# 臺灣博碩士論文加值系統

(44.192.79.149) 您好！臺灣時間：2023/06/03 00:25

:::

### 詳目顯示

:

• 被引用:0
• 點閱:238
• 評分:
• 下載:0
• 書目收藏:0
 在這篇論文中我要介紹兩種解馬可夫模型的方法-光譜拓展法和矩陣幾何法。許多二維的模型可以用這兩個方法來解，這篇論文中我所用的是M/M/N的列隊模型。在文中我們會比較兩個方法的差異。實驗中，我們主要的目的是要比較這兩個方法的速度與精確度。
 In this paper, I want to introduce spectral expansion method and matrix-geometric method on a class of Markov models. Many two-dimensional Markov models whose state space is a semi-infinite strip can be solved efficiently by these two methods. The example described in the context is an M/M/N queue with general breakdowns and repairs. The objective of experiments is to compare the effectiveness of computing the average queue size with two different methods. The detail of the algorithms will also be presented in this paper.
 Contents 1. Introduction …………………………………………………………1 2. The Markov model……………………………………………………2 3. Spectral expansion method……………………………………………4 3.1 A description of the method………………………………………4 3.2 Algorithm for spectral expansion method…………………………6 4. Matrix-geometric method……………………………………………9 4.1 A description of the method…………………………………………9 4.2 Algorithm for matrix-geometric method…………………………10 5. Examples and Numerical results……………………………………11 5.1 The multi-server example…………………………………………11 5.1.1 Numerical result………………………………………………13 5.2 Two severs in tandem……………………………………………14 5.2.1 Numerical result…………………………………………15 6. Comparison…………………………………………………………16 7. Conclusion…………………………………………………………23 Reference…………………………………………………………24 List of figures 1. Multi-server with breakdowns………………………………………12 2. Numerical result of the multi-server example…………………13 3. Two servers in tandem with feedback………………………………14 4. E(J) of the two servers in tandem example………………………15 5. E(I) of the two servers in tandem example………………………16 6. Compare two methods in computing time with different arrival rate………19 7. Compare two methods in different N with arrival rate 0.8…20 8. Compare two methods in different N with arrival rate 1.05…21 9. Number of iterations for computing R…………………………22 List of tables 1. Trade-off between accuracy and complexity………………………17 2. Trade-off between accuracy and the number h for computed E(J)……23
 [1] R. Chakka and I. Mitrani, A numerical solution method for multiprocessor systems with general breakdowns and repairs, Proceedings of the 6th International Conference on Performance Tools and Techniques, Edinburgh, 1992, page 289-304.[2] R. Chakka and I. Mitrani, Heterogeneous multiprocessor systems with breakdowns: Performance and optimal repair strategies, Theoretical Computer Science 125(1994)91-109.[3] M. Ettl and I. Mitrani, Applying spectral expansion in evaluating the performance of multiprocessor systems, Proceedings of the 3rd QMIPS Workshop Part 1, eds. O. J. Boxma and G. M. Koole, CWITRACT, Amsterdam, 1994, page 45-58.[4] R. Chakka and I. Mitrani, Approximate solutions for open networks with breakdowns and repairs, in: Stochastic Networks: Theory and Applications, eds. F. P. Kelly, S. Zachary and I. Ziedins, Oxford University Press, Oxford, 1996.[5] A. I. Elwalid, D. Mitra and T. E. Stern, Statistical multiplexing of Markov modulated sources: Theory and computational algorithms, in: Teletraffic and Data Traffic in a Period of Change, eds. A. Jensen and V. B. Iversen, International Teletraffic Congress-13, Copenhagen, 1991, page 495-500.[6] N. U. Prabhu and Y. Zhu, Markov-Modulated Queuing Systems, QUESTA 5(1989) 215-246.[7] M. F. Neuts, Matrix Geometric Solutions in Stochastic Models, John Hopkins University Press, Baltimore, Md. (1981).[8] Mitrani and R. Chakka, Spectral expansion solution for a class of Markov models: Application and comparison with the matrix-geometric method, Performance Evaluation 23(1995) 241-260.[9] Gohberg, P. Lancaster and L. Rodman, Matrix Polynomials, Academic Press, New York (1982).[10] Jennings, Matrix Computations for Engineers and Scientists, Wiley, New York (1977).[11] L. Gun, Experimental Results on Matrix-Analytical Solution Techniques- Extensions and Comparison, Stoch. Models 5(4) (1989) 669-682.[12] G. Konheim and M. Resier, A queuing model with finite waiting room and blacking, Journal of the ACM23 (1976) 328-341.[13] H. R. Gail, S. L. Hantler and B. A. Taylor, Spectral Analysis of M/G/1 Type Markov Chains, RC17765, IBM Research Division, 1992.
 國圖紙本論文
 推文當script無法執行時可按︰推文 網路書籤當script無法執行時可按︰網路書籤 推薦當script無法執行時可按︰推薦 評分當script無法執行時可按︰評分 引用網址當script無法執行時可按︰引用網址 轉寄當script無法執行時可按︰轉寄

 無相關論文

 1 關華山，台灣老人自費安養機構之類別。台灣老人的居住環境。田園城市文化。初稿發表於1992東海學報33卷897-914頁，1996。 2 關華山，台灣老人自費安養機構之類別。台灣老人的居住環境。田園城市文化。初稿發表於1992東海學報33卷897-914頁，1996。

 1 苯駢簡菠二烯衍生物之開環置換聚合反應 2 利用高效能液相層析儀搭配螢光偵檢器檢測各種DNA樣品中乙烯基腺口票呤的含量及利用氣相層析負離子化學游離質譜儀分析尿液中乙烯基腺口票呤與乙烯胞嘧口定 3 唐前果報系統的建構與融合 4 Zeta-型函數，WeierstrassP—函數與Bernoulli等式 5 網格調整下雙重網格法收斂性的評論 6 碎形與混沌 7 關於維數,深度和射影維數的階化類比 8 利用Lanczosmethod找絕對值最小的eigenvalues 9 有限元素法中數值積分對於對流主導問題之影響 10 移動網格與網格調整之探討與應用 11 漸近分析及其應用之報告 12 零維諾德環與一維諾德域 13 發散形式的橢圓偏微分方程 14 橢圓方程的極大值原理 15 繪出AttractorofIFS的新算則

 簡易查詢 | 進階查詢 | 熱門排行 | 我的研究室