政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/32611

政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/32611

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政大典藏 > College of Science > Department of Mathematical Sciences > Theses > Item 140.119/32611

Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/32611

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 Queue Coxian distributions Vector product-forms Phase-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 class of 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 92751015 94
Source URI:	http://thesis.lib.nccu.edu.tw/record/#G0927510151
Data Type:	thesis
Appears in Collections:	[Department of Mathematical Sciences] Theses

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