modelling Using I, P and B Frames Statistics -- 3.9.6 ON/OFF Model of the Video Sequences -- 3.9.7 Self-Similar Norros Model -- 3.9.8 Hurst Exponent Dependence on N -- References -- 4 Self-Similarity of Telecommunication Networks Traffic -- 4.1 Problem Statement -- 4.2 Self-Similarity and 'Heavy Tails' in Lan Traffic -- 4.2.1 Experimental Investigations of Ethernet Traffic Self-Similar -- Structure -- 4.2.2 Estimation of Testing Results -- 4.3 Self-Similarity of WAN Traffic -- 4.3.1 WAN Traffic at the Application Level -- 4.3.2 Some Limiting Results for Aggregated WAN Traffic -- 4.3.3 The Statistical Analysis of WAN Traffic at the -- Application Level -- 4.3.4 Multifractal Analysis of WAN Traffic -- 4.4 Self-Similarity of Internet Traffic -- 4.4.1 Results of Experimental Studies -- 4.4.2 Stationarity Analysis of IP Traffic -- 4.4.3 Nonstationarity of Internet Traffic -- 4.4.4 Scaling Analysis -- 4.5 Multilevel ON/OFF Model of Internet Traffic -- 4.5.1 Problem Statement -- 4.5.2 Estimation of Parameters and Model Parameterization -- 4.5.3 Parallel Buffer Structure for Active Queue Control -- References -- 5 Queuing and Performance Evaluation of Telecommunication -- Networks under Traffic Self-Similarity Conditions -- 5.1 Traffic Fractality Influence Estimate on Telecommunication -- Networks Queuing -- 5.1.1 Monofractal Traffic -- 5.1.2 Communication System Model and the Packet Loss Probability -- Estimate for the Asymptotic Self-Similar Traffic Described by. Pareto Distribution -- 5.1.3 Queuing Model with Fractal Levy Motion -- 5.1.4 Estimate of the Effect of Traffic Multifractality Effect on Queuing -- 5.2 Estimate of Voice Traffic Self-Similarity Effects on the iP Networks -- Input Parameter Optimization -- 5.2.1 Problem Statement -- 5.2.2 Simulation Structure -- 5.2.3 Estimate of the Traffic Self-Similarity Influence on QoS -- 5.2.4 TN input Parameter Optimization for Given QoS Characteristics -- 5.2.5 Conclusions -- 5.3 Telecomminication Network Parameters Optimization Using the Tikhonov -- Regularization Approach -- 5.3.1 Problem Statement -- 5.3.2 Telecommunication Network Parameter Optimization on the Basis of -- the Minimization of the Discrepancy Functional of QoS Parameters -- 5.3.3 Optimization Results -- 5.3.4 TN Parameter Optimization on the Basis of Tikhonov -- Functional Minimization -- 5.3.5 Regularization Results -- 5.3.6 Conclusions -- 5.4 Estimation of the Voice Traffic Self-Similarity Influence on QoS -- with Frame Relay Networks -- 5.4.1 Pocket Delay at Transmission through the Frame Relay Network -- 5.4.2 Frame Relay Router Modelling -- 5.4.3 Simulation Results -- 5.5 Bandwidth Prediction in Telecommunication Networks -- 5.6 Congestion Control of Self-Similar Traffic -- 5.6.1 Unimodal Ratio Loading/Productivity -- 5.6.2 Selecting Aggressiveness Control (SAC) Scheme -- References -- Appendix A List of Symbols -- Appendix B List of Acronyms -- Index. |
| Record Nr. | UNINA-9910829875703321 |
|
Sheluhin Oleg I.
|
||
| Chichester, England ; , : Wiley, , c2007 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Self-similar processes in telecommunications / / Oleg I. Sheluhin, Sergey M. Smolskiy, Andrey V. Osin
| Self-similar processes in telecommunications / / Oleg I. Sheluhin, Sergey M. Smolskiy, Andrey V. Osin |
| Autore | Sheluhin O. I (Oleg Ivanovich) |
| Pubbl/distr/stampa | Chichester, England ; ; Hoboken, NJ, : Wiley, c2007 |
| Descrizione fisica | 1 online resource (336 p.) |
| Disciplina |
621.382
621.382150151922 |
| Altri autori (Persone) |
SmolskiySergey M
OsinAndrey V |
| Soggetto topico |
Telecommunication systems - Mathematical models
Internetworking (Telecommunication) Self-similar processes |
| ISBN |
9786612346156
9781282346154 1282346156 9780470062098 0470062096 9780470062104 047006210X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
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, ARMA#p; q -- 2.3.4 Fractional Autoregressive Integrated Moving Average -- (FARIMA) Process -- 2.3.5 Parametric Estimation Methods -- 2.3.6 FARIMA#p,d,q Process Synthesis -- 2.4 Fractal Point Process -- 2.4.1 Statistical Characteristics of the Point Process -- 2.4.2 Fractal Structure of FPP -- 2.4.3 Methods of FPP Formation.
