Far Eastern Mathematical Journal

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Properties of connectivity components in parallel-sequantial connections


G. V. Grenkin, N. V. Markova, G. Sh. Tsitsiashvili

2012, issue 1, Ñ. 12–19


Abstract
In this paper recursive formulas for a calculation of generating functions, distributions and moments of random number of connectivity components in parallel-sequential graphs and their connectivity probabilities are obtained. For graphs with large number of arcs variants of the law of large numbers and the central limit theorem are formulated and proved.

Keywords:
parallel-sequential connection, connectivity component

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References

[1] R. E. Barlow, F. Proschan, Mathematical Theory of Reliability, Wiley, London and New York, 1965.
[2] Iu. K. Beliaev, V. A. Bogatyrev, V. V. Bolotin i dr., Nadezhnost' tekhnicheskikh sistem: Spravochnik, red. I. A. Ushakov, Radio i sviaz', Moskva, 1985.
[3] M. G. Shur, “O zakonakh bol'shikh chisel dlia protsessov Markova”, Teoriia veroiatnostei i ee primeneniia, VIII:2 (1963), 224–228.
[4] A. A. Borovkov, Teoriia veroiatnostei, Nauka, Moskva, 1986.
[5] S. V. Nagaev, “Nekotorye predel'nye teoremy dlia odnorodnykh tsepei Markova”, Teoriia veroiatnostei i ee primeneniia, II:4 (1957), 389–416.
[6] S. V. Nagaev, “Tsentral'naia predel'naia teorema dlia markovskikh protsessov s diskretnym vremenem”, Ivz. AN Uz SSR, seriia fiz.-mat., 1962, ¹ 2, 12–20.
[7] A. N. Shiriaev, Veroiatnost', Nauka, Moskva, 1989.

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