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A new simulation method based on the RVR principle for the rare event network reliability problem

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Abstract

In this paper we consider the evaluation of the well known -network unreliability parameter by means of a new RVR Monte-Carlo method. This method is based on series-parallel reductions and a partitioning procedure using pathsets and cutsets for recursively changing the original problem into similar ones on smaller networks. By means of several experimental results, we show that the proposed method has good performances in rare event cases and offers significant gains over other state-of-the-art variance reduction techniques.

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References

  • Ball, M. O. (1986). Computational complexity of network reliability analysis: an overview. IEEE Transactions on Reliability, R-35(3), 230–239.

    Article  Google Scholar 

  • Cancela, H., & El Khadiri, M. (1996). An improvement to the total hazard method for system reliability simulation. Probability in the Engineering and Informational Sciences, 10, 187–196.

    Article  Google Scholar 

  • Cancela, H., & El Khadiri, M. (1998). Series-parallel reductions in Monte-Carlo network reliability evaluation. IEEE Transactions on Reliability, 47(2), 159–164.

    Article  Google Scholar 

  • Cancela, H., & El Khadiri, M. (2003). The recursive variance reduction simulation algorithm for network reliability evaluation. IEEE Transactions on Reliability, 52(2), 207–212.

    Article  Google Scholar 

  • Cancela, H., El Khadiri, M., & Rubino, G. (2009). Rare events analysis by Monte Carlo techniques in static models. In G. Rubino & B. Tuffin (Eds.), Rare event simulation methods using Monte Carlo methods. New York: Wiley, Chap. 7.

    Google Scholar 

  • Chang, M. K., & Satyanarayana, A. (1983). Network reliability and the factoring theorem. Networks, 13, 107–120.

    Article  Google Scholar 

  • Colbourn, C. J. (1987). The combinatorics of network reliability. New York: Oxford University Press.

    Google Scholar 

  • Cormen, T. H., Leiserson, C. E., & Rivest, R. L. (1990). Introduction to algorithms. Cambridge: The MIT Press.

    Google Scholar 

  • Easton, M. C., & Wong, C. K. (1980). Sequential destruction method for Monte Carlo evaluation of system reliability. IEEE Transactions on Reliability, R-29(1), 27–32.

    Article  Google Scholar 

  • Elperin, T., Gertsbakh, I., & Lomonosov, M. (1991). Estimation of network reliability using graph evolution models. IEEE Transactions on Reliability, 40(5), 572–581.

    Article  Google Scholar 

  • Fishman, G. S. (1986a). A comparison of four Monte-Carlo methods for estimating the probability of s-t connectedness. IEEE Transactions on Reliability, R-35(2), 145–155.

    Article  Google Scholar 

  • Fishman, G. S. (1986b). A Monte Carlo sampling plan for estimating network reliability. Operations Research, 34(4), 581–594.

    Article  Google Scholar 

  • Hui, K. P., Bean, N., Kraetzl, M., & Kroese, D. P. (2003). The tree cut and merge algorithm for estimation of network reliability. Probability in the Engineering and Informational Sciences, 17(1), 24–45.

    Article  Google Scholar 

  • Hui, K. P., Bean, N., Kraetzl, M., & Kroese, D. P. (2005). The cross-entropy method for network reliability estimation. Annals of Operations Research, 134, 101–118.

    Article  Google Scholar 

  • Jun, C. H., & Ross, S. M. (1992). System reliability by simulation: random hazards versus importance sampling. Probability in the Engineering and Informational Sciences, 6, 119–126.

    Article  Google Scholar 

  • Karp, R., & Luby, M. G. (1983). A new Monte Carlo method for estimating the failure probability of an n-component system. Computer Science Division, University of California (Berkley).

  • Kumamoto, H., Tanaka, K., Inoue, K., & Henley, E. J. (1980). Dagger-sampling Monte Carlo for system unavailability evaluation. IEEE Transactions on Reliability, R-29(2), 122–125.

    Article  Google Scholar 

  • Lomonosov, M. (1994). On Monte-Carlo estimates in network reliability. Probability in the Engineering and Informational Sciences, 8, 245–264.

    Article  Google Scholar 

  • Ross, S. M. (1990). Variance reduction in simulation via random hazards. Probability in the Engineering and Informational Sciences, 4, 199–309.

    Google Scholar 

  • Ross, S. M. (1994). A new simulation estimator of system reliability. Journal of Applied Mathematics and Stochastic Analysis, 7(4), 331–336.

    Article  Google Scholar 

  • Satyanarayana, A., & Wood, R. K. (1985). A linear-time algorithm for computing k terminal in series-parallel networks. SIAM Journal on Computing, 14(4), 818–832.

    Article  Google Scholar 

  • Wood, K. (1985). A factoring algorithm using polygon-to-chain reductions for computing k-terminal network reliability. Networks, 15, 173–190.

    Article  Google Scholar 

  • Wood, K. (1986). Factoring algorithms for computing k-terminal network reliability. IEEE Transactions on Reliability, R-35(3), 269–278.

    Article  Google Scholar 

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Acknowledgements

This work was partially supported by project 09STIC03, funded by the STIC-AMSUD cooperation program between South American countries and France.

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Authors and Affiliations

  1. University of the Republic of Uruguay, J. Herrera y Reissig 565, Montevideo, Uruguay

    H. Cancela

  2. Saint-Nazaire Institute of Technology, University of Nantes, 58 rue Michel Ange, 44606, Saint-Nazaire Cedex, France

    M. El Khadiri

  3. INRIA, Campus de Beaulieu, 35042, Rennes Cedex, France

    G. Rubino

Authors
  1. H. Cancela
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  2. M. El Khadiri
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  3. G. Rubino
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Correspondence to M. El Khadiri.

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Cancela, H., El Khadiri, M. & Rubino, G. A new simulation method based on the RVR principle for the rare event network reliability problem. Ann Oper Res 196, 111–136 (2012). https://doi.org/10.1007/s10479-011-1017-x

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