Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/17522
標題: 含單一可移動及會故障服務者之 < p, N >-方策 M/G/1 排隊系統之最大熵値研究
A maximum entropy approach for the < p, N >-policy M/G/1 queue with a removable and unreliable server.
作者: 黃凱斌
Huang, Kai-Bin
關鍵字: < p, N >-policy
< p, N >-方策
maximum entropy
M/G/1 queue
unreliable server
最大熵値M/G/1排隊系統
不可靠服務者
出版社: 應用數學系所
引用: 1. Arizono I., Cui Y. and Ohta H. (1991) An analysis of M/M/S queueing systems based on the maximum entropy principle. Journal of the Operational Research Society 42: 69-73. 2. Bell C.E. (1971) Characterization and computation of optimal policies for operating an M/G/1 queueing system with removable server. Operations Research 19: 208-218. 3. El-Affendi M.A., Kouvatsos D.D. (1983) A maximum entropy analysis of the M/G/1 and G/M/1 queueing systems at equilibrium. Acta Information 19: 339-355. 4. Ferdinand A.E. (1970) A statistical mechanical approach to system analysis. IBM Journal Research Develop 14: 539-547. 5. Feinberg E.A. and Kim D.J. (1996) Bicriterion optimization of an M/G/1 queue with a removable server. Probability in the Engineering and Informational Sciences 10: 57-73. 6. Gakis K.G., Rhee H.K. and Sivazlian B.D. (1995) Distribution and first two moments of the busy and idle periods in controllable M/G/1 queueing models with simple and dyadic policies. Stochastic Analysis and Application 13: 47-81. 7. Heyman D.P. (1968) Optimal operating policies for M/G/1 queueing system. Operations Research 16: 362-382. 8. Kouvatsos D.D. (1986) Maximum entropy and the G/G/1/N queue. Acta Information 23: 545-565. 9. Kimura T. (1981) Optimal control of an M/G/1 queueing system with removable server via diffusion approximation. European Journal of the Operational Research: 390-398. 10. Shore J.E. (1978) Derivation of equilibrium and time-dependent solutions to M/M/1/N and M/N/1 queueing systems using entropy maximization. In Proceedings, 1978 National Computer Conference, AFIPS: 483-487. 11. Shore J.E. (1982) Information theoretic approximations for M/G/1 and G/G/1 queueing systems. Acta Information 17: 43-61. 12. Teghem Jr.J. (1987) Optimal control of a removable server in an M/G/1 queue with finite capacity. European Journal of the Operational Research 31: 358-367. 13. Tijms (1986) Stochastic Modelling and Analysis. Wiley, New York. 14. Wu J.-S., Chan W.-C. (1989) Maximum entropy analysis of multiple-server queueing systems. Journal of the Operational Research Society 40: 815- 825. 15. Wang K.-H. (1995) Optimal operation of a Markovian queueing system with a removable and non-reliable server. Microelectronics and Reliability 35: 1131-1136. 16. Wang K.-H. (1997) Optimal control of an M/EK/1 queueing system with removable service station subject to breakdowns. Journal of the Opeational Research society 48: 651-666. 17. Wang K.-H., Chang K.W. and Sivazlian B.D. (1999) Optimal control of a removable and non-reliable server in an infinite and a finite M/H_2/1 queueing system. Applied Mathematical Modelling 23: 651-666. 18. Wang K.-H. and Huang H.-M. (1995) Optimal control of an M/E_K/1 queueing system with a removable service station. Journal of the Operational Research 46: 1014-1022. 19. Wang K.-H. and Ke J.-C. (2000) A recursive method to the optimal control of an M/G/1 queueing system with finite capacity and infinite capacity. Applied Mathematical Modelling 24: 899-914. 20. Wang K.-H., Ke J.-C. (2002) Control policies of an M/G/1 queueing system with a removable and non-reliable server. International Transactions in Operations Research 9: 195-212. 21. Wang K.-H., Wang, L.-P., Ke, J.-C., Chen G. (2005) Comparative analysis for the N policy M/G/1 queueing system with a removable and unreliable server. Mathematical Methods of Operations Research 61: 505-520. 22. Wang K.-H., Shuang S.-L., Pearn W.-L. (2002) Maximum entropy analysis to the N policy M/G/1 queueing system with a removable server. Applied Mathematical Modelling 26: 1151-1162. 23. Yadin M., Naor P. (1963) Queueing systems with a removable service station. Operational Research Quarterly 14: 393-405.
摘要: 此篇論文分析研究了< p, N >-方策M/G/1排隊系統,含單一可移動及服務者會故障的情形。其中服務站的故障為一卜瓦松過程,而服務時間的分配則假設為任意分配。 我們假設當系統中的顧客數到達N時,系統將有p的機率開啟服務站,並且有(1-p)的機率保持關閉服務站。 最大熵値法在此篇論文的用處主要是去推導出系統中顧客數的估計機率分配,以及系統中顧客的估計等待時間。我們把導出的近似結果在四種不同服務時間及修 理時間下(指數、均勻、珈瑪、常數),與精確的結果作一比較分析。 由數值結果可以發現,最大熵値法在實務應用上是足夠精確的,並且在不同的服務時間及修理時間分配下,最大熵値法的表現也是夠穩定的。
This thesis analyzes a single removable and unreliable server in the <p,N >-policy M/G/1 queueing system in which the server breaks down according to a Poisson process and the repair time obeys an arbitrary distribution. We assume that when the number of customers in the system reaches N, turn the server on with probability p and leave it off with probability (1 − p). The use of maximum entropy approach is to develop the approximate formulae for the probability distributions of the number of customers and the expected waiting time in the system. We perform the comparative analysis between approximate results and exact results with four different service time and repair time distributions, including exponential,uniform, gamma, and deterministic. It appears from numerical results that the maximum entropy approach is sufficiently accurate for practical use and based on the maximum entropy approach , we demonstrate that the < p,N >-policy M/G(G)/1 queueing system is sufficiently robust to the variations of service time distribution and repair time distribution functions.
URI: http://hdl.handle.net/11455/17522
其他識別: U0005-1107200610424700
文章連結: http://www.airitilibrary.com/Publication/alDetailedMesh1?DocID=U0005-1107200610424700
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