Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-27T08:32:16.375Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  27 July 2009

T. Elperin ,
I. Gertsbakh  and
M. Lomonosov
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
Get access Rights & Permissions [Opens in a new window]

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
Information
Probability in the Engineering and Informational Sciences , Volume 6 , Issue 4 , October 1992 , pp. 457 - 469
Copyright
Copyright © Cambridge University Press 1992

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ball, M.D. & Provan, J.S. (1982). Bounds on the reliability polynomial for shellable independence systems. SIAM Journal of Algebraic Discrete Methods 3: 166–181.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: 1–12.CrossRefGoogle Scholar
Elperin, T., Gertsbakh, I., & Lomonosov, M. (1991). Network reliability estimation using graph evolution models. IEEE Transactions on Reliability R-40: 572–581.CrossRefGoogle Scholar
Fishman, G.S. (1987). A Monte Carlo sampling plan for estimating reliability parameters and related functions. Networks 17: 169–186.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: 73–81.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: 337–339.Google Scholar
Polesskii, V.P. (1990). Bounds on connectedness probability of a random graph. Problems of Information Transmission (USSR) 26: 90–98.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: 777–787.CrossRefGoogle Scholar