Properties of connectivity components in parallel-sequantial connections
Dalʹnevostočnyj matematičeskij žurnal, Tome 12 (2012) no. 1, pp. 12-19.

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
@article{DVMG_2012_12_1_a1,
     author = {G. V. Grenkin and N. V. Markova and G. Sh. Tsitsiashvili},
     title = {Properties of connectivity components in parallel-sequantial connections},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {12--19},
     publisher = {mathdoc},
     volume = {12},
     number = {1},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2012_12_1_a1/}
}
TY  - JOUR
AU  - G. V. Grenkin
AU  - N. V. Markova
AU  - G. Sh. Tsitsiashvili
TI  - Properties of connectivity components in parallel-sequantial connections
JO  - Dalʹnevostočnyj matematičeskij žurnal
PY  - 2012
SP  - 12
EP  - 19
VL  - 12
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DVMG_2012_12_1_a1/
LA  - ru
ID  - DVMG_2012_12_1_a1
ER  - 
%0 Journal Article
%A G. V. Grenkin
%A N. V. Markova
%A G. Sh. Tsitsiashvili
%T Properties of connectivity components in parallel-sequantial connections
%J Dalʹnevostočnyj matematičeskij žurnal
%D 2012
%P 12-19
%V 12
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DVMG_2012_12_1_a1/
%G ru
%F DVMG_2012_12_1_a1
G. V. Grenkin; N. V. Markova; G. Sh. Tsitsiashvili. Properties of connectivity components in parallel-sequantial connections. Dalʹnevostočnyj matematičeskij žurnal, Tome 12 (2012) no. 1, pp. 12-19. http://geodesic.mathdoc.fr/item/DVMG_2012_12_1_a1/

[1] R. E. Barlow, F. Proschan, Mathematical Theory of Reliability, Wiley, London and New York, 1965 | MR | Zbl

[2] Yu. K. Belyaev, V. A. Bogatyrev, V. V. Bolotin i dr., Nadezhnost tekhnicheskikh sistem: Spravochnik, ed. I. A. Ushakov, Radio i svyaz, Moskva, 1985

[3] M. G. Shur, “O zakonakh bolshikh chisel dlya protsessov Markova”, Teoriya veroyatnostei i ee primeneniya, VIII:2 (1963), 224–228 | MR

[4] A. A. Borovkov, Teoriya veroyatnostei, Nauka, Moskva, 1986 | MR | Zbl

[5] S. V. Nagaev, “Nekotorye predelnye teoremy dlya odnorodnykh tsepei Markova”, Teoriya veroyatnostei i ee primeneniya, II:4 (1957), 389–416 | MR

[6] S. V. Nagaev, “Tsentralnaya predelnaya teorema dlya markovskikh protsessov s diskretnym vremenem”, Ivz. AN Uz SSR, seriya fiz.-mat., 1962, no. 2, 12–20 | MR | Zbl

[7] A. N. Shiryaev, Veroyatnost, Nauka, Moskva, 1989 | MR