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Error bounds for last-column-block-augme...
Masuyama, Hiroyuki...

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Error bounds for last-column-block-augmented truncations of block-structured Markov chains by Masuyama, Hiroyuki ( Author )
Lemonjar Open Access
N.A
14-01-2016
This paper discusses the error estimation of the last-column-block-augmented northwest-corner truncation (LC-block-augmented truncation, for short) of block-structured Markov chains (BSMCs) in continuous time. We first derive upper bounds for the absolute difference between the time-averaged functionals of a BSMC and its LC-block-augmented truncation, under the assumption that the BSMC satisfies the general f-modulated drift condition. We then establish computable bounds for a special case where the BSMC is exponentially ergodic. To derive such computable bounds for the general case, we propose a method that reduces BSMCs to be exponentially ergodic. We also apply the obtained bounds to level-dependent quasi-birth-and-death processes (LD-QBDs), and discuss the properties of the bounds through the numerical results on an M/M/s retrial queue, which is a representative example of LD-QBDs. Finally, we present computable perturbation bounds for the stationary distribution vectors of BSMCs.
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Article
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36.88 KB
English
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MYR 0.01
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https://arxiv.org/abs/1601.03489
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