Informatics and Applications
2022, Volume 16, Issue 2, pp 27-34
ON MONOTONICITY OF SOME CLASSES OF MARKOV CHAINS
- Y. A. Satin
- A. L. Kryukova
- V. S. Oshushkova
- A. I. Zeifman
Abstract
The authors define a relation of partial order for Markov chains and study conditions of monotonicity for some classes of continuous-time Markov processes. The corresponding theorems of monotonicity are formulated.
The authors describe in detail the classes of processes which satisfy conditions of monotonicity. There are a lot of applications of Markov chains with interval intensities that is why the authors consider it. The monotonicity conditions obtained in this paper make it possible to advance in some way in the study of Markov processes with interval intensities. Namely, in the present paper, the authors consider as an example a queuing system Mt/Mt/S/S with interval coefficients. The results obtained are confirmed by a computational experiment and illustrated by the corresponding graphs of the limiting characteristics.
[+] References (7)
- Keilson, J., and A. Kester. 1977. Monotone matrices and monotone Markov processes. Stoch. Proc. AppL 5(3):231-241. doi: 10.1016/0304-4149(77)90033-3.
- Van Doorn, E.A. 1981. Preliminaries. Stochastic monotonicity and queueing applications of birth-death processes. New York, NY: Springer. 1–10. doi: 10.1007/978-1-4612-5883-4_1.
- Gaudio, J., S. Amin, and P. Jaillet. 2019. Exponential convergence rates for stochastically ordered Markov processes under perturbation. Syst. Control Lett. 133:104515. 7 p. doi: 10.1016/j.sysconle.2019.104515.
- Chitraganti, S., S. Aberkane, and C. Aubrun. 2013. Mean square stability of non-homogeneous Markov jump linear systems using interval analysis. European Control Conference Proceedings. 3724-3729. doi: 10.23919/ ECC.2013.6669298.
- Xie, F, B. Wu, Y. Hu, et al. 2013. A generalized Markov chain model based on generalized interval probability. Sci. China Technol. Sc. 56:2132-2136. doi: 10.1007/s11431- 013-5285-3.
- Zeifman, A., Ya. Satin, A. Kryukova, R. Razumchik, K. Kiseleva, and G. Shilova. 2020. On the three methods for bounding the rate of convergence for some continuous-time Markov chains. Int. J. Appl. Math. Comp. Sci. 30(2):251- 266. doi: 10.34768/amcs-2020-0020.
- Van Doorn, E. A., and A. I. Zeifman. 2009. On the speed of convergence to stationarity of the Erlang loss system. Queueing Syst. 63(1):241-252. doi: 10.1007/s11134-009- 9134-9.
[+] About this article
Title
ON MONOTONICITY OF SOME CLASSES OF MARKOV CHAINS
Journal
Informatics and Applications
2022, Volume 16, Issue 2, pp 27-34
Cover Date
2022-07-25
DOI
10.14357/19922264220204
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
monotonicity of Markov processes; nonstationary queuing system; Markov chains with interval intensities; limit characteristics
Authors
Y. A. Satin  , A. L. Kryukova , V. S. Oshushkova  , and A. I. Zeifman ,  ,  , 
Author Affiliations
Department of Applied Mathematics, Vologda State University, 15 Lenin Str., Vologda 160000, Russian Federation
Innovative People Ltd., 26-28 Leninskaya Sloboda Str., Moscow 115280, Russian Federation
Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
Vologda Research Center of the Russian Academy of Sciences, 56A Gorky Str., Vologda 160014, Russian Federation
Moscow Center for Fundamental and Applied Mathematics, M.V. Lomonosov Moscow State University, 1 Leninskie Gory, GSP-1, Moscow 119991, Russian Federation
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