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| 研究生： |
陳瓏元 Chen Lung Yuan |
|---|---|
| 論文名稱： |
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 |
| 指導教授： | 陸行 |
| 學位類別： |
碩士
Master |
| 系所名稱： |
理學院 - 應用數學系 Department of Mathematical Sciences |
| 論文出版年： | 2006 |
| 畢業學年度： | 94 |
| 語文別： | 英文 |
| 論文頁數： | 52 |
| 中文關鍵詞： | 等候系統 |
| 外文關鍵詞： | Queue, Coxian distributions, Vector product-forms, Phase-type probability distributions |
| 相關次數： | 點閱：114 下載：33 |
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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.
1 Introduction 1
2 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.........................14
3 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.........20
4 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............................31
5 Conclusions and Remarks 36
References 37
Appendix A 39
Appendix B 40
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