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- Nishimura Shoichi
- Department of Applied Mathematics, Faculty of Science, Science University of Tokyo
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- Sato Hajime
- Department of Applied Mathematics, Faculty of Science, Science University of Tokyo
書誌事項
- タイトル別名
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- Eigenvalue Expression for a Batch Marko
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抄録
Consider a batch Markovian arrival process (BMAP) as the counting process of an underlying Markov process representing the state of environment. Such a process is useful for representing correlated inputs for example. They are used both as a modeling tool and as a theoretical device to represent and approximate superposition of input processes and complex large systems. Our objective is to consider the first and second moments of the counting process depending on time and state. Assuming that the probability generating functions of batch size are analytic, and that eigenvalues of the infinitesimal generator are simple, we derive an analytic diagonalization for the matrix generating function of the counting process. Our main result gives the time-dependent form of the first and second factorial moments of the counting process, which is represented by eigenvalues and eigenvectors of the matrix generating function of the batch size.
収録刊行物
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- 日本オペレーションズ・リサーチ学会論文誌
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日本オペレーションズ・リサーチ学会論文誌 40 (1), 122-132, 1997
公益社団法人 日本オペレーションズ・リサーチ学会
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詳細情報 詳細情報について
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- CRID
- 1390282679086256768
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- NII論文ID
- 110001184483
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- NII書誌ID
- AA00703935
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- ISSN
- 21888299
- 04534514
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- NDL書誌ID
- 4163576
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- 本文言語コード
- en
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- データソース種別
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- JaLC
- NDL
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- 抄録ライセンスフラグ
- 使用不可