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Evaluating performability: Most probable states and bounds

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Abstract

The number of states examined by most probable state algorithms for performability computations can be reduced dramatically by incorporating simple connectivity-based bounds, even when the performability measure is much more complex than connectivity. Modifications to Yang and Kubat's most probable state method are presented that permit the use of simple auxiliary bounds with only a small effect on the time per iteration. Computational results for a variety of performability measures are given.

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References

  1. H.M.F. AboElFotoh and C.J. Colbourn, Series-parallel bounds for the two-terminal reliability problem, ORSA J. Comp. 1(1989)205–222.

    Google Scholar 

  2. M.O. Ball, C.J. Colbourn and J.S. Provan, Network reliability, in:Handbook of Operations Research: Networks, to appear.

  3. T.B. Brecht and C.J. Colbourn, Lower bounds for two-terminal network reliability, Discr. Appl. Math. 21(1988)185–198.

    Article  Google Scholar 

  4. C.J. Colbourn,The Combinatorics of Network Reliability (Oxford University Press, 1987).

  5. C.J. Colbourn, Edge-packings of graphs and network reliability, Discr. Math. 72(1988)49–61.

    Article  Google Scholar 

  6. C.J. Colbourn and E.I. Litvak, Bounding network reliability by graph transformations, in:Reliability of Computer and Communications Networks (AMS/ACM, 1991) pp. 91–104.

  7. G.S. Fishman, A Monte Carlo sampling plan for estimating network reliability, Oper. Res. 34(1986)581–594.

    Google Scholar 

  8. D.D. Harms and C.J. Colbourn, Renormalization of two-terminal reliability, Networks 23(1993)289–298.

    Google Scholar 

  9. V.A. Kaustov, E.I. Litvak and I.A. Ushakov, The computational effectiveness of reliability estimates by the method of nonedge-intersecting chains and cuts, Sov. J. Comp. Syst. Sci. 24(1986)70–73.

    Google Scholar 

  10. K. Kumamoto, T. Tanaka and K. Inoue, Efficient evaluation of system reliability by a Monte Carlo method, IEEE Trans. Rel. R-26(1977)311–315.

    Google Scholar 

  11. Y.F. Lam and V.O.K. Li, An improved algorithm for performance analysis of networks with unreliable components, IEEE Trans. Commun. COM-34(1986)496–497.

    Article  Google Scholar 

  12. J.F. Meyer, Performability: A retrospective and some pointers to the future, Perform. Eval. 14(1992)139–156.

    Article  Google Scholar 

  13. B. Sanso and F. Soumis, Communication and transportation networks reliability using routing models, IEEE Trans. Rel. R-40(1991)29–38.

    Article  Google Scholar 

  14. J.G. Shanthikumar, Bounding network reliability using consecutive minimal cutsets, IEEE Trans. Rel. R-37(1988)45–49.

    Article  Google Scholar 

  15. D.R. Shier,Network Reliability and Algebraic Structures (Oxford University Press, 1991).

  16. H.J. Strayer and C.J. Colbourn, Consecutive cuts and paths, and bounds onk-terminal reliability, Technical Report 93-23, DIMACS (1993).

  17. L.G. Valiant, The complexity of enumeration and reliability problems, SIAM J. Comput. 8(1979)410–421.

    Article  Google Scholar 

  18. R.M. Van Slyke and H. Frank, Network reliability analysis I, Networks 1(1972)279–290.

    Google Scholar 

  19. C.-L. Yang and P. Kubat, An algorithm for network reliability bounds, ORSA J. Comput. 2(1990)336–345.

    Google Scholar 

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Colbourn, C.J., Harms, D.D. Evaluating performability: Most probable states and bounds. Telecommunication Systems 2, 275–300 (1993). https://doi.org/10.1007/BF02109862

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  • DOI: https://doi.org/10.1007/BF02109862

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