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| Title: | Em/Ek/1的輸出過程
The Output Process of Em/Ek/1 |
| Authors: | 李原旭 |
| Contributors: | 陸行
李原旭 |
| Date: | 2002 |
| Issue Date: | 2016-05-09 16:39:15 (UTC+8) |
| Abstract: | 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E<sub>m</sub>/E<sub>k</sub>/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E<sub>m</sub>/E<sub>k</sub>/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 E<sub>m</sub>/E<sub>k</sub>/1 queues. From our experiments, if m>=k, the interdeparture time of E<sub>m</sub>/E<sub>k</sub>/1 remains the IFR property.
謝辭
Abstract-----i
中文摘要-----ii
Content-----iii
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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[3] Daley, D. J., The correlation structure of the output process of some single server queueing systems. Annals of Mathematical Statistics, Vol.39, pp.1007-1019, 1968.
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[5] Daniel, P. H. and Matthew, J. S., Stochastic models in operations research Volume I. McGraw-Hill Book Company, 1982.
[6] Disney, R. L. Farrel, R. L. and De Morais, P. R., A characterization of M/G/1/N queues with renewal departure processes, Management Sciences, Vol.19, pp.1222-1228, 1973.
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[9] Ishikawa, A., On the joint distribution of the departure intervals in an M/G/1/N queue. Journal of the Operations Research Society of Japan, Vol.34, pp.422-435, 1991.
[10] Jenkins, J. H., On the correlation structure of the departure process of the M/E/1 queue. Journal of the Royal Society, Series B, Vol.28, pp.336-344,1966.
[11] King, R. A., The covariance structure of the departure process from M/G/1 queues withvfinite waiting line. Journal of the Royal Statistical Society, Series B, Vol.33, pp.401-405, 1971.
[12] Laslett, G. M., Characterizing the finite capacity GI/M/1 queue with renewal output, Management Sciences, Vol.22, pp.106-110, 1975.
[13] Luh, H., Derivation of the N-step interdeparture time distribution in GI/G/1 queueing systems. European Journal of Operational Research. pp.194-212, 1999.
[14] Luh, H., The correlation structure of GI/G/1 queue. National ChengChi University, Taipei, preprint, 2001.
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[16] Osaki, S., Applied stochastic system modeling. Springer-Verlag, 1992.
[17] Ping-Cheng Yeh and Jin-Fu Chang, Characterizing the departure process of a single server queue from the embedded Markov renewal process at departures. Queueing Systems, Vol.35, pp.381-395, 2000.
[18] Ramaswami, V., The N=G=1 queue and its detailed analysis. Advances in Applied Probability, Vol.12, pp.222-261, 1980.
[19] Reich, E., Waiting times when queues are in tandem. Annals of Mathematical Statistics, Vol.28, pp.768-773, 1959.
[20] Saito, H., The departure process of an N=G=1 queue. Performance Evaluation 11, pp.241-251, 1990.
[21] Takagi, H. and Nishi, T., Correlation of interdeparture times in M/G/1 and M/G/1/K queues. Journal of the Operations Research Society of Japan, Vol.41, pp.142-151, 1998.
[22] Tijms, H. C., Stochastic Models an algorithmic approach. New York: John Wiley & Sons, 1994. |
| Description: | 碩士
國立政治大學
應用數學系
89751002 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#A2010000200 |
| Data Type: | thesis |
| Appears in Collections: | [應用數學系] 學位論文
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