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Please use this identifier to cite or link to this item: https://ah.lib.nccu.edu.tw/handle/140.119/32611
DC FieldValueLanguage
dc.contributor.advisor陸行zh_TW
dc.contributor.author陳瓏元zh_TW
dc.contributor.authorChen Lung Yuanen_US
dc.creator陳瓏元zh_TW
dc.creatorChen Lung Yuanen_US
dc.date2005en_US
dc.date.accessioned2009-09-17T05:50:46Z-
dc.date.available2009-09-17T05:50:46Z-
dc.date.issued2009-09-17T05:50:46Z-
dc.identifierG0927510151en_US
dc.identifier.urihttps://nccur.lib.nccu.edu.tw/handle/140.119/32611-
dc.description碩士zh_TW
dc.description國立政治大學zh_TW
dc.description應用數學研究所zh_TW
dc.description92751015zh_TW
dc.description94zh_TW
dc.description.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。zh_TW
dc.description.abstractIn 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.en_US
dc.description.tableofcontents1 Introduction 1\n2 The Model 4\n 2.1 Interarrival and Service Times................4\n 2.2 Matrix of Transition Rates....................6\n 2.3 Balance Equations.............................8\n 2.4 Vector Product-Form Solutions.................9\n 2.4.1 Case of Simple Roots....................9\n 2.4.2 A simple Case of Multiple Roots........12\n 2.5 Boundary State Probabilities.................13\n 2.6 Performance Measures.........................14\n3 A Summary of the Algorithm 16\n 3.1 The Algorithm................................16\n 3.2 Example of C2/C2/1/7 Systems.................17\n 3.2.1 The Example of Case 1 of rho<1.........17\n 3.2.2 The Example of Case 2 of rho>1.........20\n4 Numerical Experiments 24\n 4.1 Using the Product-Form Method by Matlab......25\n 4.2 Case 1: Ck/Cm/1/4............................27\n 4.3 Case 2: Ck/Cm/1/6............................31\n5 Conclusions and Remarks 36\nReferences 37\nAppendix A 39\nAppendix B 40zh_TW
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dc.language.isoen_US-
dc.source.urihttp://thesis.lib.nccu.edu.tw/record/#G0927510151en_US
dc.subject等候系統zh_TW
dc.subjectQueueen_US
dc.subjectCoxian distributionsen_US
dc.subjectVector product-formsen_US
dc.subjectPhase-type probability distributionsen_US
dc.title以向量表示求解有限佇列的計算方法zh_TW
dc.titleImplementation of Vector Product-Form Approach in Ck/Cm/1/N Queueing Systemsen_US
dc.typethesisen
dc.relation.referenceBellman R., Introduction to Matrix Analysis,MacGraw-Hill, London, (1960).zh_TW
dc.relation.referenceBertsimas D., An analytic approach to a general classzh_TW
dc.relation.referenceof G/G/s queueing systems. Operations Research 38, 139-155, (1990).zh_TW
dc.relation.referenceChao, X., Pinedo, M. and Shaw, D.,An Assembly Network of Queues with Product Form Solution. Journal of Applied Probability, 33, 858-869, (1996).zh_TW
dc.relation.referenceChao, X., Miyazawa, M., Serfozo, R., and Takada. H., Necessary and sufficient conditions for product form queueing networks. Queueing Systems, Vol 28, 377-401,(1998).zh_TW
dc.relation.referenceLe Boudec, J.Y., Steady-state probabilities of the PH/PH/1 queue. Queueing Systems 3, 73-88, (1988).zh_TW
dc.relation.referenceLuh, H.\\, Matrix product-form solutions of stationary probabilities in tandem queues. Journal of the Operations Research 42-4, 436-656, (1999).zh_TW
dc.relation.referenceLiu, S. Y. Invariant Subspace of Solving C_{k}/C_{m}/1, Master thesis National Chengchi University.(2004)zh_TW
dc.relation.referenceNeuts, M.F., Matrix-Geometric Solutions in Stochastic Models. The John Hopkins University Press, (1981).zh_TW
dc.relation.referenceNeuts, 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).zh_TW
dc.relation.referenceWang, S. Y. A New Approach to Analyze Stationary Probability Distribution of a PH/PH/1/N Queue, Master thesis National Chengchi University.(2002)zh_TW
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