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
Notation and Abbreviations
What is Monte Carlo Method?
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
Network Reliability Bounds
Exponentially Distributed Lifetime
Characteristic Property of the Exponential Distribution
Exponential Jump Process
Static and Dynamic Reliability
System Description. Static Reliability
Pivotal Formula. Reliability Gradient
Definition of Border States
Gradient and Border States
Order Statistics and D-spectrum
Reminder of Basics in Order Statistics
Destruction Spectrum (D-spectrum)
Number of Minimal size Min-Cuts
Monte Carlo of Convolutions
CMC for Calculating Convolutions
Conditional Densities and Modified Algorithm
How Large is Variance Reduction Comparing to the CMC?
Importance Sampling in Monte Carlo
Estimation of FN(t) = P(τ* ≤ t)
Identically Distributed Edge Lifetimes
Examples of Using D-spectra
Applications of Turnip
Importance Measures and Spectrum
Introduction: Birnbaum Importance Measure
BIM and the Cumulative C*-spectrum
BIM and the Invariance Property
Optimal Network Synthesis
Introduction to Network Synthesis
Synthesis Based on Importance Measures
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