# 臺灣博碩士論文加值系統

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 目前網路分析的重點在透過系統反應的表現值來研究系統的動態關係。一些重要的系統表現值包括：吞吐量（Throughput）、延遲時間（Delay）和存貨（Backlog）等等。由於現代網路系統的複雜度與日俱增，系統的表現值通常受到大量輸入參數的影響，所以理論分析的結果經常是不易取得的。在這種情況下，電腦模擬(Computer Simulation) 便成為分析複雜網路系統的重要工具。為了了解輸入參數和系統反應值之間的關係，文獻上傳統的作法是利用電腦模擬在整個輸入參數空間裡建構一個有母數模型 (Parametric Model)。這種作法的好處是我們可以清楚地知道輸入參數如何影響系統反應值的大小，但是這類作法在高維度的輸入空間也同時遭遇到模型選擇的問題。因此，當我們對複雜系統的反應所知不多時，使用無母數 (Nonparametric) 的方法似乎較為適當。　　此論文介紹一無母數方法來建構複雜網路系統的反應曲面模型。其目的是(i)希望用比較少的模擬次數得到不錯的反應曲面模型；(ii)希望所提出的方法可以較容易處理高維度參數空間的問題。本文也介紹一個被稱為廣泛交換系統（Generalized Switch Model）的網路模型，並以此模型示範我們所建議的方法。
 The goal of network analysis has been focused on studying the dynamics of a system throughimportant performance measures such as throughput, delay, backlog and so on. Due to thesignificant increase on the complexity of modern networks, the performance measures areusually affected by a lot of input parameters, thus analytical solutions are often invalid.Therefore, one often relies on simulation when analyzing complex network systems. Typically,a parametric model is built over the entire input space so that the relationship between theresponse measures of interest and the input parameters can be well described. However,parametric methods suffer from the issues like model selection, computational validity, etc.Therefore, non-parametric methods seem to be more plausible in analyzing complex networksystems when prior information is not valid. The goal of this study is to find an adequatenon-parametric method so that a good model for the response surface can be built usinga possibly smaller number of simulation runs and the model can also perform well in high-dimensionalinput space. Among all non-parametric methods, support vector regression (SVR)is considered in this study. This is mainly due to the following two reasons. First, it mightrequest fewer simulation runs than other approaches. Second, it can easily deal with high-dimensionalinput spaces. A particular queueing system called the generalized switch modelis introduced and used to demonstrate the proposed approach.
 1 Introduction 12 A Generalized Switch Model 43 Support Vector Regression 73.1 Risk Function 73.2 Example 83.3 Kernels 104 Apply SVR for Generalized Switch Models 124.1 Model Construction 124.1.1 The Average Sojourn Time Surfaces 144.2 Comparison with Other Approaches via Predictions 174.3 Ad Hoc Applications 194.3.1 Compare the Average-Sojourn-Time Surfaces for Two Di erent Sets ofServers 194.3.2 Compare the Average-Sojourn-Time Surfaces for Two Di erent ControlPolicies 215 Conclusion and Future Work 23Bibliography 24
 [1] Alexander, W. P. and S. D. Grimshaw. Treed regression. Journal of Computational andGraphical Statistics 5 (1996), pages 156-175.[2] Hung, Y. C. Modeling and analysis of stochastic networks with shared resources. Ph.D.thesis, Department of Statistics, The University of Michiganm, Ann Arbor, Michigan.2002.[3] Hung, Y. C., Michailidis, G. and Bingham, D. R.. Developing E cient SimulationMethodology for Complex Queueing Networks. Proceedings of the Winter Simulation Conference,New Orlean. pages 152-159, 2003.[4] Alex J. Smola and Bernhard Scholkopf. A Tutorial on Support Vector Regression. September30, 2003.[5] Nello Cristianini and John Shawe-Taylor. An Introduction to Support Vector Machinesand ither kernel-based learning methods. Cambridge University Press, 2000.[6] Vladimir N. Vapnik. The nature of Statistical Learning Theory. New York: Springer,1995.[7] P. J. Green and B. W. Silverman. Nonparametric Regression and Generalized LinearModels: A roughness penalty approach. Chapman & Hall. 1994.[8] C. J. Stone, M. Hansen, C. Kooperberg and Y. K. Truong. Polynomial Splines and theirtensor products in extended linear modeling. Annals of Statistics, 25 (1997), pages 1371-1470.[9] Jerome H. Friedman. Multivariate Adaptive Regression Splines. Annals of Statistics, 19(1991), pages 1-67.[10] W. N. Venables and B. D. Ripley. Modern Applied Statistics with S, 4th Edition. NewYork:Springer, 2002.[11] Kai-Tai Fang and Dennis K. J. Lin. Uniform Experimental Designs and their Applicationsin Industry. Handbook in Statistics: Statistics in Industry, 2003.[12] 張惠敏。設計複雜網路系統之高效率模擬方法。碩士論文，統計研究所，國立中央大學，中壢，台灣。2004。[13] 邱啟宗。可資源共享之平行分散系統的最大吞吐量控制策略。碩士論文，統計研究所，國立中央大學，中壢，台灣。2004。
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 1 設計複雜網路系統之高效率模擬方法 2 可資源共享之平行分散處理系統的最大吞吐量控制策略 3 應用MARS與SVR探討小波轉換之基底與階層在財務時間序列預測上之意涵與績效

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