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Fractal Teletraffic Modeling and Delay Bounds in Computer Communications [Kõva köide]

  • Formaat: Hardback, 220 pages, kõrgus x laius: 229x152 mm, kaal: 172 g, 29 Tables, black and white; 42 Line drawings, black and white; 42 Illustrations, black and white
  • Ilmumisaeg: 03-May-2022
  • Kirjastus: CRC Press
  • ISBN-10: 1032212861
  • ISBN-13: 9781032212869
Teised raamatud teemal:
Fractal Teletraffic Modeling and Delay Bounds in Computer CommunicationsSuurem pilt
  • Formaat: Hardback, 220 pages, kõrgus x laius: 229x152 mm, kaal: 172 g, 29 Tables, black and white; 42 Line drawings, black and white; 42 Illustrations, black and white
  • Ilmumisaeg: 03-May-2022
  • Kirjastus: CRC Press
  • ISBN-10: 1032212861
  • ISBN-13: 9781032212869
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781032212869.html
Märksõnad:
By deploying time series analysis, Fourier transform, functional analysis, min-plus convolution, and fractional order systems and noise, this book proposes fractal traffic modeling and computations of delay bounds, aiming to improve the quality of service in computer communication networks.

As opposed to traditional studies of teletraffic delay bounds, the author proposes a novel fractional noise, the generalized fractional Gaussian noise (gfGn) approach, and introduces a new fractional noise, generalized Cauchy (GC) process for traffic modeling.

Researchers and graduates in computer science, applied statistics, and applied mathematics will find this book beneficial.

