Network Reliability (eBook)

A Lecture Course

Ilya Gertsbakh, Yoseph Shpungin (Autoren)

eBook Download: PDF

2019 | 1st ed. 2020
IX, 90 Seiten
Springer Singapore (Verlag)
978-981-15-1458-6 (ISBN)

Infos

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. 

Inhalt

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

Produkt-Details

• Erscheint lt. Verlag: 15.11.2019
• Reihe/Serie: SpringerBriefs in Electrical and Computer Engineering
• Reihe/Serie: SpringerBriefs in Electrical and Computer Engineering
• Zusatzinfo: IX, 90 p. 48 illus., 27 illus. in color.
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Informatik ► Theorie / Studium
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Technik ► Elektrotechnik / Energietechnik
• Themenwelt: Technik ► Nachrichtentechnik
• Schlagworte: applied probability • Operations Research • system reliability • Textbook network reliability • Transportation and Logistic systems
• ISBN-10: 981-15-1458-5 / 9811514585
• ISBN-13: 978-981-15-1458-6 / 9789811514586