English  |  正體中文  |  简体中文  |  Items with full text/Total items : 88295/117812 (75%)
Visitors : 23407455      Online Users : 233
RC Version 6.0 © Powered By DSPACE, MIT. Enhanced by NTU Library IR team.
Scope Tips:
  • please add "double quotation mark" for query phrases to get precise results
  • please goto advance search for comprehansive author search
  • Adv. Search
    HomeLoginUploadHelpAboutAdminister Goto mobile version
    政大機構典藏 > 理學院 > 應用數學系 > 學位論文 >  Item 140.119/95618
    Please use this identifier to cite or link to this item: http://nccur.lib.nccu.edu.tw/handle/140.119/95618


    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
    Reference: [1] Burke, P. J., The output of a queueing system. Operations Research, Vol.4, pp.699-704, 1956.
    [2] Buzacott, J. A. and Shanthikumar J.G., Stochastic models of manufacturing systems. Prentice-Hall, 1993.
    [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.
    [4] Daley, D. J., Queueing output processes. Advances in Applied Probability, Vol.8, pp.395-415, 1976.
    [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.
    [7] Finch, P. D., The output process of the queueing system M/G/1. Journal of Royal Statistical Society, Series B, Vol.21, pp.375-380, 1959.
    [8] Fischer, W. and Meier-Hellstern, K., The Markov-modulated Poisson process (MMPP) cookbook. Performance Evaluation, Vol.18, pp.149-171, 1993.
    [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.
    [15] Neuts, M. F., Structured stochastic matrices of M/G/1 type and their applications. New York: Marcel Dekker, 1989.
    [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

    Files in This Item:

    File SizeFormat
    index.html0KbHTML200View/Open


    All items in 政大典藏 are protected by copyright, with all rights reserved.


    社群 sharing

    著作權政策宣告
    1.本網站之數位內容為國立政治大學所收錄之機構典藏,無償提供學術研究與公眾教育等公益性使用,惟仍請適度,合理使用本網站之內容,以尊重著作權人之權益。商業上之利用,則請先取得著作權人之授權。
    2.本網站之製作,已盡力防止侵害著作權人之權益,如仍發現本網站之數位內容有侵害著作權人權益情事者,請權利人通知本網站維護人員(nccur@nccu.edu.tw),維護人員將立即採取移除該數位著作等補救措施。
    DSpace Software Copyright © 2002-2004  MIT &  Hewlett-Packard  /   Enhanced by   NTU Library IR team Copyright ©   - Feedback