Ming Li, PhD, is a professor at Ocean College, Zhejiang University, and the East China Normal University. He has been an active contributor for many years to the fields of computer communications, applied mathematics and statistics, particularly network traffic modeling, fractal time series, and fractional oscillations. He has authored more than 200 articles and 5 monographs on the subjects. He was identified as the Most Cited Chinese Researcher by Elsevier in 20142020. Professor Li was recognized as a top 100,000 scholar in all fields in 20192020 and a top 2% scholar in the field of Numerical and Computational Mathematics in 2021 by Prof. John P. A. Ioannidis, Stanford University.
Preface xiii
Acknowledgments xv
Author xvii
Chapter 1 Time Series
1(16)
1.1 Random Processes
1(2)
1.2 Ergodicity
3(1)
1.3 Probability Density Function
3(4)
1.3.1 PDF of Brownian Motion
4(1)
1.3.2 Gaussian Distribution
5(1)
1.3.3 Poisson Distribution
5(1)
1.3.4 Cauchy Distribution
6(1)
1.4 Correlation Functions
7(5)
1.4.1 Auto-Correlation Functions
7(2)
1.4.2 Auto-Covariance Functions
9(1)
1.4.3 Cross-Correlation Functions
10(1)
1.4.4 Cross-Covariance Functions
11(1)
1.5 Power Spectra
12(2)
1.5.1 Power Auto-Spectrum Density Functions
12(1)
1.5.2 Power Cross-Spectrum Density Functions
13(1)
1.6 White Noise
14(1)
1.7 Random Functions of Interest in Traffic Theory
14(3)
References
15(2)
Chapter 2 Fourier Transform
17(32)
2.1 Basic in Fourier Transform
17(4)
2.2 Delta Function
21(8)
2.3 Nascent Delta Functions
29(1)
2.4 Basic Properties of Fourier Transform
30(12)
2.5 Convolution
42(7)
References
47(2)
Chapter 3 Applied Functional
49(26)
3.1 Linear Spaces
49(3)
3.1.1 Notion of Linear Spaces
49(1)
3.1.2 Isomorphism of Linear Spaces
50(1)
3.1.3 Subspaces and Affine Manifold
50(1)
3.1.4 Convex Sets
51(1)
3.2 Metric Spaces
52(4)
3.2.1 Concept of Metric Spaces
52(2)
3.2.2 Limit in Metric Spaces
54(1)
3.2.3 Balls Viewed from Metric Spaces
54(2)
3.2.4 Postscript
56(1)
3.3 Linear Normed Spaces
56(5)
3.3.1 Notion of Norm and Normed Spaces
56(1)
3.3.2 Norms
57(2)
3.3.3 Equivalence of Norms
59(2)
3.3.4 Equivalence of Linear Normed Spaces
61(1)
3.4 Banach Spaces
61(5)
3.4.1 Concept of Banach Spaces
61(1)
3.4.2 Completeness
62(1)
3.4.3 Series in Banach Spaces
63(1)
3.4.4 Separable Banach Spaces and Completion of Spaces
64(2)
3.5 Hubert Spaces
66(5)
3.5.1 Inner Product Spaces
66(1)
3.5.1.1 Concept of Inner Product Spaces
66(2)
3.5.1.2 Orthogonality
68(1)
3.5.1.3 Continuity
68(1)
3.5.2 Hilbert Spaces
69(2)
3.6 Bounded Linear Operators
71(4)
References
73(2)
Chapter 4 Min-Plus Convolution
75(20)
4.1 Conventional Convolution
75(7)
4.2 Min-Plus Convolution
82(3)
4.3 Identity in the Min-Plus Convolution
85(1)
4.4 Problem Statements
85(2)
4.5 Existence of Min-Plus De-Convolution
87(4)
4.5.1 Preliminaries
87(2)
4.5.2 Proof of Existence
89(2)
4.6 The Condition of the Existence Of Min-Plus De-Convolution
91(1)
4.7 Representation of the Identity In Min-Plus Convolution
91(4)
References
93(2)
Chapter 5 Noise and Systems of Fractional Order
95(14)
5.1 Derivatives and Integrals of Fractional Order
95(5)
5.2 Mikusinski Operator of Fractional Order
100(1)
5.3 Fractional Derivatives: A Convolution View
101(2)
5.4 Fractional Order Delta Function
103(1)
5.5 Linear Systems Driven By Fractional Noise
104(1)
5.6 Fractional Systems Driven By Non-Fractional Noise
104(1)
5.7 Fractional Systems Driven By Fractional Noise
105(4)
References
105(4)
Chapter 6 Fractional Gaussian Noise and Traffic Modeling
109(18)
6.1 Fractional Gaussian Noise
109(3)
6.2 Fractional Gaussian Noise In Traffic Modeling
112(7)
6.3 Approximation Of The Acf Of Fractional Gaussian Noise
119(2)
6.4 Fractal Dimension Of Fractional Gaussian Noise
121(2)
6.5 Problem Statements
123(4)
References
124(3)
Chapter 7 Generalized Fractional Gaussian Noise and Traffic Modeling
127(18)
7.1 Generalized Fractional Gaussian Noise
128(4)
7.2 Traffic Modeling Using Generalized Fractional Gaussian Noise
132(10)
7.3 Approximation Of The Acf Of Generalized Fractional Gaussian Noise
142(1)
7.4 Fractal Dimension Of Generalized Fractional Gaussian Noise
143(2)
References
144(1)
Chapter 8 Generalized Cauchy Process and Traffic Modeling
145(20)
8.1 Meaning Of Generalized Cauchy Process In The Book
146(1)
8.2 Historical View
147(1)
8.3 GC Process
147(5)
8.4 Traffic Modeling Using The GC Process
152(13)
References
162(3)
Chapter 9 Traffic Bound of Generalized Cauchy Type
165(12)
9.1 Problem Statements and Research Aim
166(2)
9.2 Upper Bound of the Generalized Cauchy Process
168(4)
9.3 Discussions
172(5)
References
174(3)
Chapter 10 Fractal Traffic Delay Bounds
177(12)
10.1 Background
177(5)
10.2 Fractal Delay Bounds
182(2)
10.2.1 Fractal Delay Bound 1
182(1)
10.2.2 Fractal Delay Bound 2
182(1)
10.2.3 Fractal Delay Bound 3
183(1)
10.2.4 Fractal Delay Bound 4
183(1)
10.3 Discussion
184(5)
References
185(4)
Chapter 11 Computations of Scale Factors
189(22)
11.1 Background
189(4)
11.2 Problem Statement
193(2)
11.3 Research Thoughts For Problem Solving
195(1)
11.3.1 Ideal
195(1)
11.3.2 Idea 2
195(1)
11.4 Results
195(5)
11.4.1 Computation Formulas of r and a
195(3)
11.4.2 Asymptotic Computation Formulas of r and a
198(2)
11.5 Case Study
200(2)
11.5.1 Traffic Data
200(1)
11.5.2 Computations of r0min and a-1∞min of Traffic Traces
200(1)
11.5.2.1 Computations of σ and ρ of Traffic Traces
201(1)
11.5.2.2 Values of r0min and a-1∞min of Traffic Traces
201(1)
11.6 APPLICATIONS
202(4)
11.6.1 Physical Meaning of Asymptotic Scale Factors
202(1)
11.6.2 Applications
202(1)
11.6.2.1 Approximations of Traffic Bound
202(1)
11.6.2.2 Applications to Fractal Delay Bounds
203(3)
11.7 Concluding Remarks
206(5)
References
206(5)
Chapter 12 Postscript
211(6)
12.1 Local Versus Global Of Fractal Time Series
211(2)
12.2 Local Versus Global Of Traffic Time Series
213(1)
12.3 Problem
213(4)
References
214(3)
Index 217
Ming Li, PhD, is a professor at Ocean College, Zhejiang University, as well as at the East China Normal University. He has been an active contributor for many years to the fields of computer communications, applied mathematics and statistics,particularly network traffic modeling, fractal time series, and fractional oscillations. He has authored more than 200 articles and 5 monographs on the subjects. He was identified as the Most Cited Chinese Researcher by Elsevier in 20142020. Professor Li was recognized as a top 100,000 scholar in all fields in 20192020 and a top 2% scholar in the field of Numerical and Computational Mathematics in 2021 by Prof. John P. A. Ioannidis, Stanford University. (https://orcid.org/my-orcid?orcid=0000-0002-2725-353X)