Models of Network Reliability: Analysis, Combinatorics and Monte Carlo
Publishers
:
CRC Press, Boca Raton
Authors
:
Ilya B. Gertsbakh and Yoseph Shpungin
Title
:
Models of Network Reliability: Analysis, Combinatorics and Monte Carlo
Year of Publication
:
2010
Pages
:
203
ISBN
:
9781439817414
Reviewer
:
Krishna B. Misra
Status
:
Review published in IJPE, Vol. 7, No.3, May 2011, p.262
The book consists of the following 13 chapters followed by Authors’ Preface and Notation and Abbreviations:
Preface
04 Pages
Notation and Abbreviations
02 Pages
Chapter 1
What is Monte Carlo Method?
20 Pages
Chapter 2
What is Network Reliability?
28 Pages
Chapter3
Exponentially Distributed Lifetme
10 Pages
Chapter 4
Static and Dynamic Reliability
16 Pages
Chapter 5
Reliability Gradient
06 Pages
Chapter 6
Order Statistics and D-spectrum
09 Pages
Chapter 7
Monte Carlo of Convolutions
09 Pages
Chapter 8
Network Destruction
17 Pages
Chapter 9
Lomonosov’s “Turnip”
19 Pages
Chapter 10
Importance Measures and Spectrum
13 Pages
Chapter 11
Optimal Network Synthesis
12 Pages
Chapter 12
Dynamic Networks
06 Pages
Chapter 13
Examples of Network Reliability
14 Pages
Appendix A: O(.) and 0(.) Symbols
02 Pages
Appendix B: Convolution of exponentials
02 Pages
Appendix C: Glossary of D-spectra
06 Pages
References
04 Pages
Index
05 Pages
It is concise and compact book on the subject of how to compute k-terminal reliability (probability that k-terminals remain connected) of a given communication network, where the edges or links can fail. This is a combinatorial problem and using standard analytical techniques, even a small well-connected (where each node is connected to the other nodes of the network) a two-state network of 10 nodes may require 245 number of states to reckon with. The reliability computation with such a large number of states is computationally unwieldy if not impossible. So the authors suggest the most practical approach of computing system reliability using Monte Carlo simulation. Another reason for using Monte Carlo approach appears in the fact that the availability of repairable system elements can be used in place of reliability (of non-repairable elements) without much hassle. This assumed interchangeability of approach is reflected in all the chapters of the book. 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. This 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 in the book. Approximate approaches, wherever essential, have been dealt with necessary explanation. In another generalization, the authors have considered that network nodes can fail, in addition to allowing edges to be unreliable. An indication to multi mode failure analysis is also indicated.
The students and teachers pursuing reliability of communication reliability will find this book of interest. In general, the book would be very useful for reliability engineers and those dealing with design of communication networks would find it highly indispensable.
is connected to the other nodes of the network) a two-state network of 10 nodes may require 245 number of states to reckon with. The reliability computation with such a large number of states is computationally unwieldy if not impossible. So the authors suggest the most practical approach of computing system reliability using Monte Carlo simulation. Another reason for using Monte Carlo approach appears in the fact that the availability of repairable system elements can be used in place of reliability (of non-repairable elements) without much hassle. This assumed interchangeability of approach is reflected in all the chapters of the book. 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. This 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 in the book. Approximate approaches, wherever essential, have been dealt with necessary explanation. In another generalization, the authors have considered that network nodes can fail, in addition to allowing edges to be unreliable. An indication to multi mode failure analysis is also indicated.