Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Bond Graphs in System Modelling Read chapter Read first chapter

2017 | OriginalPaper | Chapter

Structural Importance and Local Importance in Network Reliability

Authors : P. Tittmann, S. Kischnick

Published in: Graph-Based Modelling in Engineering

Publisher: Springer International Publishing

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

Network reliability analysis has interesting applications in areas such as computer and mobile networks. However, the computation of many important reliability measures (all-terminal reliability, reachability) turns out to be NP-hard. This statement applies to the computation of relevant reliability importance measures, too. In this paper we introduce local importance measures that describe the importance of an edge or vertex of the network in its local network neighborhood. Suitable scaling of the local neighborhood renders the computation of generally intractable reliability measures possible.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter Bond Graphs in System Modelling
next chapter Access Distribution Scheme to the Computer System Based on Fuzzy Logic
Literature
1.
2.
Armstrong, M.J.: Joint reliability-importance of components. IEEE Trans. Rel. 44, 408–412 (1995)CrossRef
3.
Beichelt, F., Tittmann, P.: Reliability and maintenance: Networks and systems. CRC Press (2012)
4.
Birnbaum, Z. W.: On the importance of different components in a multicomponent system. In: Krishnaiah, P. R. (ed.) Multivariate Analysis–II, pp. 581–592. Academic Press (1969)
5.
Bollobás, B.: Modern Graph Theory. Springer (1998)
6.
Borgonovo, E.: The reliability importance of components and prime implicants in coherent and non-coherent systems including total-order interactions. Eur. J. Oper. Res. 204, 485–495 (2010)CrossRefMATH
7.
Freeman, L.C.: A set of measures of centrality based on betweenness. Sociometry 40, 35–41 (1977)CrossRef
8.
Freixas, J., Puente, M.A.: Reliability importance measures of the components in a system based on semivalues and probabilistic values. Ann. Oper. Res. 109, 331–342 (2002)MathSciNetCrossRefMATH
9.
Gertsbakh, I., Shpungin, Y.: Network Reliability and Resilience. Springer (2011)
10.
Girvan, M., Newman, M. E. J.: Community structure in social and biological networks. In: Proceedings of the National Academy of Sciences, vol. 99, pp. 7821–7826 (2002)
11.
Kirchhoff, G.R.: Über die Auflösung der Gleichungen, auf welche man bei der Untersuchung der linearen Verteilung galvanischer Ströme geführt wird. Ann. Phys. Chem. 72, 497–508 (1847)CrossRef
12.
Kochar, S., Mukerjee, H., Samaniego, F.J.: The signature of a coherent system and its application to comparisons among systems. Naval Res. Logistics 5, 507–523 (1999)MathSciNetCrossRefMATH
13.
Koschützki, D., Lehmann, K. A., Peeters, L., Richter, S., Tenfelde-Podehl, D., Zlotowski, O.: Centrality Indices. In: Network analysis. Springer (2005)
14.
Levitin, G., Lisnianski, A.: Importance and sensitivity analysis of multi-state systems using the universal generating function method. Reliab. Eng. Syst. Saf. 65, 271–282 (1999)CrossRef
15.
Meng, F.C.: On some structural importance of system components. J. Data Sci 7, 277–283 (2009)
16.
Myrvold, W.: Reliable network synthesis: Some recent developments. Proceed. Eighth Quadrennial Int. Conf. Graph Theor, Combinatorics, Algorithms, Appl. II, 650–660 (1999)MathSciNet
17.
Navarro, J., Rychlik, T.: Reliability and expectation bounds for coherent systems with exchangeable components. J. Multivar. Anal. 98, 102–113 (2007)MathSciNetCrossRefMATH
18.
Provan, J.S., Ball, M.O.: The complexity of counting cuts and of computing the probability that a graph is connected. SIAM J. Comput. 4, 777–788 (1983)MathSciNetCrossRefMATH
19.
Rausand, M., Høyland, A.: System reliability theory: Models, statistical methods, and applications, 2nd edn. Wiley, Hoboken (2004)MATH
20.
21.
Welsh, D.J.A.: Complexity: Knots. Cambridge University Press, Colorings and Counting (1993)MATH
Metadata
Title
Structural Importance and Local Importance in Network Reliability
Authors
P. Tittmann
S. Kischnick
Copyright Year
2017
Book
Graph-Based Modelling in Engineering

Print ISBN: 978-3-319-39018-5

Electronic ISBN: 978-3-319-39020-8

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-3-319-39020-8_2

Premium Partners

    Image Credits