Please use this identifier to cite or link to this item: `https://ah.nccu.edu.tw/handle/140.119/32568`

 Title: Invariant Subspace of Solving Ck/Cm/1計算 Ck/Cm/1 的機率分配之不變子空間 Authors: 劉心怡Liu,Hsin-Yi Contributors: 陸行劉心怡Liu,Hsin-Yi Keywords: 不變子空間矩陣多項式飽和機率invariant subspacematrix polynomialKronecker products Date: 2003 Issue Date: 2009-09-17 13:45:59 (UTC+8) Abstract: 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 systemCk/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 polynomialinvolving the Laplace transforms of the interarrival and servicetimes distributions. In the Ek/Em/1 queueing system, it is proved that the roots of the characteristic polynomial aredistinct if the arrival and service rates are real. Whenmultiple 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. Reference: [1] Bellman R. Introduction to Matrix Analysis, MacGraw-Hill, London, (1960).[2] Bertsimas D., An analytic approach to a general class ofG/G/s queueing systems. Operations Research 38,139-155,(1990).[3] Bertsimas D., An exact FCFS waiting time analysis for ageneral class of G/G/s queueing systems. Queueing systems3, 305-320, (1988).[4] Le Boudec, J. Y., Steady-state probabilities of thePH/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 Spectralanalysis 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. Matrixpolynomials. Academic Press, New York (1982).[8] Gohberg, I. C., Lancaster, P. and Rodman, L. Matrix Topicsin Matrix (1991).[9] Neuts, M. F. Matrix-Geomatric Solutions in StochasticModels. The John Hopkins University Press, (1981).[10] Wang, H. S. A new Approach to Analyze StationaryProbabilities Distributions of a PH/PH/1/N Queue, Masterthesis National Chengchi University, (2002).[11] Wallace, V. The solution of quasi birth and deathprocesses arising from multiple access computer systems,Ph. D. diss. Systems Engineering Laboratory, Universityof Michigan, Tech. Report N 07742-6-T, (1969). Description: 碩士國立政治大學應用數學研究所9175100692 Source URI: http://thesis.lib.nccu.edu.tw/record/#G0091751006 Data Type: thesis Appears in Collections: [Department of Mathematical Sciences] Theses

Files in This Item:

File Description SizeFormat