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- W2268727185 abstract "This paper considers continuous-time block-monotone Markov chains (BMMCs) and their block-augmented truncations. We first introduce the block monotonicity and block-wise dominance relation for continuous-time Markov chains, and then provide some fundamental results on the two notions. Using these results, we show that the stationary distribution vectors obtained by the block-augmented truncation converge to the stationary distribution vector of the original BMMC. We also show that the last-column-block-augmented truncation (LC-block-augmented truncation) provides the best (in a certain sense) approximation to the stationary distribution vector of a BMMC among all the block-augmented truncations. Furthermore, we present computable upper bounds for the total variation distance between the stationary distribution vectors of a Markov chain and its LC-block-augmented truncation, under the assumption that the original Markov chain itself may not be block-monotone but is block-wise dominated by a BMMC with exponential ergodicity. Finally, we apply the obtained bounds to a queue with a batch Markovian arrival process and state-dependent departure rates." @default.
- W2268727185 created "2016-06-24" @default.
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- W2268727185 date "2017-02-01" @default.
- W2268727185 modified "2023-09-29" @default.
- W2268727185 title "Continuous-time block-monotone Markov chains and their block-augmented truncations" @default.
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- W2268727185 doi "https://doi.org/10.1016/j.laa.2016.10.014" @default.
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