کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
8898085 1631081 2017 52 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Continuous-time block-monotone Markov chains and their block-augmented truncations
ترجمه فارسی عنوان
زنجیره مارکوف بلوک-مونوتوپی پیوسته و کوتاه شدن بلوک-تکمیل شده
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
چکیده انگلیسی
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.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 514, 1 February 2017, Pages 105-150
نویسندگان
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