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Lomonosov’s Turnip

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

Abstract

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 arbitrary values of edge (or node) failure probabilities. An outstanding feature of this algorithm is that it enables obtaining estimates with high accuracy for very small network failure probabilities known as “rare event situation”. The name “turnip” comes from a diagram reminding a turnip which describes so-called evolution process which is central to the main idea of the algorithm.

Keywords

Evolution process Turnip diagram Closure Edge and node failure 

References

  1. 1.
    Lomonosov, M. (1994). On Monte Carlo estimates in network reliability. Probability in the Engineering and Informational Sciences, 8, 245–264.CrossRefGoogle Scholar
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    Lomonosov, M., & Shpungin, Y. (1999). Combinatorics and reliability Monte Carlo. Random Structures and Algorithms, 14, 329–343.MathSciNetCrossRefGoogle Scholar
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    Gertsbakh, I., & Shpungin, Y. (2011). Network reliability and resilience. New York: Springer.Google Scholar
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    Gertsbakh, I., Shpungin, Y., & Vaisman, R. (2014). Network reliability Monte Carlo with nodes subject to failure. International Journal of Performability Engineering, 10(2), 161–170.zbMATHGoogle Scholar
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    Kroese, D., Taimre, T., & Botev, Z. I. (2011). Handbook of Monte Carlo methods. New York: Wiley.Google 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

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