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Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)



Stability of a tandem of queueing systems with Bernoulli noninstantaneous transfer of customers

Author: A. V. Zorin
Translated by: N. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 84 (2011).
Journal: Theor. Probability and Math. Statist. 84 (2012), 173-188
MSC (2010): Primary 60K25, 90B22
Published electronically: August 2, 2012
MathSciNet review: 2857427
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Abstract | References | Similar Articles | Additional Information

Abstract: A tandem of queueing systems with cyclic control algorithm and with independent conflict input flows is considered. The customers served in the first queueing system are transferred to the second system with random speeds. A cybernetic approach is used to construct a mathematical model in terms of a multidimensional denumerable Markov chain. The classification of the states of this Markov chain is carried out, and a sufficient condition for the existence of the stationary distribution is obtained.

References [Enhancements On Off] (What's this?)

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Additional Information

A. V. Zorin
Affiliation: Department of Applied Probability Theory, Faculty for Computational Mathematics and Cybernetics, Lobachevskiĭ State University of Nizhniĭ Novgorod — National Research University, Gagarin Avenue 23, Nizhniĭ Novgorod 603950, Russia

Keywords: Controlled queueing system, cybernetic approach, nonlocal description of the input flow, Markov chain, stationary distribution
Received by editor(s): October 13, 2010
Published electronically: August 2, 2012
Additional Notes: This work is supported by the State Scientific Research Project # 0120.0602598 “The analysis of discrete control queueing systems and systems for the evaluation of Boolean functions” at the Lobachevskiĭ State University of Nizhniĭ Novgorod
Article copyright: © Copyright 2012 American Mathematical Society

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