Solution of balance equations and investigation of Poisson flows in Jackson networks
Dalʹnevostočnyj matematičeskij žurnal, Tome 18 (2018) no. 1, pp. 117-122.

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

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.
@article{DVMG_2018_18_1_a14,
     author = {G. Sh. Tsitsiashvili},
     title = {Solution of balance equations and investigation of {Poisson} flows in {Jackson} networks},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {117--122},
     publisher = {mathdoc},
     volume = {18},
     number = {1},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2018_18_1_a14/}
}
TY  - JOUR
AU  - G. Sh. Tsitsiashvili
TI  - Solution of balance equations and investigation of Poisson flows in Jackson networks
JO  - Dalʹnevostočnyj matematičeskij žurnal
PY  - 2018
SP  - 117
EP  - 122
VL  - 18
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DVMG_2018_18_1_a14/
LA  - ru
ID  - DVMG_2018_18_1_a14
ER  - 
%0 Journal Article
%A G. Sh. Tsitsiashvili
%T Solution of balance equations and investigation of Poisson flows in Jackson networks
%J Dalʹnevostočnyj matematičeskij žurnal
%D 2018
%P 117-122
%V 18
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DVMG_2018_18_1_a14/
%G ru
%F DVMG_2018_18_1_a14
G. Sh. Tsitsiashvili. Solution of balance equations and investigation of Poisson flows in Jackson networks. Dalʹnevostočnyj matematičeskij žurnal, Tome 18 (2018) no. 1, pp. 117-122. http://geodesic.mathdoc.fr/item/DVMG_2018_18_1_a14/

[1] G. P. Basharin, A. L. Tolmachev, Teoriya setei massovogo obsluzhivaniya i ee prilozheniya k analizu informatsionno-vychislitelnykh sistem, v. 21, Itogi nauki i tekhniki, “Teoriya veroyatnostei. Matematicheskaya statistika. Teoreticheskaya kibernetika”, VINITI, Moskva, 1983

[2] J. R. Jackson, “Networks of Waiting Lines”, Oper. Res., 5:4 (1957), 518–521 | DOI | MR

[3] F. J. Beutler, B. Melamed, “Decomposition and customer streams of feedback networks of queues in equilibrium”, Oper. Res., 26:6 (1978), 1059–1072 | DOI | MR | Zbl

[4] G. Sh. Tsitsiashvili, M. A. Osipova, “Statsionarnye potoki v atsiklicheskikh setyakh massovogo obsluzhivaniya”, DVMZh, 16:2 (2016), 223–228 | MR | Zbl

[5] G. Sh. Tsitsiashvili, M. A. Osipova, A. S. Losev, “Algoritmy klasterizatsii grafov”, Vestnik Voronezhskogo gosudarstvennogo universiteta, 1 (2016), 145–149 | Zbl