臺灣博碩士論文加值系統

摘 要
在本篇論文裡，我們研究用Maximum entropy principle來分析 N 方策的M/G/1 排隊系統。首先，利用Maximum entropy principle推導出此系統之穩態解，然後，運用其推導出來的結果來獲得平均等待時間。最後，針對標準的M/M/1、M/E2/1和M/H2/1排隊系統及N方策的M/M/1、M/E2/1和M/H2/1排隊系統作數值比較分析。

In this thesis, the maximum entropy principle is used to analyze the N policy M/G/1 queueing system. We first derive the steady state solutions for the N policy M/G/1 queueing system by using the maximum entropy principle. Next, we use the derived results to obtain the mean waiting time in the queue. Finally, we present numerical comparisons between the established exact results and the corresponding approximate results to the ordinary M/M/1, M/E2/1, and M/H2/1 queueing systems and the N policy M/M/1, M/E2/1, and M/H2/1 queueing systems.

CONTENTS
Abstract
1 Introduction …………………………………………………………..1
1.1Problem Statement ……………………………………………...1
1.2Literature Review ……………………………………………….2
1.3Scope of the Study ………………………………………………4
2 Steady-State Results ……………………………………………...…..5
2.1 Assumptions …………………………………………………….6
2.2 Maximum Entropy Formalism ………………………………….6
2.3 Maximum Entropy Solution …………………………………….7
2.4 Special Cases …………………………………………………..14
3 Comparative Analysis ………………………………………………16
3.1 The Exact and Approximate Formulae …………………….…..17
3.2 Comparative Analysis Between the Exact and the Approximate Results to the Ordinary M/M/1, M/E2/1, M/H2/1 Queueing Systems ………………………………………………………...19
3.3 Comparative Analysis Between the Exact and the Approximate Results to the N Policy M/M/1, M/E2/1, M/H2/1 Queueing Systems ………………………………………………………...22
4 Conclusions and Future Research …………………………………30
4.1 Conclusions ……………………………………………………30
4.2 Future Research ………………………………………………..30
Reference ………………………………………………………………32

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