Far Eastern Mathematical Journal

To content of the issue


Calculation of cohesiveness probability for recursively defined random networks


A. S. Losev, G. Sh. Tsitsiashvili

2010, issue 1, P. 60–65


Abstract
For recursively defined random networks in this paper recursive and asymptotic formulas of a calculation of cohesiveness probability are constructed. A comparison with known algorithms shows that in suggested algorithms it is not necessary to find maximal systems of frames. That accelerates calculations significantly. Numerical experiments which confirm an operation speed of suggested algorithms and an accuracy of assumed asymptotic formulas has made.

Keywords:
cohesiveness probability, radial-circle network, a recursive formula

Download the article (PDF-file)

References

[1] R. E. Barlow, F. Proschan, Mathematical Theory of Reliability, Wiley, London and New York, 1965.
[2] I. A. Ushakov i dr., Nadezhnost' texnicheskix sistem, Spravochnik, Radio i svyaz', M., 1985.
[3] E. D. Solozhencev, “Osobennosti logiko-veroyatnostnoj teorii riska s gruppami nesovmestnyx sobytij”, Avtomatika i telemexanika, 2003, № 7, 187–203.
[4] I. A. Ryabinin, Nadezhnost' i bezopasnost' strukturno-slozhnyx sistem, Izd-vo S.-Peterb. un-ta, SPb., 2007.
[5] C. Tanguy, “Exact solutions for the two-terminal Reliability of recursive structures: a few directions.”, MMR 2009 – Mathematical methods in reliability, Moscow, 2009, 220–224.
[6] L. Cui, X. Zhao, “Recursive Equations of Reliability for Linear Consecutive-k-out-of-n: F Systems with Sparse d.”, MMR 2009 – Mathematical methods in reliability, Moscow, 2009, 45.
[7] M. O. Ball, C. J. Colbourn, J. S. Provan, “Network reliability”, In Network Models, Handbook of Operations Research and Management Science, 7, North-Holland, Amsterdam, 1995, 673–762.
[8] V. P. Polesskij, “Ocenki veroyatnosti svyaznosti sluchajnogo grafa”, Problemy peredachi informacii, 26:1 (1990), 90–98.
[9] V. P. Polesskij, “Nizhnie ocenki veroyatnosti svyaznosti dlya nekotoryx klassov sluchajnyx grafov”, Problemy peredachi informacii, 29:2 (1993), 85–95.
[10] V. P. Polesskij, “Nizhnie ocenki veroyatnosti svyaznosti v klassax sluchajnyx grafov, porozhdennyx dvusvyaznymi grafami s zadannym bazovym spektrom”, Problemy peredachi informacii, 28:2 (1992), 86–95.

To content of the issue