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.
Ilya B. Gertsbakh
, Yoseph Shpungin
CRC Press Inc
Country of Publication:
22 December 2009
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) 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
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.
Reviews for Models of Network Reliability: Analysis, Combinatorics, and Monte Carlo
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