2.5 Fractional Levy Motion and its Application to Network -- Traffic Modelling -- 2.5.1 Fractional Levy Motion and Its Properties -- 2.5.2 Algorithm of Fractional Levy Motion Modelling -- 2.5.3 Fractal Traffic Formation Based on FLM -- 2.6 Models of Multifractal Network Traffic -- 2.6.1 Multiplicative Cascades -- 2.6.2 Modified Estimation Method of Multifractal Functions -- 2.6.3 Generation of Traffic the Multifractal Model -- 2.7 LRD Traffic Modelling with the Help of Wavelets -- 2.8 M/G/1Model -- 2.8.1 M/G/1Model and Pareto Distribution -- 2.8.2 M/G/1Model and Log-Normal Distribution -- References -- 3 Self-Similarity of Real Time Traffic -- 3.1 Self-Similarity of Real Time Traffic Preliminaries -- 3.2 Statistical Characteristics of Telecommunication Real Time Traffic -- 3.2.1 Measurement Organization -- 3.2.2 Pattern of TN Traffic -- 3.3 Voice Traffic Characteristics -- 3.3.1 Voice Traffic Characteristics at the Call Layer -- 3.3.2 Voice Traffic Characteristics at the Packet Layer -- 3.4 Multifractal Analysis of Voice Traffic -- 3.4.1 Basics -- 3.4.2 Algorithm for the Partition Function Sm#q Calculation -- 3.4.3 Multifractal Properties of Multiplexed Voice Traffic -- 3.4.4 Multifractal Properties of Two-Component Voice Traffic -- 3.5 Mathematical Models of VoIP Traffic -- 3.5.1 Problem Statement -- 3.5.2 Voice Traffic Models at the Call Layer -- 3.5.3 Estimation of Semi-Markovian Model Parameters and the Modelling -- Results of the Voice Traffic at the Call Layer -- 3.5.4 Mathematical Models of Voice Traffic at the Packets Layer -- 3.6 Simulation of the Voice Traffic -- 3.6.1 Simulation Structure -- 3.6.2 Parameters Choice of Pareto Distributions for Voice -- Traffic Source in ns2 -- 3.6.3 Results of Separate Sources Modelling -- 3.6.4 Results of Traffic Multiplexing for the Separate -- ON/OFF Sources -- 3.7 Long-Range Dependence for the VBR-Video -- 3.7.1 Distinguished Characteristics of Video Traffic -- 3.7.2 Video Conferences -- 3.7.3 Video Broadcasting -- 3.7.4 MPEG Video Traffic. 3.7.5 Nonstationarity of VBR Video Traffic -- 3.8 Self-Similarity Analysis of Video Traffic -- 3.8.1 Video Broadcasting Wavelet Analysis -- 3.8.2 Numerical Results -- 3.8.3 Multifractal Analysis -- 3.9 Models and Modelling of Video Sequences -- 3.9.1 Nonstationarity Types for VBR Video Traffic -- 3.9.2 Model of the Video Traffic Scene Changing Based on the -- Shifting Level Process -- 3.9.3 Video Traffic Models in the Limits of the Separate Scene -- 3.9.4 Fractal Autoregressive Models of p-Order -- 3.9.5 MPEG Data Modelling Using I, P and B Frames Statistics -- 3.9.6 ON/OFF Model of the Video Sequences -- 3.9.7 Self-Similar Norros Model -- 3.9.8 Hurst Exponent Dependence on N -- References -- 4 Self-Similarity of Telecommunication Networks Traffic -- 4.1 Problem Statement -- 4.2 Self-Similarity and 'Heavy Tails' in Lan Traffic -- 4.2.1 Experimental Investigations of Ethernet Traffic Self-Similar -- Structure -- 4.2.2 Estimation of Testing Results -- 4.3 Self-Similarity of WAN Traffic -- 4.3.1 WAN Traffic at the Application Level -- 4.3.2 Some Limiting Results for Aggregated WAN Traffic -- 4.3.3 The Statistical Analysis of WAN Traffic at the -- Application Level -- 4.3.4 Multifractal Analysis of WAN Traffic -- 4.4 Self-Similarity of Internet Traffic -- 4.4.1 Results of Experimental Studies -- 4.4.2 Stationarity Analysis of IP Traffic -- 4.4.3 Nonstationarity of Internet Traffic -- 4.4.4 Scaling Analysis -- 4.5 Multilevel ON/OFF Model of Internet Traffic -- 4.5.1 Problem Statement -- 4.5.2 Estimation of Parameters and Model Parameterization -- 4.5.3 Parallel Buffer Structure for Active Queue Control -- References -- 5 Queuing and Performance Evaluation of Telecommunication -- Networks under