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題名: | 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 |
作者: | 陳瓏元 Chen Lung Yuan |
貢獻者: | 陸行 陳瓏元 Chen Lung Yuan |
關鍵詞: | 等候系統 Queue Coxian distributions Vector product-forms Phase-type probability distributions |
日期: | 2005 | 上傳時間: | 17-Sep-2009 | 摘要: | 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. |
參考文獻: | 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) |
描述: | 碩士 國立政治大學 應用數學研究所 92751015 94 |
資料來源: | http://thesis.lib.nccu.edu.tw/record/#G0927510151 | 資料類型: | thesis |
Appears in Collections: | 學位論文 |
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51015110.pdf | 207.01 kB | Adobe PDF2 | View/Open |
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