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A Controllable M/M/2 Machine Repair Problem Operating under the triadic (0,Q,N,M) Policy
|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:|| C.E. Bell, “Optimal operation of an M/M/2 queue with removable servers.” Operations Research, Vol. 2, 1189-1204, 1980.  D.B. Bunday and R.E. Scraton, “The G/M/R machine interference model.” European Journal of Operational Research, Vol. 4, 399-402, 1980.  D. Gross and C.M. Harris, Fundamentals of Queueing Theory, 3rd edn. Wiley, New York, 1998.  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.  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.  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.  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.  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.  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.  M. Yadin and P. Naor, “Queueing system with a removable service station.” Operations Research, Vol. 14, 393-405, 1963.||摘要:||
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.
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