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On geometric and algebraic transience for block-structured Markov chains

Part of: Inference from stochastic processes Markov processes

Published online by Cambridge University Press:  23 November 2020

Yuanyuan Liu ,
Wendi Li  and
Xiuqin Li
Xiuqin Li*
Affiliation:
Central South University
*
*Postal address: School of Mathematics and Statistics, Central South University, Changsha, Hunan, 410075, China.
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Abstract

Block-structured Markov chains model a large variety of queueing problems and have many important applications in various areas. Stability properties have been well investigated for these Markov chains. In this paper we will present transient properties for two specific types of block-structured Markov chains, including M/G/1 type and GI/M/1 type. Necessary and sufficient conditions in terms of system parameters are obtained for geometric transience and algebraic transience. Possible extensions of the results to continuous-time Markov chains are also included.

Keywords

Geometric transiencealgebraic transienceMarkov chainsblock structuresspectral analysis

MSC classification

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 62M15: Spectral analysis
Type
Research Papers
Information
Journal of Applied Probability , Volume 57 , Issue 4 , December 2020 , pp. 1313 - 1338
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Copyright
© Applied Probability Trust 2020

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