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 through
important performance measures such as throughput, delay, backlog and so on. Due to the
significant increase on the complexity of modern networks, the performance measures are
usually 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 the
response 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 network
systems when prior information is not valid. The goal of this study is to find an adequate
non-parametric method so that a good model for the response surface can be built using
a possibly smaller number of simulation runs and the model can also perform well in high-dimensional
input 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 might
request fewer simulation runs than other approaches. Second, it can easily deal with high-dimensional
input spaces. A particular queueing system called the generalized switch model
is introduced and used to demonstrate the proposed approach.

1 Introduction 1
2 A Generalized Switch Model 4
3 Support Vector Regression 7
3.1 Risk Function 7
3.2 Example 8
3.3 Kernels 10
4 Apply SVR for Generalized Switch Models 12
4.1 Model Construction 12
4.1.1 The Average Sojourn Time Surfaces 14
4.2 Comparison with Other Approaches via Predictions 17
4.3 Ad Hoc Applications 19
4.3.1 Compare the Average-Sojourn-Time Surfaces for Two Di erent Sets of
Servers 19
4.3.2 Compare the Average-Sojourn-Time Surfaces for Two Di erent Control
Policies 21
5 Conclusion and Future Work 23
Bibliography 24

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