Basic research of multi-server queues with abadonment
| Project/Area Number |
17K01244
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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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| Research Field |
Social systems engineering/Safety system
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| Research Institution | Gunma University |
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Principal Investigator |
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| Project Period (FY) |
2017-04-01 – 2021-03-31
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| Project Status |
Completed (Fiscal Year 2020)
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| Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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| Keywords | 待ち行列理論 / 応用確率過程論 / モデル化 / 性能評価 / 数理工学 / システム工学 / 応用数学 |
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| Outline of Final Research Achievements |
In this research, we analyzed multi-server queues with customer abandonment. Customers arrive according to Poisson process, and service times of customers are distributed according to phase-type distribution. We assume that the time to abandon of waiting customers is generally distributed. Exploiting the results of exact analysis of multi-server queues where the time to abandon is constant, we obtained an algorithm to compute the probability density function of attained waiting time of the queues. We also obtained performance measures of the queues and obtained upper and lower bounds of customer abandonment probability, delay probability.
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| Academic Significance and Societal Importance of the Research Achievements |
待ち行列理論におけるM/G/cモデルの厳密な解析は困難であることが知られており，サービス時間を相型分布で近似する方法がこれまでに検討されてきた．同じことが本研究で扱った途中退去が伴う場合にも当てはまる．解決策として，途中退去時間も相型分布で近似する方法が考えられるが，状態空間が指数関数的に増大するため数値計算には不向きである．本研究では途中退去時間を階段関数で近似する方法を検討し，数値計算に適した途中退去が伴う複数窓口をもつ待ち行列モデルが解析できることを示した．M/G/cモデルの厳密解が困難であることを鑑みれば，本研究成果はそれと同程度の困難な問題に対して，一つの解決策を与えたと言える．
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Report
(5 results)
Research Products
(8 results)
