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 Title: 以向量表示求解有限佇列的計算方法Implementation of Vector Product-Form Approach in Ck/Cm/1/N Queueing Systems Authors: 陳瓏元Chen Lung Yuan Contributors: 陸行陳瓏元Chen Lung Yuan Keywords: 等候系統QueueCoxian distributionsVector product-formsPhase-type probability distributions Date: 2005 Issue Date: 2009-09-17 13:50:46 (UTC+8) Abstract: 這一篇論文裡，我們討論如何計算開放式有限容量等候系統的穩定機率。其中到達時間和服務時間的機率分配都是Coxian分配。我們利用向量表示法（Product-Form Method）求解穩定機率，並建立C_{k}/C_{m}/1/4與C_{k}/C_{m}/1/6的穩定機率之表格。在使用向量表示法的過程中，計算所需的時間與系統容量無關。因此，在我們計算穩定機率的經驗中，當N>100時，我們可以明顯感覺出向量表示法比一般傳統方法有更快的計算速度。In this thesis, we study the C_{k}/C_{m}/1/N open queueing system with finite capacity, N. We use the product-form method to solve the steady-state probabilities and give tables of numerical results in examples of C_{k}/C_{m}/1/4 and C_{k}/C_{m}/1/6. The merit of this method is that the computation time is independent of N. In our computational experiments, we have observed that when the capacity size of queueing system, N>100, the computing efficiency of the product-form method is much better than that of a traditional method. Reference: Bellman R., Introduction to Matrix Analysis,MacGraw-Hill, London, (1960).Bertsimas D., An analytic approach to a general classof G/G/s queueing systems. Operations Research 38, 139-155, (1990).Chao, X., Pinedo, M. and Shaw, D.,An Assembly Network of Queues with Product Form Solution. Journal of Applied Probability, 33, 858-869, (1996).Chao, X., Miyazawa, M., Serfozo, R., and Takada. H., Necessary and sufficient conditions for product form queueing networks. Queueing Systems, Vol 28, 377-401,(1998).Le Boudec, J.Y., Steady-state probabilities of the PH/PH/1 queue. Queueing Systems 3, 73-88, (1988).Luh, H.\, Matrix product-form solutions of stationary probabilities in tandem queues. Journal of the Operations Research 42-4, 436-656, (1999).Liu, S. Y. Invariant Subspace of Solving C_{k}/C_{m}/1, Master thesis National Chengchi University.(2004)Neuts, M.F., Matrix-Geometric Solutions in Stochastic Models. The John Hopkins University Press, (1981).Neuts, M.F., and Takahashi, Y., Asymptotic behavior of the stationary distributions in the GI/PH/c queue with heterogeneous servers. Z.\ Wahrscheinlichkeitstheorie verw.\ Gebiete, 57, 441-452, (1988).Wang, S. Y. A New Approach to Analyze Stationary Probability Distribution of a PH/PH/1/N Queue, Master thesis National Chengchi University.(2002) Description: 碩士國立政治大學應用數學研究所9275101594 Source URI: http://thesis.lib.nccu.edu.tw/record/#G0927510151 Data Type: thesis Appears in Collections: [應用數學系] 學位論文

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