Gertsbakh / Shpungin Network Reliability

A Lecture Course
1. Auflage 2020
ISBN: 978-981-15-1458-6
Verlag: Springer Nature Singapore
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 96 Seiten

Reihe: SpringerBriefs in Electrical and Computer Engineering

This introductory book equips the reader to apply the core concepts and methods of network reliability analysis to real-life problems. It explains the modeling and critical analysis of systems and probabilistic networks, and requires only a minimal background in probability theory and computer programming. Based on the lecture notes of eight courses taught by the authors, the book is also self-contained, with no theory needed beyond the lectures. The primary focus is on essential 'modus operandi,' which are illustrated in numerous examples and presented separately from the more difficult theoretical material.



Ilya B. Gertsbakh is Professor Emeritus in the Department of Mathematics at Ben-Gurion University of the Negev, Israel. He is author or coauthor of seven books, the recent of which is 'Ternary networks: Reliability and Monte Carlo' (with Yoseph Shpungin and Radislav Vaisman), published by Springer in 2014. Ilya Gertsbakh has published some 100 papers on topics in operations research, reliability, applied probability and applied statistics. He received M.Sc degrees in mechanical engineering and mathematics (1961) from Latvian State University in Riga, Latvia, and the Ph.D. degree (1964) in applied probability and statistics from Latvian Academy of Sciences, also in Riga.    Yoseph Shpungin is Professor Emeritus in the Software Engineering Department, at Shamoon College of Engineering, Beer Sheva, Israel. He is a coauthor of three books and numerous publications in international scientific journals. He received his M.Sc degree in mathematics (1969) from Latvian State University in Riga, Latvia, and Ph.D. degree (1997) in mathematics from Ben Gurion University, Beer Sheva, Israel. 

Autoren/Hrsg.

Gertsbakh, Ilya

Shpungin, Yoseph

Inhaltsverzeichnis

1;Preface;6
2;Contents;8
3;Notations and Abbreviations;10
4;1 Probability-Reminder;11
4.1;1.1 Algebra of Events;11
4.2;1.2 Random Variables;12
4.3;1.3 The Law of Total Probability;16
4.4;1.4 Order Statistics;16
4.5;1.5 Average, Variance;18
4.6;References;19
5;2 Networks and Examples;20
5.1;2.1 Nodes, Edges, Terminals;20
5.2;2.2 Series-Parallel Networks;26
5.3;References;28
6;3 Direct Network Reliability Calculation;29
6.1;3.1 Static Reliability and Structure Function;29
6.2;3.2 Counting Paths and Cuts;33
6.3;3.3 Using Inclusion/Exclusion Formula;35
6.4;3.4 Pivotal Formula;37
6.5;3.5 Burtin-Pittel Approximation;37
6.6;3.6 Network Resilience;39
6.7;3.7 Static and Dynamic Reliability;41
6.8;References;42
7;4 Elementary Methods for Reliability Evaluation;43
7.1;4.1 Exact Method for Computing Network Reliability;43
7.2;4.2 Crude Monte Carlo (CMC);45
7.3;4.3 Relative Error of CMC;47
7.4;4.4 CMC for Network Dynamic Reliability Evaluation;49
7.5;4.5 Checking Network State;50
7.6;References;55
8;5 Element Importance;56
8.1;5.1 Birnbaum Importance Measure (BIM);56
8.2;5.2 Direct Computation of BIM;57
8.3;5.3 Monte Carlo for Computing BIM;61
8.4;References;63
9;6 Destruction Monte Carlo;64
9.1;6.1 Individual and Comparative Network Reliability Analysis;64
9.2;6.2 Network Destruction;66
9.3;6.3 BIM Spectrum;70
9.4;6.4 CD-Spectrum and BIM Spectra Monte Carlo;72
9.5;References;76
10;7 Lomonosov's Turnip;77
10.1;7.1 Evolution Process;77
10.2;7.2 Lomonosov's Algorithm;80
10.3;7.3 Turnip for Networks with Unreliable Nodes;82
10.4;7.4 Convolution of Exponents;85
10.5;References;86
11;8 Examples of Network Analysis;87
11.1;8.1 Network Structure and Resilience Against Node Attack;87
11.2;8.2 Road/Highway Reinforcement;90
11.3;8.3 Flow in Network with Unreliable Edges;93
11.4;References;96