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Detailed review of: 

Network Reliability and Resilience





Springer, Heidelberg




Ilya Gertsbakh and Yoseph Shpungin 




Network Reliability and Resilience


Year of Publication














Krishna B. Misra




Review published in IJPE, Vol. 8, No.3, May 2012, p.299. 


The book consists of only 2 chapters followed by Authors' Preface, Notation and Abbreviations:


Table of Contents


03 pages

Notation and Abbreviations 02 Pages

Chapter 1


50 Pages

Chapter 2


21 Pages


01 Page



03 Pages

This is not a book of usual size but a booklet of 75 pages and basically complements the authors' earlier book, Models of Network Reliability: Analysis, Combinatorics and Monte Carlo, published by CRC Press, Boca Raton, U.S.A. in 2009, whose review was published in the IJPE in Vol.7, No. 3, May 2011, on page 262. Whereas the authors' earlier had confined itself only to the two-state modeling of a system, the present book extends reliability computation to multi-state systems and can consider degraded state of a component of system. The

978-3-642-22373-0tool that the authors have made use of handling such systems is multi-dimensional D-spectrum and marginal D-spectrum. D-spectrum is basically a multi-dimensional discrete probability distribution. The D-spectrum is combinatorial in nature and depends solely on the system structure. Since combinatorial reliability computation often results in a large number of states and is computationally unwieldy if not impossible. Here, the authors suggest the use of Monte Carlo simulation. D-spectrum approach allows an efficient Monte Carlo procedure by approximating system D-spectrum to compute system reliability and its resilience. Usually it is not easy to compute network component importance, more specifically the Birnbaum's Importance factor which involves computation of a gradient. However a modification of the D-spectrum called BIM-spectrum makes its computation as well as the computation of the Joint Reliability Index an easy task. The authors further propose a simple analytic method of calculating the D-spectrum for series-parallel and hierarchical systems, knowing the D-spectra of their subsystems. As is evident from the table of contents, the book has only two chapters. While the first chapter deals extensively with the theory involved in the proposed approach, the authors have taken pains to illustrate the methodology through several examples, which include pre-disaster management of a road network and a resilience comparison of regular and scale-free networks subject to random attack on the nodes. Actually, the book uses the probabilistic description of a network in the process of its successive degradation due to removal of its components (links, nodes) as a result of failures, natural disasters or intentional attacks. It is focused on a practical approach to network reliability, based on application of Monte Carlo methodology to numerical evaluation of network most important structural parameters. This allows obtaining a probabilistic description of the network in the process of its degradation, to identify most important components and to develop efficient heuristic algorithms for network optimal design. The approach can be used satisfactorily for small–to-medium size networks.


Krishna B. Misra

Review published in the International Journal of Performability Engineering, Vol. 8, No. 3, May 2012, p.299. 

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