Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/18062
標題: 在<0,Q,N,M>-方策下之可控制M/M/2機器修理問題
A Controllable M/M/2 Machine Repair Problem Operating under the triadic (0,Q,N,M) Policy
作者: 劉孟瑋
Liu, Meng-Wei
關鍵字: cost;成本分析;controllable;<0,Q,N,M> policy;direct search method;控制系統;<0,Q,N,M>-方策;直接尋找法;牛頓法
出版社: 應用數學系所
引用: [1] C.E. Bell, “Optimal operation of an M/M/2 queue with removable servers.” Operations Research, Vol. 2, 1189-1204, 1980. [2] D.B. Bunday and R.E. Scraton, “The G/M/R machine interference model.” European Journal of Operational Research, Vol. 4, 399-402, 1980. [3] D. Gross and C.M. Harris, Fundamentals of Queueing Theory, 3rd edn. Wiley, New York, 1998. [4] U.C. Gupta and T.S.S. Srinivasa Rao, “A recursive method to compute the steady state probabilities of the machine interference model:(M/G/1)/K.” Computers and Operations Research, Vol. 21, 597-605, 1994. [5] D.G. Maritas and D.A. Xirokostas, “The M/Ek/R machine interference model: steady state equations and numerical solutions” European Journal of Operational Research, Vol. 1, 112-123, 1977. [6] H.K. Rhee and B.D. Sivazlian, “Distribution of the busy period in a controllable M/M/2 queue operating under the triadic (0, K, N, M) policy.” Journal of Applied Probability, Vol. 27 425-432, 1990. [7] B.D. Sivazlian and K.-H. Wang, “Diffusion approximation to the G/G/R machine repair problem with warm standby spares.” Naval Research Logistics, Vol. 37, 753-772, 1990. [8] K.-H. Wang and C.-L. Chang, “Reliability of a repairable system with warm standbys operating under the triadic (0, Q, N, M) policy.” Computers and Industrial Engineering, Vol. 28, 163-178, 1995. [9] K.-H. Wang and Y.-L. Wang, “Optimal control of an M/M/2 queueing system with finite capacity operating under the triadic (0, Q, N, M) policy.” Mathematical Methods of Operations Research, Vol. 55, 447-460, 2002. [10] M. Yadin and P. Naor, “Queueing system with a removable service station.” Operations Research, Vol. 14, 393-405, 1963.
摘要: 
此篇論文研究了在<0,Q,N,M>-方策下之可控制的M/M/2機器修理問題。我們假設可使用之修理者的數目取決於系統中的故障機器數。我們使用遞迴方法建構出穩態的機率解,接著建立一個每單位時間內每台機器的成本函數。運用直接尋找法跟數學上的牛頓法來尋找<0,Q,N,M>-方策跟不同修理率的最佳解。我們也提供了一些數值的例子來解釋我們的牛頓法。

This thesis considers the controllable M/M/2 machine repair problem with L operating machines operating under the triadic (0, Q, N, M) policy. We suppose that the number of active servers depends on the number of failed machines in the system which can be adjusted at any arrival epoch or any service completion epoch. We use a recursive method to develop steady-state analytic solutions. A cost model is derived to determine the optimal values of (M, L) and the optimal service rate μ. We use the direct search method and the Newton's method to find the global minimum value. Two numerical examples are provided to illustrate the Newton's method.
URI: http://hdl.handle.net/11455/18062
其他識別: U0005-0207200916052600
Appears in Collections:應用數學系所

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