Cybernetics and Systems Analysis

, Volume 50, Issue 3, pp 358–367 | Cite as

Fast Simulation of the Functional Failure of an s – t-Network with Repair

  • N. Yu. Kuznetsov
  • A. A. Shumskaya
  • O. N. Homyak
Systems Analysis


An s – t-network with highly reliable edges with repair and variable external load is considered. A fast simulation method is proposed to evaluate the probability of functional failure when the real capacity of the network is less than the required capacity. It is proved that under some conditions the estimate has a bounded relative error as edges reliability increases. The numerical example illustrates the efficiency of the method.


s – t-network functional failure minimal cutset fast simulation method variance of the estimate relative standard deviation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    I. B. Gertsbakh and Y. Shpungin, Models of Network Reliability: Analysis, Combinatorics, and Monte Carlo, CRC Press, Boca Raton (2009).Google Scholar
  2. 2.
    I. B. Frenkel, A. Karagrigoriou, A. Lisnianski, and A. V. Kleyner, Applied Reliability Engineering and Risk Analysis: Probabilistic Models and Statistical Inference, Wiley, New York (2013).CrossRefGoogle Scholar
  3. 3.
    P. Heidelberger, “Fast simulation of rare events in queueing and reliability models,” ACM Trans. Modeling Comput. Simul., 5, No. 1, 43–85 (1995).CrossRefMATHGoogle Scholar
  4. 4.
    J. Li, A. Mosleh, and R. Kang, “Likelihood ratio gradient estimation for dynamic reliability applications,” Reliab. Engin. and System Safety, 96, No. 12, 1667–1679 (2011).CrossRefGoogle Scholar
  5. 5.
    P. Glasserman. Monte Carlo Methods in Financial Engineering, Springer, New York (2004).MATHGoogle Scholar
  6. 6.
    I. N. Kovalenko, Analys of Rare Events in Systems Efficiency and Reliability Analysis [in Russian], Sov. Radio, Moscow (1980).Google Scholar
  7. 7.
    I. N. Kovalenko and N. Yu. Kuznetsov, Methods to Design Highly Reliable Systems [in Russian], Radio i Svyaz’, Moscow (1988).Google Scholar
  8. 8.
    N. Yu. Kuznetsov, “Fast simulation technique in reliability evaluation of Markov and non-Markov systems,” in: Simulation and Optimization Methods in Risk and Reliability Theory, Nova Sci. Publ., New York (2009), pp. 69–112.Google Scholar
  9. 9.
    N. Yu. Kuznetsov and A. A. Shumskaya, “Evaluation of the hazard of failure of the redundant system by fast simulation methods,” J. Autom. Inform. Sci., 45, No. 5, 38–51 (2013).CrossRefGoogle Scholar
  10. 10.
    A. A. Shumskaya, “Fast simulation of unavailability of a repairable system with a bounded relative error of estimate,” Cybern. Syst. Analysis, 39, No. 3, 357–366 (2003).CrossRefMATHMathSciNetGoogle Scholar
  11. 11.
    P. Glasserman, Ph. Heidelberger, P. Shahabuddin, and T. Zajic, “Multilevel splitting for estimating rare event probabilities,” Oper. Res., 47, No. 4, 585–600 (1999).CrossRefMATHMathSciNetGoogle Scholar
  12. 12.
    I. N. Kovalenko, N. Yu. Kuznetsov, and Ph. A. Pegg, Mathematical Theory of Reliability of Time Dependent Systems with Practical Applications, Wiley, Chichester (1997).MATHGoogle Scholar
  13. 13.
    A. Lagnoux, “Rare event simulation,” Probab. Eng. and Inf. Sci., 20, No. 1, 45–66 (2006).CrossRefMATHMathSciNetGoogle Scholar
  14. 14.
    J. Blanchet and H. Lam, “Rare event simulation techniques,” in: Proc. 2011 Winter Simulation Conf. (2011), pp. 217–231.Google Scholar
  15. 15.
    O. N. Khomyak, “Determination of probability of intersection of trajectory functionals for two Markovian chains by the method of significant sampling,” J. Autom. Inform. Sci., 45, No. 8, 75–81 (2013).CrossRefGoogle Scholar
  16. 16.
    O. N. Khomyak, “Fast simulation method for the evaluation of intersection probability of random level by Markov process,” J. Autom. Inform. Sci., 46, No. 2, 76–84 (2014).CrossRefGoogle Scholar
  17. 17.
    O. B. Samoilov, G. B. Usynin, and A. M. Bakhmet’ev, Safety of Nuclear Power Plants [in Russian], Energoatomizdat, Moscow (1989).Google Scholar
  18. 18.
    H.-Y. Lin, S.-Y. Kuo, and F.-M. Yeh, “Minimal cutset enumeration and network reliability evaluation by recursive merge and BDD,” in: Proc. 8th IEEE Intern. Symp. on Comput. and Commun. (2003), pp. 1341–1346.Google Scholar
  19. 19.
    M. Benaddy and M. Wakrim, “Cutset enumerating and network reliability computing by a new recursive algorithm and inclusion exclusion principle,” Intern. J. Comput. Appl., 45, No. 16, 22–25 (2012).Google Scholar
  20. 20.
    Y. Chen, A. Q. Hu, K. W. Yip, et al., “A modified combined method for computing terminal-pair reliability in networks with unreliable nodes,” in: Proc. 2nd Int. Conf. on Machine Learning and Cybernetics (2003), pp. 2426–2429.Google Scholar
  21. 21.
    S.-Y. Kuo, F.-M. Yeh, and H.-Y. Lin, “Efficient and exact reliability evaluation for networks with imperfect vertices,” IEEE Trans. on Reliability, 56, No. 2, 288–300 (2007).CrossRefGoogle Scholar
  22. 22.
    I. N. Kovalenko, “Reliability assessment of complex systems,” Vopr. Radioelektroniki, 12, No. 9, 50–68 (1965).Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • N. Yu. Kuznetsov
    • 1
  • A. A. Shumskaya
    • 2
  • O. N. Homyak
    • 1
  1. 1.V. M. Glushkov Institute of CyberneticsNational Academy of Sciences of UkraineKyivUkraine
  2. 2.Institute of Physics and Technology, National Technical University “KPI” of the Ministry of Education and Science of Ukraine and National Academy of Sciences of UkraineKyivUkraine

Personalised recommendations