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Non-Uniqueness of the Minimal Realization Problem Representation of the Markovian Arrival Process of Order 2 and Moment Fitting
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Publication Year
2021-08
Journal
한국경영과학회지
Publisher
한국경영과학회
Citation
한국경영과학회지, Vol.46 No.3, pp.1-8
Keyword
Markovian Arrival ProcessesMinimal Realization ProblemMinimal RepresentationUniqueness of the Representation
Abstract
Markovian arrival processes (MAPs) can be represented in many different ways such as the Markovian representation, Laplace transform, Jordan representation, and minimal realization problem (MRP) representation, to name a few. The MRP representation is given in two real-valued matrices (K’, R’) and can be used to determine the Markovian representation (D0, D1) by similarity transformation. The MRP representation has been claimed to be unique but redundant. In this paper, we show that the MRP representation is not unique and then provide a non-redundant MRP representation of MAP(2)s. We also present closed-form formulas for the transformation from the MRP representation to the Markovian representation (D0, D1) for MAP(2)s.
ISSN
1225-1119
Language
Eng
URI
https://aurora.ajou.ac.kr/handle/2018.oak/35458
Type
Article
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Kim, Sunkyo김선교
Department of Business Administration
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