Gertsbakh / Shpungin Models of Network Reliability

Analysis, Combinatorics, and Monte Carlo
1. Auflage 2011
ISBN: 978-1-4398-1742-1
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 217 Seiten

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—including medium-sized computer networks—are 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 manual—making it ideal for self-study and practical use.

Zielgruppe

Software engineering, operations research, industrial engineering, and reliability engineering students, researchers, and engineers.

Autoren/Hrsg.

Gertsbakh, Ilya B.

Shpungin, Yoseph

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Diskrete Mathematik, Kombinatorik
• Mathematik | Informatik Mathematik Operations Research
• Wirtschaftswissenschaften Betriebswirtschaft Unternehmensforschung
• Mathematik | Informatik EDV | Informatik Technische Informatik

Inhaltsverzeichnis

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(t* = 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

Über Autor(innen)

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.