Far Eastern Mathematical Journal

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Construction of queueing networks with stationary product distributions

G. Sh. Tsitsiashvili, M. A. Osipova

2004, issue 1, P. 82–88

Abstract

In this article some new product theorems for opened and closed queuing networks with finite number of states have been proved. Each network is characterized by a graph with states in its nodes and positive transition intensities in its edges. For different graphs and systems of motion equations stationary product distributions of Markov processes, which describe queuing networks with different prohibited transitions, have been obtained. An algorithm of route matrices calculations in accordance with modified systems of motion equations have been constructed.

Keywords: queuing networks, product theorems, prohibited transitions, systems of motion equations

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References

[1] J. R. Jackson, “Networks of Waiting Lines”, Oper. Res., 5:4 (1957), 518–521. [2] K. D. Gordon, G. F. Newell, “Closed Queuing Systems with Exponential Servers”, Oper. Research, 15:2 (1967), 254–265. [3] G. I. Ivchenko, V. A. Kashtanov, I. N. Kovalenko, Teoriya massovogo obsluzhivaniya, Vysshaya shkola, M., 1982, 256 s. [4] R. Gabasov, F. M. Kirillova, Metody linejnogo programmirovaniya, t. 2, BGU, Minsk, 1978, 239 s.

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