Numerical algorithm for block-structured Markov chains wth level-dependent transitions

Research Project

Project/Area Number	18K04622
Research Category	Grant-in-Aid for Scientific Research (C)
Allocation Type	Multi-year Fund
Section	一般
Review Section	Basic Section 25010:Social systems engineering-related
Research Institution	Kanagawa Institute of Technology
Principal Investigator	Inoie Atsushi 神奈川工科大学, 情報学部, 准教授 (30434418)
Project Period (FY)	2018-04-01 – 2024-03-31
Project Status	Completed (Fiscal Year 2023)
Budget Amount *help	¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000) Fiscal Year 2020: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000) Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000) Fiscal Year 2018: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000)
Keywords	待ち行列 / マルコフ連鎖 / 行列解析法 / アルゴリズム / マルコフ過程 / 待ち行列理論 / 数値計算
Outline of Final Research Achievements	A block-structured Markov chain with level-dependent transitions is recently used in applications in the field of queueing theory. When using this Markov chain for performance evaluation of a system, obtaining its stationary distribution is necessary. However, it is difficult to obtain the stationary distribution analytically because this Markov chain has a complicated structure. Therefore, in many applications, the stationary distribution is obtained numerically using a numerical algorithm. However, traditional numerical algorithms do not analytically guarantee the accuracy of the stationary distribution . Therefore, the goal of this study is to propose an algorithm for computing stationary distributions that takes the above-mentioned problem into account.
Academic Significance and Societal Importance of the Research Achievements	レベル依存型のブロック構造を持つマルコフ連鎖は、情報通信ネットワークをはじめとした、複雑なシステムを性能評価する際のモデル化に適している。ゆえに、近年のコンピュータの性能向上に伴い、計算機シミュレーションに代わる性能評価ツールとして注目されており、将来的に工学を含めた様々な分野で多く利用されると予想している。しかしながら、レベル依存型のブロック構造を持つマルコフ連鎖はその構造の複雑さゆえに、理論的追求がほとんどされていない。ゆえに、本研究がその一助になることを期待している。