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An Evolution Model for Monte Carlo Estimation of Equilibrium Network Renewal Parameters

Published online by Cambridge University Press:  27 July 2009

T. Elperin
Affiliation:
Ben-Gurion University of the Negev Beer-Sheva, 84105, Israel
I. Gertsbakh
Affiliation:
Ben-Gurion University of the Negev Beer-Sheva, 84105, Israel
M. Lomonosov
Affiliation:
Ben-Gurion University of the Negev Beer-Sheva, 84105, Israel

Abstract

This paper presents Monte Carlo techniques for evaluating equilibrium availability and mean up and down periods of a renewable network for a wide class of network operational criteria. The suggested method is based on a graph evolution model that overcomes the main difficulty–hitting low-probability “border” states of the criterion. Theoretical efficiency of the method is briefly discussed and numerical results are presented.

Type
Articles
Copyright
Copyright © Cambridge University Press 1992

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References

Ball, M.D. & Provan, J.S. (1982). Bounds on the reliability polynomial for shellable independence systems. SIAM Journal of Algebraic Discrete Methods 3: 166181.CrossRefGoogle Scholar
Colbourn, C.J. (1987). The combinatorics of network reliability. New York and Oxford: Oxford University Press.Google Scholar
Colbourn, C.J. & Harms, D.D. (1988). Bounding all-terminal reliability in computer networks. Networks 18: 112.CrossRefGoogle Scholar
Elperin, T., Gertsbakh, I., & Lomonosov, M. (1991). Network reliability estimation using graph evolution models. IEEE Transactions on Reliability R-40: 572581.CrossRefGoogle Scholar
Fishman, G.S. (1987). A Monte Carlo sampling plan for estimating reliability parameters and related functions. Networks 17: 169186.CrossRefGoogle Scholar
Gnedenko, B.V. (ed.). (1983). Mathematical methods of reliability theory. Moscow: Nauka Publ. House (in Russian).Google Scholar
Keilson, J. (1979). Markov chain models – Rarity and exponentiality. New York: Springer-Verlag.CrossRefGoogle Scholar
Lomonosov, M.V. (1974). Bernoulli scheme with closure. Problems of Information Transmission (USSR) 10: 7381.Google Scholar
Lomonosov, M.V. (to appear). Tender-spot of a reliable network. Discrete Applied Mathematics.Google Scholar
Lomonosov, M.V. & Polesskii, V.P. (1971). An upper bound for the reliability of information networks. Problems of Information Transmission (USSR) 7: 337339.Google Scholar
Polesskii, V.P. (1990). Bounds on connectedness probability of a random graph. Problems of Information Transmission (USSR) 26: 9098.Google Scholar
Provan, J.S. & Ball, M.O. (1982). The complexity of counting cuts and of computing the probability that a graph is connected. SIAM Journal on Computing 12: 777787.CrossRefGoogle Scholar