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題名 Kronecker product-forms of steady-state probabilities with Ck/Cm/1 by matrix polynomial approaches
作者 Luh, Hsing Paul
陸行
Liu, Hsin Yi
貢獻者 應數系
關鍵詞 Matrix polynomials; Phase-type distributions; Quasi-birth-and-death process
日期 2011-11
上傳時間 22-六月-2015 14:26:31 (UTC+8)
摘要 In this paper, we analyze a single server queueing system Ck/Cm/1. We construct a general solution space of vector product-forms for steady-state probability and express it in terms of singularities and vectors of the fundamental matrix polynomial Q(ω). It is shown that there is a strong relation between the singularities of Q(ω) and the roots of the characteristic polynomial involving the Laplace transforms of the inter-arrival and service times distributions. Thus, some steady-state probabilities may be written as a linear combination of vectors derived in expression of these roots. In this paper, we focus on solving a set of equations of matrix polynomials in the case of multiple roots. As a result, we give a closed-form solution of unboundary steady-state probabilities of Ck/Cm/1, thereupon considerably reducing the computational complexity of solving a complicated problem in a general queueing model.
關聯 Numerical Algebra, Control and Optimization, 1(4), 691-711
資料類型 article
DOI http://dx.doi.org/10.3934/naco.2011.1.691
dc.contributor 應數系-
dc.creator (作者) Luh, Hsing Paul-
dc.creator (作者) 陸行zh_TW
dc.creator (作者) Liu, Hsin Yien_US
dc.date (日期) 2011-11-
dc.date.accessioned 22-六月-2015 14:26:31 (UTC+8)-
dc.date.available 22-六月-2015 14:26:31 (UTC+8)-
dc.date.issued (上傳時間) 22-六月-2015 14:26:31 (UTC+8)-
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/76004-
dc.description.abstract (摘要) In this paper, we analyze a single server queueing system Ck/Cm/1. We construct a general solution space of vector product-forms for steady-state probability and express it in terms of singularities and vectors of the fundamental matrix polynomial Q(ω). It is shown that there is a strong relation between the singularities of Q(ω) and the roots of the characteristic polynomial involving the Laplace transforms of the inter-arrival and service times distributions. Thus, some steady-state probabilities may be written as a linear combination of vectors derived in expression of these roots. In this paper, we focus on solving a set of equations of matrix polynomials in the case of multiple roots. As a result, we give a closed-form solution of unboundary steady-state probabilities of Ck/Cm/1, thereupon considerably reducing the computational complexity of solving a complicated problem in a general queueing model.-
dc.format.extent 176 bytes-
dc.format.mimetype text/html-
dc.relation (關聯) Numerical Algebra, Control and Optimization, 1(4), 691-711-
dc.subject (關鍵詞) Matrix polynomials; Phase-type distributions; Quasi-birth-and-death process-
dc.title (題名) Kronecker product-forms of steady-state probabilities with Ck/Cm/1 by matrix polynomial approaches-
dc.type (資料類型) articleen
dc.identifier.doi (DOI) 10.3934/naco.2011.1.691-
dc.doi.uri (DOI) http://dx.doi.org/10.3934/naco.2011.1.691-