Please use this identifier to cite or link to this item: `https://ah.nccu.edu.tw/handle/140.119/51313`

 Title: 以矩陣分解法計算特別階段形機率分配並有多人服務之排隊模型A phase-type queueing model with multiple servers by matrix decomposition approaches Authors: 顏源亨Yen, Yuan Heng Contributors: 陸行Luh, Hsing顏源亨Yen, Yuan Heng Keywords: 階段形機率分配多重服務器穩定狀態機率Phase-type distributionmultiple serversstationary probability Date: 2010 Issue Date: 2011-10-05 14:39:41 (UTC+8) Abstract: 穩定狀態機率是讓我們了解各種排隊網路性能的基礎。在擬生死過程(Quasi-Birth-and-Death) Phase-type 分配中求得穩定狀態機率，通常是依賴排隊網路的結構。在這篇論文中，我們提出了一種計算方法-LU分解，可以求得在排隊網路中有多台服務器的穩定狀態機率。此計算方法提供了一種通用的方法，使得複雜的大矩陣變成小矩陣，並減低計算的複雜性。當需要計算一個複雜的大矩陣，這個成果變得更加重要。文末，我們提到了離開時間間隔，並用兩種方法 (Matlab 和 Promodel) 去計算期望值和變異數，我們發現兩種方法算出的數據相近，接著計算離開顧客的時間間隔相關係數。最後，我們提供數值實驗以計算不同服務器個數產生的離去過程和相關係數，用來說明我們的方法。Stationary probabilities are fundamental in response to various measures of performance in queueing networks. Solving stationary probabilities in Quasi-Birth-and-Death(QBD) with phase-type distribution normally are dependent on the structure of the queueing network. In this thesis, a new computing scheme is developed for attaining stationary probabilities in queueing networks with multiple servers. This scheme provides a general approach of consindering thecomplexity of computing algorithm. The result becomes moresignificant when a large matrix is involved in computation. After determining the stationary probability, we study the departure process and the moments of inter-departure times. We can obtain the moment of inter-departure times. We compute the moments of inter-departure times and the variance by applying two numerical methods (Matlab and Promodel). The lag-k correlation of inter-departure times is also introduced in the thesis. The proposed approach is proved theoretically and verifieded with illustrative examples. Reference: 1.Bitran, G.R., Dasu, S., Analysis of the Ph/Ph/1 queue.Operations Research, Vol. 42, No. 1, pp.158--174, 1994.2.Bodrog, L., Horvath, A., Telek, M.,Momentcharacterization of matrix exponential and Markovianarrival processes. Annals of operations Reseach, toappear, 2008.3.Chuan, Y.W., Luh, H., Solving a two-node closed queueingnetwork by a new approach, International Journal ofInformation and Management Sciences, Vol. 16, No. 4, pp.49--62, 2004.4.Curry, G.L., Gautam, N., Characterizing the departureprocess from a two server Markovian queue: A non-renewalapproach, Proceedings of the 2008 Winter SimulationConference, pp. 2075--2082, 2008.5.El-Rayes, A., Kwiatkowska, M., Norman, G., Solvinginfinite stochastic process algebra model through martix-geometric methods, Proceedings of 7th Process Algebrasand Performance Modelling Workshop (PAPM99), J. Hillstonand M. Silva (Eds.), pp. 41--62, University of Zaragoza,1999.6.Gene H. Golub, Charles F. Van Loan, Matrix Computations,3rd Edition, The Johns Hopkins University Press, 1996.7.Latouche, G., Ramaswami, V., Introduction to MatrixAnalytic Methods in Stochastic Modeling, ASA-SIAM Serieson Statistics and Applied Probability (SIAM), Society forIndustrial Mathematics, Philadelphia, PA, 2000.8.Neuts, M.F., Matrix-Geometric Solutions in StochasticModels, The John Hopkins University Press, 1981.9.Roger, A.H., Charles, R.J., Matrix analysis, 4thEdition,The Press Syndicate of the University ofCambrige, 1990.10.Sikdar, K., Gupta, U.C., The queue length distributionsin the finite buffer bulk-service \$MAP/G/1\$ queue withmultple vacations, Sociedad de Estadistica eInvestigacion Operativa, Vol. 13, No.1, pp. 75--103, 2005.11.Telek, M., Horvath, G., A minimal representation ofMarkov arrival processes and a moments matching method.Performance Evaluation, Vol. 64, pp. 1153--1168, 2007.12.Whitt, W. The queueing network analyzer, The Bell systemTechnical Journal, Vol. 62, No. 9, pp. 2779--2814, 1983.13.The MathWorks Company,MATLAB The Language of Technical Computing: UsingMALTAB, Version 6, 2002.14.Promodel Corp., Promodel User Guide, Promodel Corp.,2001. Description: 碩士國立政治大學應用數學系數學教學碩士在職專班9797200499 Source URI: http://thesis.lib.nccu.edu.tw/record/#G0097972004 Data Type: thesis Appears in Collections: [應用數學系] 學位論文

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