Far Eastern Mathematical Journal

To content of the issue

Investigation of stationary characteristics in some variable queueing systems

G. Sh. Tsitsiashvili, M. A. Osipova

2000, issue 1, Ñ. 58–62

A stationary distribution in simplest queueing system with variable intensity of input flow and constant load coefficient is calculated. A generalization of this result in a form of some multiplicative theorem is made. An algorythm of a calculation of stationary distributions for discrete Markovian processes with finite number of states, devoted to investigation of queueing systems with variable load coefficient, is constructed.


Download the article (PDF-file)


[1] D. M. Lucantoni, “New results on the single server queue with a batch Markovian arrival process”, Communications in Statistic Models, 7:1 (1991), 1–46, Marcel Dekker Inc.
[2] D. M. Lucantoni, “The BMAP/G|1 Queue: A Tutorial”, Models and Techniques for Perfomance Evalution of Computer and Communication Systems, eds. L. Donatello, R. Nelson, Springer, Berlin, 1991, 1–46.
[3] D. Baum, On Markovian Spatial Arrival Processes for the Performance Analysis of Mobile Communication Networks, Research Rep. ¹98-07, University of Trier, Submitted to Advances in Performance Analysis, Notable Publications, Inc.
[4] F. Machihara, “The BMAP/SM/1 Queue With Service Times Depending on the Arrival Process”, Queueing systems, 32:1-3 (1999), 1–15.
[5] N. I. Golovko, V. I. Katraxov, T. A. Pisarenko, “Analiz sistem massovogo obsluzhivaniya s diffuzionnoj intensivnost'yu vxodnogo potoka”, Dal'nevostochnyj matematicheskij sbornik, 1999, ¹ 7.
[6] G. I. Ivchenko, V. A. Kashtanov, I. N. Kovalenko, Teoriya massovogo obsluzhivaniya, Vysshaya shkola, M., 1982, 256 s.
[7] A. N. Shiryaev, Veroyatnost', Nauka, M., 1989, 640 s.

To content of the issue