Far Eastern Mathematical Journal

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Invariant properties of queuing systems with multiple flows


Tsitsiashvili G.Sh.

2018, issue 2, Ñ. 267-270


Abstract
It is proved that in a single-server queuing system with exponentially distributed service time and intervals between the arrivals of customers, the stationary output flows coincide in distribution with independent Poisson input flows, provided that the server works if there are customers in the system.

Keywords:
queuing system with multiple flows, ergodicity, service discipline

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References

[1] P.J. Burke, “The output of a queuing system”, Operations Research, 4, (1956), 699–704.
[2] B.V. Gnedenko, I.N. Kovalenko, Vvedeniye v teoriyu massovogo obsluzhivaniya, Nauka, Moskva, 1966.
[3] N.P. Buslenko, Modelirovaniye slozhnykh sistem, Nauka, Moskva, 1968.
[4] G.Sh. Tsitsiashvili, M.A. Osipova, “Generalization and Extension of Burke Theorem”, Reliability: Theory and Applications, 2018, ¹ 1, 59–62.
[5] A.YA. KHinchin, Raboty po matematicheskoy teorii massovogo obsluzhivaniya, Nauka, Moskva, 1963.
[6] G.Sh. Tsitsiashvili, “Ergodicity and invariance of flows in queuing systems”, Journal of Applied Mathematics and Physics, 6:7, (2018).
[7] D. SHtoyyan, Kachestvennyye svoystva i otsenki stokhasticheskikh modeley, Mir, Moskva, 1979.
[8] G.P. Klimov, “Ergodicheskaya teorema dlya regeneriruyushchikh protsessov”, Teoriya veroyatnostey i eye primeneniya, 21:2, (1976), 402–405.
[9] V.I. Tikhonov, M.A. Mironov, Markovskiye protsessy, Sovetskoye radio, Moskva, 1977.

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