2014 Fiscal Year Final Research Report
Asymptotic behaviors of a multidimensional stochastic process and their applications for safety design of a queueing network.
| Project/Area Number |
24310115
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Partial Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Social systems engineering/Safety system
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| Research Institution | Tokyo University of Science |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
KOBAYASHI Masahiro 東海大学, 理学部, 講師 (90609356)
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Keywords | 待ち行列ネットワーク / 安全設計 / 稀少事象 / 多次元ブラウン運動 / 定常分布の漸近特性 / マルコフ変調過程 / 大偏差値理論 / 国際研究者交流 |
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| Outline of Final Research Achievements |
A multidimensional semi-martingale reflecting Brownian motion, SRBM for short, has been used for approximating a queueing network as a simple model with relatively less modeling parameters. However, its properties are not well studied except for special cases. We study asymptotic behaviors and decomposability of its stationary distribution. The SRBM is known as a process limit of the joint queue length process of a generalized Jackson network, which is known as a more realistic queueing network model, in heayy traffic. We give more credit about this approximation by proving that the tail decay rates of their stationary distributions are asymptotically identical in heavy traffic. Based on those studies, we give procedures to see how large queues arise in the queueing network, which provide various measures for safety design of the queueing network.
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| Free Research Field |
待ち行列理論，応用確率過程，大偏差値理論
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