臺灣博碩士論文加值系統

在本篇論文中，我們研究PH/G/1模型的輸出過程。首先我們建構輸出間隔機率分配的LST轉換式，並給定一些分析輸出過程的指標，如輸出間隔的平均值、變異數和變異係數。特別是分析輸出間隔的IFR性質，我們目的在於討論在何種條件下其輸出間隔保有IFR特性。由於系統穩態機率分配的複雜性，我們藉由電腦協助演算Em/Ek/1的輸出間隔並展示其數值結果。我們發現即使到達間隔及服務時間均具有IFR性質，其輸出間隔也未必保有IFR特性。然而在我們的實驗中，我們發現對於Em/Ek/1模型中，當m大於或等於k時，其輸出間隔保有IFR性質。

In this thesis, we study the departure process of PH/G/1 queue.
We first construct the Laplace-Stieltjes transform (LST) of the
interdeparture time and give some indices for the performance
evaluation of the departure process of PH/G/1 queue, such as the
variance and the square coefficient of variation. Especially, we
analyze the failure rate of the stationary interdeparture time.
Our goal is to investigate the output process under what conditions the interdeparture time will preserve the IFR property.
Because of the complexity of the stationary probability density, we take advantage of computer to visualize the performance of the output process. We found the interdeparture time doesn't always preserve the IFR property even if the interarrival time and service time are Erlang distributions with IFR. We give several theoretic analysis and present some numerical results of Em/Ek/1 queues. From our experiments, if m>=k, the interdeparture time of Em/Ek/1 remains the IFR property.

1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Literature Review .. . . . . . . . . . . . . . . . . . 2
1.3 Importance of the study . . . . . . . . . . . . . . . . 4
1.4 Organization of the thesis . . . . . . . . . . . .. . . 4
2 The Model 5
2.1 Description and notation . . . . . . . . . . . . . . . .5
2.2 Departure process . . . . . . . . . . . . . . . .. . . 10
2.3 Performance analysis of the departure process . . . . 11
2.4 Departure process of PH/D/1 queues. . . . .. . . . . . 16
3 The performance analysis of departure processes of Em/Ek/1 queue 18
3.1 Laplace-Stieltjes transform . . . . . . . . . . . . . .18
3.2 Performance analysis . . . . . . . . . . . . . . . . . 20
3.3 Stochastic properties . . . . . . . . . . . .. . . . . 22
3.4 Hazard rate analysis of Em/D/1 queues. . . . . . . . 25
4 Numerical examples and discussion 26
4.1 Case study . . . . . . . . . . . . . . . . . . . . . . 26
4.2 Discussion . . . . . . . . . . . . . . . . . . . . . . 36
5 Conclusions and future research 38
5.1 Conclusions . . . . . . . . . . . . . . . . . . . . . 38
5.2 Future research . . . . . . . . . . . . . . . . . . . 38
References 40
Appendix 42

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