Stability of a tandem of queueing systems with Bernoulli noninstantaneous transfer of customers
Author:
A. V. Zorin
Translated by:
N. Semenov
Journal:
Theor. Probability and Math. Statist. 84 (2012), 173-188
MSC (2010):
Primary 60K25, 90B22
DOI:
https://doi.org/10.1090/S0094-9000-2012-00867-3
Published electronically:
August 2, 2012
MathSciNet review:
2857427
Full-text PDF Free Access
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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
- M. A. Fedotkin, Optimal control of conflicting flows and marked point processes with an isolated discrete component. I, Litovsk. Mat. Sb. 28 (1988), no. 4, 783–794 (Russian). MR 987873
- M. A. Fedotkin, Queueing processes and control systems, Mathematical problems in cybernetics, No. 6 (Russian), Mat. Vopr. Kibern., vol. 6, FizMatLit, Moscow, 1996, pp. 51–70 (Russian). MR 1856119
- M. A. Fedotkin, A nonlocal method for determining controlled random processes, Mathematical problems in cybernetics, No. 7 (Russian), Mat. Vopr. Kibern., vol. 7, FizMatLit, Moscow, 1998, pp. 333–344 (Russian). MR 1843047
- A. V. Zorin and M. A. Fedotkin, Optimization of the control of doubly stochastic nonordinary flows in time-sharing systems, Avtomat. i Telemekh. 7 (2005), 102–111 (Russian, with Russian summary); English transl., Autom. Remote Control 66 (2005), no. 7, 1115–1124. MR 2167835, DOI https://doi.org/10.1007/s10513-005-0152-8
References
- M. A. Fedotkin, Optimal control for conflicting flows and marked point processes with an isolated discrete component. I, Litovsk. Mat. Sb. 28 (1988), no. 4, 783–794. (Russian) MR 987873 (90e:90056)
- M. A. Fedotkin, Queueing processes and control systems, Mathematical problems in cybernetics 6 (1996), Nauka, Moscow, pp. 51–70. (Russian) MR 1856119
- M. A. Fedotkin, A nonlocal method for determining control random processes, Mathematical problems in cybernetics 7 (1998), Nauka, Moscow, pp. 333–344. (Russian) MR 1843047
- A. V. Zorin and M. A. Fedotkin, Optimization of control of doubly stochastic nonordinary flows in time-sharing systems, Avtomat. i Telemekh. 66 (2005), no. 7, 102–111; English transl. in Autom. Remote Control 66 (2005), no. 7, 1115–1124. MR 2167835
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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
Email:
zoav1602@gmail.com
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