Traffic Self-Similarity Conditions -- 5.1 Traffic Fractality Influence Estimate on Telecommunication -- Networks Queuing -- 5.1.1 Monofractal Traffic -- 5.1.2 Communication System Model and the Packet Loss Probability -- Estimate for the Asymptotic Self-Similar Traffic Described by. Pareto Distribution -- 5.1.3 Queuing Model with Fractal Levy Motion -- 5.1.4 Estimate of the Effect of Traffic Multifractality Effect on Queuing -- 5.2 Estimate of Voice Traffic Self-Similarity Effects on the iP Networks -- Input Parameter Optimization -- 5.2.1 Problem Statement -- 5.2.2 Simulation Structure -- 5.2.3 Estimate of the Traffic Self-Similarity Influence on QoS -- 5.2.4 TN input Parameter Optimization for Given QoS Characteristics -- 5.2.5 Conclusions -- 5.3 Telecomminication Network Parameters Optimization Using the Tikhonov -- Regularization Approach -- 5.3.1 Problem Statement -- 5.3.2 Telecommunication Network Parameter Optimization on the Basis of -- the Minimization of the Discrepancy Functional of QoS Parameters -- 5.3.3 Optimization Results -- 5.3.4 TN Parameter Optimization on the Basis of Tikhonov -- Functional Minimization -- 5.3.5 Regularization Results -- 5.3.6 Conclusions -- 5.4 Estimation of the Voice Traffic Self-Similarity Influence on QoS -- with Frame Relay Networks -- 5.4.1 Pocket Delay at Transmission through the Frame Relay Network -- 5.4.2 Frame Relay Router Modelling -- 5.4.3 Simulation Results -- 5.5 Bandwidth Prediction in Telecommunication Networks -- 5.6 Congestion Control of Self-Similar Traffic -- 5.6.1 Unimodal Ratio Loading/Productivity -- 5.6.2 Selecting Aggressiveness Control (SAC) Scheme -- References -- Appendix A List of Symbols -- Appendix B List of Acronyms -- Index. |
| Record Nr. | UNINA-9911019242903321 |
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Sheluhin O. I (Oleg Ivanovich)
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| Chichester, England ; ; Hoboken, NJ, : Wiley, c2007 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Selfsimilar processes [[electronic resource] /] / Paul Embrechts and Makoto Maejima
| Selfsimilar processes [[electronic resource] /] / Paul Embrechts and Makoto Maejima |
| Autore | Embrechts Paul <1953-> |
| Edizione | [Course Book] |
| Pubbl/distr/stampa | Princeton, N.J., : Princeton University Press, c2002 |
| Descrizione fisica | 1 online resource (123 p.) |
| Disciplina | 519.2/4 |
| Altri autori (Persone) | MaejimaMakoto |
| Collana | Princeton series in applied mathematics |
| Soggetto topico |
Distribution (Probability theory)
Self-similar processes |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-282-08759-2
9786612087592 1-4008-2510-5 1-4008-1424-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Front matter -- Contents -- Chapter 1. Introduction -- Chapter 2. Some Historical Background -- Chapter 3. Self similar Processes with Stationary Increments -- Chapter 4. Fractional Brownian Motion -- Chapter 5. Self similar Processes with Independent Increments -- Chapter 6. Sample Path Properties of Self similar Stable Processes with Stationary Increments -- Chapter 7. Simulation of Self similar Processes -- Chapter 8. Statistical Estimation -- Chapter 9. Extensions -- References -- Index |
| Record Nr. | UNINA-9910454785603321 |
|
Embrechts Paul <1953->
|
||
| Princeton, N.J., : Princeton University Press, c2002 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Selfsimilar processes [[electronic resource] /] / Paul Embrechts and Makoto Maejima
| Selfsimilar processes [[electronic resource] /] / Paul Embrechts and Makoto Maejima |
| Autore | Embrechts Paul <1953-> |
| Edizione | [Course Book] |
| Pubbl/distr/stampa | Princeton, N.J., : Princeton University Press, c2002 |
