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Models of Network Reliability
Analysis, Combinatorics, and Monte Carlo
By Ilya
B Gertsbakh, Yoseph Shpungin
ISBN: 978-1-4398-1741-4
Binding: Hardback
Published by: CRC Press
Publication Date: 22/12/2009
Pages: 217
About the Book
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
problems are presented in the
form of efficient Monte Carlo algorithms and illustrated with numerical
examples and tables—including medium sized computer networks.
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 manual—making it ideal for self-study and practical
use.
Table of Contents
Preface
Notation and Abbreviations
What is Monte Carlo Method?
Area
Estimation
Optimal Location of Components
Reliability of a Binary System
Statistics: a Short Reminder
What is Network Reliability?
Introduction
Spanning Trees and Kruskal’s Algorithm
Introduction to Network Reliability
Multistate Networks
Network Reliability Bounds
Exponentially Distributed Lifetime
Characteristic
Property of the Exponential Distribution
Exponential Jump Process
Examples
Static and Dynamic Reliability
System
Description. Static Reliability
Dynamic Reliability
Stationary Availability
Burtin-Pittel Formula
Pivotal Formula. Reliability Gradient
Reliability Gradient
Definition of
Border States
Gradient and Border States
Order Statistics and D-spectrum
Reminder of
Basics in Order Statistics
Min-Max Calculus
Destruction Spectrum (D-spectrum)
Number of Minimal size Min-Cuts
Monte Carlo of Convolutions
CMC for
Calculating Convolutions
Analytic Approach
Conditional Densities and Modified Algorithm
Generating Bm(T)
How Large is Variance Reduction Comparing to the CMC?
Importance Sampling in Monte Carlo
Network Destruction
Introduction
Estimation of FN(t) = P(τ* ≤ t)
Unreliable Nodes
Identically Distributed Edge Lifetimes
Examples of Using D-spectra
Lomonosov’s "Turnip"
Introduction
The Turnip
Applications of Turnip
Unreliable Nodes
Importance Measures and Spectrum
Introduction: Birnbaum Importance Measure
Cumulative Spectrum
BIM and the Cumulative C*-spectrum
BIM and the Invariance Property
Examples
Optimal Network Synthesis
Introduction to Network Synthesis
"Asymptotic" Synthesis
Synthesis Based on Importance Measures
Dynamic Networks
Introduction:
Network Exit Time
Bounds on the Network Exit Time
Examples of Network Reliability
Colbourn &
Harms’ Ladder Network
Integrated Communication Network (ICN)
Appendix A: O(·)
and o(·) symbols
Appendix B: Convolution
of exponentials
Appendix C: Glossary
of D-spectra
References
Index
Each chapter includes problems
and exercises
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