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1
On geometric and algebraic transience for block-structured Markov chains.
J Appl Probab
2020. [DOI:
10.1017/jpr.2020.69
]
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[Indexed: 11/07/2022]
Abstract
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.
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2
Pérez JF
, Telek M, Van Houdt B. A Fast Newton's Iteration for M/G/1-Type and GI/M/1-Type Markov Chains.
STOCH MODELS
2012. [DOI:
10.1080/15326349.2012.726038
]
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Citation(s) in
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Impact Index Per Article: 0.4
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[Indexed: 10/27/2022]
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3
Duality results for Markov-modulated fluid flow models.
J Appl Probab
2011. [DOI:
10.1017/s0021900200099307
]
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[Indexed: 11/08/2022]
Abstract
We establish some interesting duality results for Markov-modulated fluid flow models. Though fluid flow models are continuous-state analogues of quasi-birth-and-death processes, some duality results do differ by the inclusion of a scaling factor.
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