Advertisement

Direct Network Reliability Calculation

  • Ilya GertsbakhEmail author
  • Yoseph Shpungin
Chapter
  • 197 Downloads
Part of the SpringerBriefs in Electrical and Computer Engineering book series (BRIEFSELECTRIC)

Abstract

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 probability in an explicit form. More elegant and efficient are the methods based on using network structural parameters—the so-called minimal path and minimal cut sets. Knowing these parameters allows us to construct rather accurate upper and lower bounds on network reliability. For very reliable networks in which node/edge failure reliability tends to zero, very good results are obtained by using so-called Burtin-Pittel approximation. We present it in Sect. 3.5. Network reliability as a function of the number of failed elements is an important characteristic of so-called resilience, see Sect. 3.6. The chapter is concluded by introducing so-called dynamic reliability which is network reliability behaviour in time. This is obtained by replacing element static reliability p by survival probability \(1-G(t)\) depending on time t.

Keywords

Min cuts Min paths Reliability bounds B-P approximation Network resilience Dynamic reliability 

References

  1. 1.
    Gertsbakh, I. (2000). Reliability theory with applications to preventive maintenance. Berlin: Springer.Google Scholar
  2. 2.
    Gertsbakh, I., & Shpungin, Y. (2009). Models of network reliability: analysis, combinatorics and Monte Carlo. Boca Raton: CRC Press.zbMATHGoogle Scholar
  3. 3.
    Brandes, T., & Erlebach, U. (2005). Network analysis: methodological foundation. Berlin: Springer.Google Scholar
  4. 4.
    Gertsbakh, I., & Shpungin, Y. (2011). Network reliability and resilience. Berlin: Springer.Google Scholar
  5. 5.
    Barlow, R. E., & Proschan, F. (1981). Statistical theory of reliability and life testing. To Begin With; Reprint Edition.Google Scholar
  6. 6.
    Gertsbakh, I., & Shpungin, Y. (2012). Stochastic models of network survivability. Quality Technology of Quantitative Management, 9(1), 45–58.CrossRefGoogle Scholar

Copyright information

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Department of MathematicsBen Gurion UniversityBeer-ShevaIsrael
  2. 2.Software Engineering DepartmentShamoon College of EngineeringBeer-ShevaIsrael

Personalised recommendations