Models of Network Reliability: Analysis, Combinatorics, and Monte Carlo, 1st Edition (Hardback) book cover

Models of Network Reliability

Analysis, Combinatorics, and Monte Carlo, 1st Edition

By Ilya B. Gertsbakh, Yoseph Shpungin

CRC Press

217 pages | 48 B/W Illus.

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Hardback: 9781439817414
pub: 2009-12-22
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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 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.


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

Table of Contents


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?


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


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


Estimation of FN(t) = P(τ* ≤ t)

Unreliable Nodes

Identically Distributed Edge Lifetimes

Examples of Using D-spectra

Lomonosov’s "Turnip"


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


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



Each chapter includes problems and exercises

About the Authors

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.

Subject Categories

BISAC Subject Codes/Headings:
COMPUTERS / Computer Engineering
MATHEMATICS / Combinatorics
TECHNOLOGY & ENGINEERING / Operations Research