2014 Fiscal Year Final Research Report
Asymptotic analysis of queueing models and collective risk models with correlation structure
| Project/Area Number |
24710165
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Social systems engineering/Safety system
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| Research Institution | Kyoto University |
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Principal Investigator |
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Keywords | 待ち行列モデル / 集合的リスクモデル / 希少事象確率 / 漸近解析 / 構造化マルコフ連鎖 / GI/G/1型マルコフ連鎖 / 再生型累積過程 / 確率変数のランダム和 |
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| Outline of Final Research Achievements |
The goal of this research project is to establish mathematical tools for the estimation of the rare event probabilities in queueing models and collective risk models with correlation structure. To achieve the goal, we studied the tail asymptotics of GI/G/1-type Markov chains and regenerative cumulative processes sampled at random times. We also utilized the obtained results to derive asymptotic formulas for the loss probability of a single-server queue with a finite capacity fed by an ON-OFF batch Markovian arrival process and deterministic service times. In addition, we presented a computable error bound for the last-block-column-augmented truncation of block-monotone Markov chains.
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| Free Research Field |
待ち行列
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