Expansion of Applicability of Phase Approximation for Non-Markovian Models
| Project/Area Number |
17K00033
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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 |
Mathematical informatics
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| Research Institution | Hiroshima University |
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Principal Investigator |
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| Project Period (FY) |
2017-04-01 – 2020-03-31
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| Project Status |
Completed (Fiscal Year 2019)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2019: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2018: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2017: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | システムモデリング / 位相型近似 / 性能評価 / マルコフモデル / シミュレーション / システム工学 / 確率モデル / ペトリネット / モデル検査 |
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| Outline of Final Research Achievements |
This project partially solved the problems of accuracy guarantee and state explosion in the phase type approximation in MRGP, and expanded the applicability of the phase type approximation in practical use. In particular, as the accuracy guarantee for the phase approximation, we evaluated the upper and lower bounds by using the stochastic order and the total variation. Furthermore, we have developed perfect sampling for Markov model with phase type approximation, and relaxed the problem of state explosion. In perfect sampling, we defined a mathematical programming problem to obtain the upper and lower bounds of system states, and it is solved with an SMT solver. Our algorithm made it possible to apply the perfect sampling to a wide class of models.
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| Academic Significance and Societal Importance of the Research Achievements |
ここで得られた成果は位相型近似で従来から指摘されてきた精度保証と状態爆発の問題をある程度可決し，その適用可能性を大幅に向上させた．確率モデルによるシステム評価は，これからIoT/CPSシステムで利用されるモデルベース開発などでのシステム検証に対して有効である．そのため，ここで得られた成果はシステム全体の高信頼化に対して大きく寄与するものと考えられる．
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Report
(4 results)
Research Products
(11 results)