| Descrizione fisica | 1 online resource (123 p.) |
| Disciplina | 519.2/4 |
| Altri autori (Persone) | MaejimaMakoto |
| Collana | Princeton series in applied mathematics |
| Soggetto topico |
Distribution (Probability theory)
Self-similar processes |
| Soggetto non controllato |
Almost surely
Approximation Asymptotic analysis Autocorrelation Autoregressive conditional heteroskedasticity Autoregressive–moving-average model Availability Benoit Mandelbrot Brownian motion Central limit theorem Change of variables Computational problem Confidence interval Correlogram Covariance matrix Data analysis Data set Determination Fixed point (mathematics) Foreign exchange market Fractional Brownian motion Function (mathematics) Gaussian process Heavy-tailed distribution Heuristic method High frequency Inference Infimum and supremum Instance (computer science) Internet traffic Joint probability distribution Likelihood function Limit (mathematics) Linear regression Log–log plot Marginal distribution Mathematica Mathematical finance Mathematics Methodology Mixture model Model selection Normal distribution Parametric model Power law Probability theory Publication Random variable Regime Renormalization Result Riemann sum Self-similar process Self-similarity Simulation Smoothness Spectral density Square root Stable distribution Stable process Stationary process Stationary sequence Statistical inference Statistical physics Statistics Stochastic calculus Stochastic process Technology Telecommunication Textbook Theorem Time series Variance Wavelet Website |
| ISBN |
1-282-08759-2
9786612087592 1-4008-2510-5 1-4008-1424-3 |
| Classificazione | SK 820 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Front matter -- Contents -- Chapter 1. Introduction -- Chapter 2. Some Historical Background -- Chapter 3. Self similar Processes with Stationary Increments -- Chapter 4. Fractional Brownian Motion -- Chapter 5. Self similar Processes with Independent Increments -- Chapter 6. Sample Path Properties of Self similar Stable Processes with Stationary Increments -- Chapter 7. Simulation of Self similar Processes -- Chapter 8. Statistical Estimation -- Chapter 9. Extensions -- References -- Index |
| Record Nr. | UNINA-9910779907303321 |
|
Embrechts Paul <1953->
|
||
| Princeton, N.J., : Princeton University Press, c2002 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Selfsimilar processes / / Paul Embrechts and Makoto Maejima
| Selfsimilar processes / / Paul Embrechts and Makoto Maejima |
| Autore | Embrechts Paul <1953-> |
| Edizione | [Course Book] |
| Pubbl/distr/stampa | Princeton, N.J., : Princeton University Press, c2002 |
| Descrizione fisica | 1 online resource (123 p.) |
| Disciplina | 519.2/4 |
| Altri autori (Persone) | MaejimaMakoto |
| Collana | Princeton series in applied mathematics |
| Soggetto topico |
Distribution (Probability theory)
Self-similar processes |
| ISBN |
9786612087592
9781282087590 1282087592 9781400825103 1400825105 9781400814244 1400814243 |
| Classificazione | SK 820 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Front matter -- Contents -- Chapter 1. Introduction -- Chapter 2. Some Historical Background -- Chapter 3. Self similar Processes with Stationary Increments -- Chapter 4. Fractional Brownian Motion -- Chapter 5. Self similar Processes with Independent Increments -- Chapter 6. Sample Path Properties of Self similar Stable Processes with Stationary Increments -- Chapter 7. Simulation of Self similar Processes -- Chapter 8. Statistical Estimation -- Chapter 9. Extensions -- References -- Index |
| Record Nr. | UNINA-9910969630003321 |
|
Embrechts Paul <1953->
|
||
| Princeton, N.J., : Princeton University Press, c2002 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
