Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/18747
標題: 以機率全域搜尋分析可控制M/G/1排隊系統
Controllable M/G/1 Queueing System Using Probabilistic Global Search Lausanne
作者: 楊擇中
Yang, Ze-Zhong
關鍵字: M/G/1 排隊系統;M/G/1 queueing system;最大熵理論;最佳化方法;機率全域搜尋法;maximum entropy principle;optimization;Probabilistic Global Search Lausanne
出版社: 統計學研究所
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,” The 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] Bell, C.E. (1972), “Optimal Operation of an M/G/1 Priority Queue with Removable Server,” Operations Research, 21, 1281–1289. [4] El-Affendi, M.A. and 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. [5] Ferdinand, A.E. (1970) “A Statistical Mechanical Approach to Systems Analysis,” IBM Journal of Research and Development, 14, 539–547. [6] Goldberg, D. and Lingle, R. (1989) “Alleles, Loci, and the Traveling Salesman Problem,” In Proceedings of the First International Conference on Genetic Algorithms and Their Applications, 154–159. [7] Holland, J. H. (1975) “Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence, ” University of Michigan Press, Ann Arbour. [8] Heyman, D.P. (1968) “Optimal Operating Policies for M/G/1 Queueing System, ” Operations Research, 16, 362–382. [9] Jaynes, E.T. (1957) “Information Theory and Statistical Mechanics. II., ” Physical Review, 108, 171–190 41 [10] Kouvatsos, D.D. (1986) “Maximum Entropy and the G/G/l/N Queue,” Acta Information, 23, 545–565. [11] Kimura, T. (1981) “Optimal Control of an M/G/1 Queueing System with Removable Server via Diffusion Approximation, ” European Journal of Operational Research, 8, 390–398. [12] Ke, J. -C. and Wang, K.-H. (2002) “A Recursive Method for the N Policy G/M/1 Queueing System with Finite Capacity,” European Journal of Operational Research, 142, 577–594. [13] Ke, J.-C. (2003) “The Operating Characteristic Analysis on a General input Queue with N policy and a Startup Time, ” Mathematical Methods of Operations Research, 57, 235–254. [14] Ke, J.-C. and Lin C.-H. (2008) “Maximum Entropy Approach for Batch-Arrival Queue under N Policy with an Un-Reliable Server and Single Vacation, ” Journal of Computational and Applied Mathematics, 221, 1–15. [15] Ke, J.-C., Lin C.-H., and Huang H.-I. (2009) “Entropy Maximization and NT Vacation M/G/1 Model with a Startup and Unreliable Server: Comparative Analysis on the First Two Moments of System Size, ” International Journal of Computer Mathematics, 86, 703–718. [16] Pearn, W. L., Ke, J. C., and Chang, Y. C. (2004) “Sensitivity Analysis of the Optimal Management Policy for a Queueing System with a Removable and Non-Reliable Server, ” Computers & Industrial Engineering 46, 87–99. [17] Raphael, B. and Smith, I. F. C. (2003) “A Direct Stochastic Algorithm for Global Search,” Applied Mathematics and Computation, 146, 729-758. [18] Shore, J.E. (1982) “Information Theoretic Approximations for M/G/1 and G/G/1 Queueing Systems, ” Acta Information, 17, 43–61. 42 [19] Tijms, H.C. (1986) “Stochastic Modelling and Analysis, ” Wiley, New York. [20] Wang, K.-H. (1995) “Optimal Operation of a Markovian Queueing System with a Removable and Non-Reliable Server,” Microelectronics and Reliability, 35, 1131-1136. [21] Wang, K.-H. and Huang, H.-M. (1995) “Optimal Control of an M/Ek/1 Queueing System with a Removable Service Station, ” Journal of the Operational Research Society, 46, 1014-1022. [22] Wang, K. -H. and Yen, K. -L. (2003) “Optimal Control of an M/Hk/1 Queueing System with a Removable Server,” Mathematical Methods of Operations Research 57, 255–262. [23] 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. [24] Wang, K.-H., Chuang, S.-L., and 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. [25] Wang, K.-H., Wang, T.-Y., and Pearn, W.L. (2007) “Optimal Control of the N Policy M/G/1 Queueing System with Server Breakdowns and General Startup Times, ” Applied Mathematical Modelling, 31, 2199–2212. [26] Wang, K.-H., Yang, D.-Y., and Pearn, W.L. (2011) “Comparative Analysis of a Randomized N-Policy Queue: An Improved Maximum Entropy Method,” Expert Systems with Applications, 38, 9461–9471. [27] Yadin, M. and Naor, P. (1963) “Queueing Systems with a Removable Service Station, ” Operational Research Quarterly, 14, 393-405.
摘要: 
此篇論文從最佳化理論的角度研究分析可控制N 方策M/G/1 排隊系統。其中服務時間的分配假設為任意分配。並假設當系統中顧客數到達N 時,系統將會開啟服務器;當無顧客在系統中時,則服務器會關閉。
此論文中我們以最大熵方程式和幾個熟知的限制式做為我們的目標函數和限制式,並以最佳化方法中的機率全域搜尋法藉由電腦程式運算獲得系統中顧客
數的最佳穩態解。我們以三個不同服務時間分配(指數、超指數、厄朗)為例,並在該系統中以不同的參數假設運算獲得其數值結果,接著將其與理論穩態機率和Wang et al. (2002)推導的顧客數機率分配的近似公式進行分析比較。
由數值結果可以發現,以機率全域搜尋法獲得的最佳化解在該系統參數設定ρ<0.6 時,其結果較Wang et al.(2002)推導出的顧客數機率分配的近似公式來的接近於理論穩態機率的結果;而在ρ>0.6 時(heavily traffic)則Wang et al.(2002)提出的近似公式會有較好的表現。所以機率全域搜尋法在特定參數設定之下,確實能得到較接近該系統中理論穩態機率的結果。
URI: http://hdl.handle.net/11455/18747
其他識別: U0005-2808201212512200
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