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E-raamat: Models of Network Reliability: Analysis, Combinatorics, and Monte Carlo

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  • Formaat: 217 pages
  • Ilmumisaeg: 19-Apr-2016
  • Kirjastus: CRC Press Inc
  • Keel: eng
  • ISBN-13: 9781439817421
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Models of Network Reliability: Analysis, Combinatorics, and Monte CarloSuurem pilt
  • Formaat: 217 pages
  • Ilmumisaeg: 19-Apr-2016
  • Kirjastus: CRC Press Inc
  • Keel: eng
  • ISBN-13: 9781439817421
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Unique in its approach, Models of Network Reliability: Analysis, Combinatorics, and Monte Carlo provides a brief introduction to Monte Carlo methods along with a concise exposition of reliability theory ideas. From there, the text investigates a collection of principal network reliability models, such as terminal connectivity for networks with unreliable edges and/or nodes, network lifetime distribution in the process of its destruction, network stationary behavior for renewable components, importance measures of network elements, reliability gradient, and network optimal reliability synthesis.





Solutions to most principal network reliability problemsincluding medium-sized computer networksare presented in the form of efficient Monte Carlo algorithms and illustrated with numerical examples and tables. Written by reliability experts with significant teaching experience, this reader-friendly text is an excellent resource for software engineering, operations research, industrial engineering, and reliability engineering students, researchers, and engineers.





Stressing intuitive explanations and providing detailed proofs of difficult statements, this self-contained resource includes a wealth of end-of-chapter exercises, numerical examples, tables, and offers a solutions manualmaking it ideal for self-study and practical use.

Arvustused

The 13 chapters and three appendixes make the material accessible to readers with a basic background in reliability. ... Formal proofs are minimally presented, the methods are widely supported by examples and exercises, and guidelines for developing computer programs are provided. -Ron S. Kenett, KPA, Raanana, Israel, in Quality Progress ... a concise and compact book on the subject of how to compute k-terminal reliability of a given communication network, where the edges or links can fail. ... To make a beginner understand the subject matter, the treatment in a chapter starts with examples and leads a reader to the definitions and theorems that are incidental to the explanation of an approach. ... helps in understanding the intricacies involved in the problem of computing network reliability. The concept of spanning trees is used to ensure connectivity of nodes of interest. Other measures of interest in reliability of networks such as component criticality and Birnbaum Importance are also discussed ... students and teachers pursuing reliability of communication reliability will find this book of interest. ...very useful for reliability engineers and those dealing with design of communication networks ... . -Krishna B. Misra, in Performability Engineering, May 2011, Vol. 7, No. 3

