Mathematical study on the effect of flexibility in complex queueing systems
| Project/Area Number |
26540008
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Mathematical informatics
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| Research Institution | Tokyo University of Science |
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Principal Investigator |
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| Project Period (FY) |
2014-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2015: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | 複合待ち行列 / 柔軟性の効果 / 定常分布の裾の漸近特性 / 重負荷近似 / マルチンゲール / 大偏差値理論 / 複数種類の客をもつ待ち行列ネットワーク / 一般化最小行列選択待ち行列 / 並列待ち行列 / マルコフ過程 / 客とサーバーの柔軟性 / サービス時間分布の効果 / 定常分布の漸近特性 / 定常分布の重負荷近似 / 多次元ランダムウォーク / 確率論 |
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| Outline of Final Research Achievements |
We study a new method for mathematical study on the effect of flexibility in complex queueing systems including networks. This method describes those systems, which may have generally distributed inter-arrival and service times, by a piewise deterministic Markov process, PDMP for short, and uses a martingale decomposition of the PDMP by exponential type of test functions. It differs from our original plan, which uses a reflecting random walk assuming that inter-arrival and service times are exponentially distributed. We apply this method to study the stationary queue length distributions of various systems through their tail asymptotics and their limits in heavy traffic. Those results are used to study flexibility in multiclass queueing networks with static buffer priority service and parallel queues with dedicated and join shortest queue arrivals.
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Report
(3 results)
Research Products
(13 results)
