政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/32568

政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/32568

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政大機構典藏 > 理學院 > 應用數學系 > 學位論文 > Item 140.119/32568

請使用永久網址來引用或連結此文件: https://nccur.lib.nccu.edu.tw/handle/140.119/32568

題名:	Invariant Subspace of Solving Ck/Cm/1 計算 Ck/Cm/1 的機率分配之不變子空間
作者:	劉心怡 Liu,Hsin-Yi
貢獻者:	陸行劉心怡 Liu,Hsin-Yi
關鍵詞:	不變子空間矩陣多項式飽和機率 invariant subspace matrix polynomial Kronecker products
日期:	2003
上傳時間:	2009-09-17 13:45:59 (UTC+8)
摘要:	在這一篇論文中，我們討論 Ck/Cm/1 的等候系統。我們利用矩陣多項式的奇異點及向量造 C_k/C_m/1 的機率分配的解空間。而矩陣多項式的非零奇異點和一個由抵達間隔時間與服務時間所形成的方程式有密切的關係。我們證明了在 E_k/E_m/1 的等候系統中，方程式的所有根都是相異的。但是當方程式有重根時，我們必須解一組相當複雜的方程式才能得到構成解空間的向量。此外，我們建立了一個描述飽和機率為 Kronecker products 線性組合的演算方法。 In this thesis, we analyze the single server queueing system Ck/Cm/1. We construct a general solution space of the vector for stationary probability and describe the solution space in terms of singularities and vectors of the fundamental matrix polynomial Q(w). There is a relation between the singularities of Q(w) and the roots of the characteristic polynomial involving the Laplace transforms of the interarrival and service times distributions. In the Ek/Em/1 queueing system, it is proved that the roots of the characteristic polynomial are distinct if the arrival and service rates are real. When multiple roots occur, one needs to solve a set of equations of matrix polynomials. As a result, we establish a procedure for describing those vectors used in the expression of saturated probability as linear combination of Kronecker products.
參考文獻:	[1] Bellman R. Introduction to Matrix Analysis, MacGraw- Hill, London, (1960). [2] Bertsimas D., An analytic approach to a general class of G/G/s queueing systems. Operations Research 38,139-155, (1990). [3] Bertsimas D., An exact FCFS waiting time analysis for a general class of G/G/s queueing systems. Queueing systems 3, 305-320, (1988). [4] Le Boudec, J. Y., Steady-state probabilities of the PH/PH/1 queue. Queueing systems 3, 73-88, (1988). [5] Evans, R. V. Geometric distribution in some two- dimensional queueing systems. Operations Research 15, 830- 846, (1967). [6] Gail, H. R., Hantler, S. L. and Taylor, B., A Spectral analysis of M/G/1 and G/M/1 Type Markov chaons. Adv. Appl. Prob. 28, 114-165, (1996). [7] Gohberg, I. C., Lancaster, P. and Rodman, L. Matrix polynomials. Academic Press, New York (1982). [8] Gohberg, I. C., Lancaster, P. and Rodman, L. Matrix Topics in Matrix (1991). [9] Neuts, M. F. Matrix-Geomatric Solutions in Stochastic Models. The John Hopkins University Press, (1981). [10] Wang, H. S. A new Approach to Analyze Stationary Probabilities Distributions of a PH/PH/1/N Queue, Master thesis National Chengchi University, (2002). [11] Wallace, V. The solution of quasi birth and death processes arising from multiple access computer systems, Ph. D. diss. Systems Engineering Laboratory, University of Michigan, Tech. Report N 07742-6-T, (1969).
描述:	碩士國立政治大學應用數學研究所 91751006 92
資料來源:	http://thesis.lib.nccu.edu.tw/record/#G0091751006
資料類型:	thesis
顯示於類別:	[應用數學系] 學位論文

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75100601.pdf		94Kb	Adobe PDF2	951	檢視/開啟
75100602.pdf		161Kb	Adobe PDF2	1078	檢視/開啟
75100603.pdf		170Kb	Adobe PDF2	1050	檢視/開啟
75100604.pdf		63Kb	Adobe PDF2	1123	檢視/開啟
75100605.pdf		120Kb	Adobe PDF2	1145	檢視/開啟
75100606.pdf		163Kb	Adobe PDF2	1302	檢視/開啟
75100607.pdf		150Kb	Adobe PDF2	1192	檢視/開啟
75100608.pdf		192Kb	Adobe PDF2	1199	檢視/開啟
75100609.pdf		59Kb	Adobe PDF2	1027	檢視/開啟
75100610.pdf		68Kb	Adobe PDF2	1151	檢視/開啟
75100611.pdf		98Kb	Adobe PDF2	968	檢視/開啟
75100612.pdf		108Kb	Adobe PDF2	1035	檢視/開啟
75100613.pdf		84Kb	Adobe PDF2	1040	檢視/開啟
75100614.pdf		85Kb	Adobe PDF2	1002	檢視/開啟
75100615.pdf		117Kb	Adobe PDF2	1056	檢視/開啟

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