| dc.contributor.advisor | 陸行 | zh_TW |
| dc.contributor.author (作者) | 陳瓏元 | zh_TW |
| dc.contributor.author (作者) | Chen Lung Yuan | en_US |
| dc.creator (作者) | 陳瓏元 | zh_TW |
| dc.creator (作者) | Chen Lung Yuan | en_US |
| dc.date (日期) | 2005 | en_US |
| dc.date.accessioned | 17-九月-2009 13:50:46 (UTC+8) | - |
| dc.date.available | 17-九月-2009 13:50:46 (UTC+8) | - |
| dc.date.issued (上傳時間) | 17-九月-2009 13:50:46 (UTC+8) | - |
| dc.identifier (其他 識別碼) | G0927510151 | en_US |
| dc.identifier.uri (URI) | https://nccur.lib.nccu.edu.tw/handle/140.119/32611 | - |
| dc.description (描述) | 碩士 | zh_TW |
| dc.description (描述) | 國立政治大學 | zh_TW |
| dc.description (描述) | 應用數學研究所 | zh_TW |
| dc.description (描述) | 92751015 | zh_TW |
| dc.description (描述) | 94 | zh_TW |
| dc.description.abstract (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。 | zh_TW |
| dc.description.abstract (摘要) | 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. | en_US |
| dc.description.tableofcontents | 1 Introduction 12 The Model 4 2.1 Interarrival and Service Times................4 2.2 Matrix of Transition Rates....................6 2.3 Balance Equations.............................8 2.4 Vector Product-Form Solutions.................9 2.4.1 Case of Simple Roots....................9 2.4.2 A simple Case of Multiple Roots........12 2.5 Boundary State Probabilities.................13 2.6 Performance Measures.........................143 A Summary of the Algorithm 16 3.1 The Algorithm................................16 3.2 Example of C2/C2/1/7 Systems.................17 3.2.1 The Example of Case 1 of rho<1.........17 3.2.2 The Example of Case 2 of rho>1.........204 Numerical Experiments 24 4.1 Using the Product-Form Method by Matlab......25 4.2 Case 1: Ck/Cm/1/4............................27 4.3 Case 2: Ck/Cm/1/6............................315 Conclusions and Remarks 36References 37Appendix A 39Appendix B 40 | zh_TW |
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| dc.language.iso | en_US | - |
| dc.source.uri (資料來源) | http://thesis.lib.nccu.edu.tw/record/#G0927510151 | en_US |
| dc.subject (關鍵詞) | 等候系統 | zh_TW |
| dc.subject (關鍵詞) | Queue | en_US |
| dc.subject (關鍵詞) | Coxian distributions | en_US |
| dc.subject (關鍵詞) | Vector product-forms | en_US |
| dc.subject (關鍵詞) | Phase-type probability distributions | en_US |
| dc.title (題名) | 以向量表示求解有限佇列的計算方法 | zh_TW |
| dc.title (題名) | Implementation of Vector Product-Form Approach in Ck/Cm/1/N Queueing Systems | en_US |
| dc.type (資料類型) | thesis | en |
| dc.relation.reference (參考文獻) | Bellman R., Introduction to Matrix Analysis,MacGraw-Hill, London, (1960). | zh_TW |
| dc.relation.reference (參考文獻) | Bertsimas D., An analytic approach to a general class | zh_TW |
| dc.relation.reference (參考文獻) | of G/G/s queueing systems. Operations Research 38, 139-155, (1990). | zh_TW |
| dc.relation.reference (參考文獻) | Chao, 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.reference (參考文獻) | 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). | zh_TW |
| dc.relation.reference (參考文獻) | Le Boudec, J.Y., Steady-state probabilities of the PH/PH/1 queue. Queueing Systems 3, 73-88, (1988). | zh_TW |
| dc.relation.reference (參考文獻) | Luh, 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.reference (參考文獻) | Liu, S. Y. Invariant Subspace of Solving C_{k}/C_{m}/1, Master thesis National Chengchi University.(2004) | zh_TW |
| dc.relation.reference (參考文獻) | Neuts, M.F., Matrix-Geometric Solutions in Stochastic Models. The John Hopkins University Press, (1981). | zh_TW |
| dc.relation.reference (參考文獻) | 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). | zh_TW |
| dc.relation.reference (參考文獻) | Wang, 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 |