Preface xi
Notation and Abbreviations xv
What is Monte Carlo Method?
1(20)
Area Estimation
1(2)
Optimal Location of Components
3(3)
Reliability of a Binary System
6(1)
Statistics: a Short Reminder
7(7)
Unbiased estimators
7(2)
Variance behavior of an estimator as sample size increases
9(2)
Variance in a multinomial experiment
11(1)
Confidence interval for population mean based on the normal approximation
12(1)
Confidence interval for the binomial parameter: Poisson approximation
13(1)
Problems and Exercises
14(7)
What is Network Reliability?
21(28)
Introduction
21(5)
General description
21(1)
Networks: Topology
22(2)
Networks: Reliability perspective
24(2)
Spanning Trees and Kruskal's Algorithm
26(10)
Spanning tree: definitions, algorithms
26(4)
DSS - disjoint set structures
30(6)
Introduction to Network Reliability
36(4)
Static networks
36(4)
Dynamic networks
40(1)
Multistate Networks
40(2)
Network Reliability Bounds
42(1)
Problems and Exercises
43(6)
Exponentially Distributed Lifetime
49(10)
Characteristic Property of the Exponential Distribution
49(1)
Exponential Jump Process
50(2)
Examples
52(4)
Problems and Exercises
56(3)
Static and Dynamic Reliability
59(16)
System Description. Static Reliability
59(2)
Dynamic Reliability
61(1)
Stationary Availability
62(1)
Burtin-Pittel Formula
63(4)
Pivotal Formula. Reliability Gradient
67(3)
Problems and Exercises
70(5)
Reliability Gradient
75(6)
Definition of Border States
75(2)
Gradient and Border States
77(3)
Problems and Exercises
80(1)
Order Statistics and D-spectrum
81(10)
Reminder of Basics in Order Statistics
81(2)
Min-Max Calculus
83(1)
Destruction Spectrum (D-spectrum)
84(2)
Number of Minimal size Min-Cuts
86(2)
Problems and Exercises
88(3)
Monte Carlo of Convolutions
91(10)
CMC for Calculating Convolutions
91(1)
Analytic Approach
92(2)
Conditional Densities and Modified Algorithm
94(1)
Generating Bm(T)
95(1)
How Large is Variance Reduction Comparing to the CMC?
96(1)
Importance Sampling in Monte Carlo
97(1)
Problems and Exercises
98(3)
Network Destruction
101(18)
Introduction
101(1)
Estimation of FN(t) = P(T* ≤ t)
102(4)
Unreliable Nodes
106(1)
Identically Distributed Edge Lifetimes
107(4)
Examples of Using D-spectra
111(4)
Problems and Exercises
115(4)
Lomonosov's ``Turnip''
119(20)
Introduction
119(1)
The Turnip
120(7)
The idea of the turnip
120(1)
Artificial creation process
120(1)
The closure
121(1)
Turnip as evolution process with closure
122(5)
Applications of Turnip
127(8)
Availability Av(N)
127(1)
The mean stationary UP and DOWN periods
127(2)
Estimation of φ(N) for all-terminal connectivity
129(1)
Estimation of φ(N) for T-terminal connectivity
130(2)
Monte Carlo algorithm for the gradient
132(3)
Unreliable Nodes
135(1)
Problems and Exercises
135(4)
Importance Measures and Spectrum
139(14)
Introduction: Birnbaum Importance Measure
139(1)
Cumulative Spectrum
140(2)
BIM and the Cumulative C*-spectrum
142(3)
BIM and the Invariance Property
145(2)
Examples
147(3)
Problems and Exercises
150(3)
Optimal Network Synthesis
153(12)
Introduction to Network Synthesis
153(5)
``Asymptotic'' Synthesis
158(2)
Synthesis Based on Importance Measures
160(4)
Problems and Exercises
164(1)
Dynamic Networks
165(6)
Introduction: Network Exit Time
165(1)
Bounds on the Network Exit Time
166(5)
Examples of Network Reliability
171(14)
Colbourn & Harms' Ladder Network
171(3)
Integrated Communication Network (ICN)
174(11)
General description
174(2)
ICN reliability
176(3)
Network reinforcement
179(6)
Appendix A: O(.) and o(.) symbols 185(2)
Appendix B: Convolution of exponentials 187(2)
Appendix C: Glossary of D-spectra 189(6)
References 195(4)
Index 199
Ilya B. Gertsbakh, Professor Emeritus, Department of Mathematics, Ben Gurion University, Beer Sheva, Israel.





Dr. Gertsbakh has authored more than 70 research papers and six books. He has taught courses in Probability, Statistics, Reliability Theory, and Operations Research. His research interests include Reliability Theory, Probabilistic Methods in Operations Research, and Monte Carlo Methods.





Yoseph Shpungin, Department Head, Software Engineering Department, Shamoon College of Engineering, Beer Sheva, Israel.





Throughout his career, Dr. Shpungin has gained extensive experience in both practical and theoretical operations research and software engineering issues. He has taught courses in Probability, Statistics, Reliability, Algorithms, Databases, and Programming Languages. His field of research is Reliability Theory and Monte Carlo Methods, in which he has authored one book and many publications in international scientific journals and in the proceedings of international conferences.
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