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Markov Chains with Hybrid Repeating Rows - Upper-Hessenberg, Quasi-Toeplitz Structure of the Block Transition Probability Matrix

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Alexander Dudin ,
Chesoong Kim  and
Valentina Klimenok
Alexander Dudin*
Affiliation:
Belarusian State University
Chesoong Kim*
Affiliation:
Sangji University
Valentina Klimenok*
Affiliation:
Belarusian State University
*
∗Postal address: Laboratory of Applied Probabilistic Analysis, Department of Applied Mathematics and Computer Sciences, Belarusian State University, 4 Independence Avenue, 220030 Minsk-30, Belarus.
∗∗∗Postal address: Department of Industrial Engineering, Sangji University, Wonju, Kangwon, 220-702, Korea. Email address: dowoo@sangji.ac.kr
∗Postal address: Laboratory of Applied Probabilistic Analysis, Department of Applied Mathematics and Computer Sciences, Belarusian State University, 4 Independence Avenue, 220030 Minsk-30, Belarus.
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Abstract

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In this paper we consider discrete-time multidimensional Markov chains having a block transition probability matrix which is the sum of a matrix with repeating block rows and a matrix of upper-Hessenberg, quasi-Toeplitz structure. We derive sufficient conditions for the existence of the stationary distribution, and outline two algorithms for calculating the stationary distribution.

Keywords

Multidimensional Markov chainqueueing systemergodicityalgorithmcensoring

MSC classification

Secondary: 60K25: Queueing theory 60K30: Applications (congestion, allocation, storage, traffic, etc.)
Type
Research Article
Information
Journal of Applied Probability , Volume 45 , Issue 1 , March 2008 , pp. 211 - 225
Copyright
Copyright © Applied Probability Trust 2008 

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