| Project/Area Number |
18K11181
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Review Section |
Basic Section 60020:Mathematical informatics-related
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| Research Institution | Kyoto University |
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Principal Investigator |
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| Project Period (FY) |
2018-04-01 – 2021-03-31
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| Project Status |
Completed (Fiscal Year 2020)
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| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2020: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2019: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2018: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | 戦略的待ち行列 / 待ち行列ゲーム / ブロック構造化マルコ連鎖 / ランダムウォーク型マルコフ連鎖 / 切断近似 / エルゴード解析 / ブロック構造化マルコフ連鎖 / レベル依存 / 状態依存型待ち行列 / レベル依存型 / 意思決定 |
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| Outline of Final Research Achievements |
This study is concerned with block-structured Markov chains and random-walk-type ones for analyzing state-dependent queues including strategic ones. The main results are as follows. First, we derived an upper bound for the general truncation approximation to the stationary distribution in countable-state Markov chains. We then presented some convergence formulas for the last-column-block-augmented truncation approximation and level-increment truncation approximation to the stationary distribution in M/G/1-type Markov chains. We also established an iterative method for computing the stationary distribution in upper block-Hessenberg Markov chains. Besides, we analyzed the equilibrium arrival distribution in a discrete-time single-server queueing game with a Poisson population of customers trying to minimizing their mean waiting times.
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| Academic Significance and Societal Importance of the Research Achievements |
戦略的待ち行列は, 不特定多数の利用者を収容するサービスシステムでの競合状況を模した数理モデルであり, サービス利用者・提供者の最適な意思決定について分析するために用いられる. 戦略的待ち行列を含む状態依存型待ち行列の解析は, ブロック構造化マルコフ連鎖やランダムウォーク型マルコフ連鎖の解析に帰着される．これらのマルコフ連鎖に関する本研究の成果は, 不確実性下のサービスシステムにおけるサービス利用者・提供者の最適な意思決定法の確立に貢献するものである.
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