Study of level-dependent structured Markov chains and queues
| Project/Area Number |
15K00034
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Mathematical informatics
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| Research Institution | Kyoto University |
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Principal Investigator |
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2017: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | マルコフ連鎖 / 待ち行列理論 / 漸近解析 / 切断近似 / 誤差評価 / 数値計算 / 構造化マルコフ連鎖 / 待ち行列 / レベル依存型 |
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| Outline of Final Research Achievements |
We first studied the subexponentially asymptotic analysis of upper block Hessenberg Markov chains with asymptotic level independence. Next, we derived computable upper bounds for the last-column-block-augmented truncation approximation to the stationary distribution in block-monotone Markov chains. Associated with this result, we also studied the convergence speed of the last-column-block-augmented truncation approximation of M/G/1-type Markov chains. Then, for general level-dependent structured Markov chains, we presented computable upper bounds for the last-column-block-augmented truncation approximation to the stationary distribution and a limit formula for the normalized fundamental matrix of the northwest-corner truncation. In addition, we derived computable upper bounds for the quasi-birth-and-death approximation to the stationary distribution in a special two-dimensional reflecting random walk.
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Report
(4 results)
Research Products
(15 results)
