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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
Chen Lung Yuan
Keywords: 等候系統
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
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Data Type: thesis
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