Far Eastern Mathematical Journal

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Calculation of stationary distributions in adoptive queueing networks

M. A. Osipova, G. Sh. Tsitsiashvili, N. V. Koliev

2001, issue 2, Ñ. 99–105

Queueing networks with random varying intensities are convenient models of computer and telecommunication systems. A behaviour of these systems depends on human activity which intensity is defined by intradaily dynamics of physiological and mental indexes. So random current intensities of input flow and servicing for systems arranged in the same time zone are to be proportional. This hypothesis, called adoptation hypothesis, allows to make generalization of Jackson product theorem as for opened so for closed queueing networks. So it relieves analysis of queueing networks with varying intensities and makes its results more realistical.


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[1] D. M. Lucantoni, “New results on the single server queue with a batch Markovian arrival process”, Communications in Statistics: Stochastic 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, 330–358.
[3] D. Baum, On Markovian Spatial Arrival Processes for the Performance Analysis of Mobile Communication Networks, Research Rep., 98–07, University of Trier, Submitted to Advances in Performance Analysis, Notable Publications, Inc.
[4] F. Machihara, “A BMAP/SM/1 Queue with Service Times Depending on the Arrival Process”, Queueing systems, 32:1-3 (1999), 1–15.
[5] L. Ya. Glybin, Ritm zhizni chelovecheskogo obshhestva. Otkrytie fenomena, Vladivostok, 1996, 154 s.
[6] G. Sh. Ciciashvili, M. A. Osipova, “Issledovanie stacionarnyx xarakteristik nekotoryx peremennyx sistem obsluzhivaniya”, DV mat. zhurnal, 1 (2000), 58–62.
[7] G. I. Ivchenko, V. A. Kashtanov, I. N. Kovalenko, Teoriya massovogo obsluzhivaniya, Vysshaya shkola, M., 1982, 256 s.
[8] Yu. A. Rozanov, Teoriya veroyatnostej, sluchajnye processy i matematicheskaya statistika, Nauka, M., 1985, 318 s.
[9] I. N. Kovalenko, N. Yu. Kuznecov, V. M. Shurenkov, Sluchajnye processy, Kiev, 1983, 366 s.
[10] Teoriya veroyatnostej. Matematicheskaya statistika. Teoreticheskaya kibernetika, Itogi nauki i texniki, 1983, 180 s.

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