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Network Reliability

Part of the SpringerBriefs in Electrical and Computer Engineering Book Series

DOI: 10.1007/978-981-15-1458-6

ISBN: 978-981-15-1457-9

Publisher: Springer Singapore - Springer Journals

Nov 16, 2019

Available

Probability-Reminder

Gertsbakh, Ilya; Shpungin, Yoseph

Pages: 1 –9

[This chapter contains material which you certainly have learned some time ago and which is familiar to you. No doubt, you have met some elements of algebra of events, random variables, distribution function and have heard about binomial distribution. Among the material of this chapter is a...
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Networks and Examples

Gertsbakh, Ilya; Shpungin, Yoseph

Pages: 11 –19

[This chapter starts with network definition, describes various types of network failure and presents an overview of various network failure criteria. For finite networks, most of these criteria are related to the loss of connectivity between special nodes called terminals. Classical network...
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Direct Network Reliability Calculation

Gertsbakh, Ilya; Shpungin, Yoseph

Pages: 21 –34

[This chapter is a collection of several direct methods for calculating network reliability. These methods are good for small networks having not more than 8–10 elements subject to failure. The most straightforward is network state enumeration method. It allows obtaining network UP/DOWN...
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Elementary Methods for Reliability Evaluation

Gertsbakh, Ilya; Shpungin, Yoseph

Pages: 35 –47

[This chapter describes elementary approaches to network reliability evaluation. The first method is based on making a list of all \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy}...
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Element Importance

Gertsbakh, Ilya; Shpungin, Yoseph

Pages: 49 –56

[Birnbaum Importance Measure (BIM) of element j is defined as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}...
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Destruction Monte Carlo

Gertsbakh, Ilya; Shpungin, Yoseph

Pages: 57 –69

[In this chapter we introduce a new and very important network structural invariant—so-called cumulative destruction spectrum (CD-spectrum). This parameter allows to investigate network behaviour when the network is subject to a flow of external “shocks” which randomly destroy network elements...
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Lomonosov’s Turnip

Gertsbakh, Ilya; Shpungin, Yoseph

Pages: 71 –80

[Lomonosov’s turnip is a very powerful Monte Carlo algorithm for estimating Network reliability. It was invented by M.V. Lomonosov in 1986 and first described in [1]. This algorithm is applicable to finding the probability of network terminal (or all-node) connectivity probability for the case of...
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Examples of Network Analysis

Gertsbakh, Ilya; Shpungin, Yoseph

Pages: 81 –90

[This chapter presents three applications of the theory developed in previous chapters to practical analysis of network-type systems. The first section is a comparison of networks resilience under random attack on their nodes. It is shown that regular networks are considerably more resilient than...

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