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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: | Nov-2011 | 上傳時間: | 22-Jun-2015 | 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 |
Appears in Collections: | 期刊論文 |
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