2018 Fiscal Year Final Research Report
Tail asymptotics of a stationary distribution of a reflecting random walk and its application to queueing networks
| Project/Area Number |
17K18126
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Mathematical informatics
Social systems engineering/Safety system
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| Research Institution | Tokai University |
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Principal Investigator |
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| Research Collaborator |
Miyazawa Masakiyo
Ozawa Toshihisa
Masuyama Hiroyuki
Inoie Atsushi
Sakuma Yutaka
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| Project Period (FY) |
2017-04-01 – 2019-03-31
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| Keywords | 反射型ランダムウォーク / 待ち行列 / 定常分布 / 漸近解析 / 誤差上界 |
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| Outline of Final Research Achievements |
We are interested in a stationary analysis of a two-dimensional reflecting random walk. Here, the two-dimensional reflecting random walk is a discrete time stochastic process on the non-negative quadrant. For the reflecting random walk, a distribution in the steady state is called a stationary distribution.
In this study, we obtain an error upper bound of the stationary distribution between theoretical and numerical solutions. In addition, we also obtain the tail asymptotics of the stationary distribution of a discrete time two-dimensional quasi-birth-and-death process which is generalization of the two-dimensional reflecting random walk.
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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 |
反射型ランダムウォークは，待ち行列理論のみならず他分野にも応用されるモデルである．さらに，定常分布は確率モデルの性能評価をする上で非常に重要な指標となっている．
反射型ランダムウォークの定常分布について，理論的な特性を求めている研究は多くある．しかし，ほとんどの研究が強い仮定をしている．本研究では，その仮定を取り除き，定常分布の理論的な特性を新たな証明により得ることができた．本研究の結果は，より一般的な待ち行列ネットワークに応用を可能とする．さらに新しい証明方法は，さらなるモデルの一般化を可能とすることが予想される．
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