Far Eastern Mathematical Journal

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Solution of balance equations and investigation of Poisson flows in Jackson networks


Tsitsiashvili G.Sh.

2018, issue 1, Ñ. 117-122


Abstract
In this paper a decomposition of a solution of balance equations for intensities of flows departing from nodes of the Jackson network is constructed. Sets of independent stationary Poisson flows departing from nodes of Jackson network are enumerated. Procedures of the decomposition and the enumeration are based on a definition of classes of cyclically equivalent nodes in a directed graph consistent with the Jackson network.

Keywords:
the Jackson network, a system of balance equations, classes of cyclic equivalence in directed graph

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References

[1] G.P. Basharin, A. L. Tolmachev, Teorija setej massovogo obsluzhivanija i ee prilozhenija k analizu informacionno-vychislitel'nyh sistem, Itogi nauki i tehniki, "Teorija verojatnostej. Matematicheskaja statistika. Teoreticheskaja kibernetika", t. 21, VINITI, Moskva, 1983.
[2] J.R. Jackson, “Networks of Waiting Lines”, Oper. Res., 5:4, (1957), 518–521.
[3] F.J. Beutler, B. Melamed, “Decomposition and customer streams of feedback networks of queues in equilibrium”, Oper. Res., 26:6, (1978), 1059–1072.
[4] G.SH. Ciciashvili, M.A. Osipova, “Stacionarnye potoki v aciklicheskih setjah massovogo obsluzhivanija”, DVMZH, 16:2, (2016), 223–228.
[5] G.SH. Ciciashvili, M.A. Osipova, A.S. Losev, “Algoritmy klasterizacii grafov”, Vestnik Voronezhskogo gosudarstvennogo universiteta, 1, (2016), 145–149.

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