2018 Fiscal Year Final Research Report
Unified approach for studying large queues and its application to complex network models
| Project/Area Number |
16H02786
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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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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| Co-Investigator(Renkei-kenkyūsha) |
SKUMA Yutaka 防衛大学, 情報工学科, 講師 (00434027)
KOBAYASHI Masahiro 東海大学, 理学部情報数理学科, 准教授 (90609356)
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| Research Collaborator |
Dai Jim G. Cornell University, Professor
Foss Sergey Heriot-Watt University, Professor
Blanchet Jose Stanford University, Associate professor
Rolski Tomasz The University of Wroclaw, Professor emeritus
Zwart Bert Centrum Wiskunde & Informatica, Professor
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| Project Period (FY) |
2016-04-01 – 2019-03-31
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| Keywords | 待ち行列ネットワーク / セミマルチンゲール / 定常分布 / 漸近特性 / 拡散近似 / 流体待ち行列ネットワーク / 優先権のあるサービス / 状態空間の崩壊 |
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| Outline of Final Research Achievements |
In these days, service systems are of networks, and widely used in our daily life and economic activities, e.g., for communication, physical distribution and production. In those systems, congestions may largely degrade service or performance quality. This study aims to establish a mathematical method to find a mechanism to cause large congestions, and to apply it to various queueing networks such as generalized Jackson networks, multiclass queueing networks with priority service and Markov modulated fluid queueing networks. We here mainly focus on the stationary distributions of multidimensional queue length processes in those network models, and consider their tail asymptotics and diffusion approximations under the heavy traffic conditions. We study these two different type of asymptotic problems by a unfied approach, while they have been separately studied in the literature. We also study some related asymptotic problem for the sojourn time in a network.
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| Free Research Field |
待ち行列理論
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| Academic Significance and Societal Importance of the Research Achievements |
（学術的意義）本研究は待ち行列ネットワークを表す確率過程において定常分布の裾の漸近特性や重負荷の下での拡散近似を求める理論的な枠組みをセミマルチンゲールを用いて構築し，新しい形の時間展開式を導き，各種の漸近問題を統一的に解くことができることを示した．これは確率過程の漸近理論に新たな展開を切り開くものである．
（社会的意義）今日サービスネットワークは私達の生活や経済活動に欠かせないが，混雑がサービス品質を劣化させる大きな原因となっている．本研究はこれらのシステムを待ち行列ネットワークにより表し，混雑の発生や影響を明らかにした．これは生活の質の向上や経済活動の円滑化に貢献するものである．
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