Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/18139
標題: 含有會調整工作效率之 M/M/R 的機器修理 問題之成本分析
Cost Analysis of the M/M/R Machine Repair Problem with Multiple Working Vacations
作者: 陳詩嘉
Chen, Shi Jia
關鍵字: cost
調整工作效率
optimization
working vacation
transition rate matrix
direct search method
Newton-Quasi method
成本函數
直接尋找法
最佳解
類似牛頓法
出版社: 應用數學系所
引用: [1] Y. Baba, Analysis of a GI/M/1 queue with multiple working vacations. Operations Research Letters 33 (2005) 201-209. [2] A.D. Banik, U.C. Gupta, S.S. Pathak, On the GI/M/1/N queue with multiple working vacations-analytic analysis and computation. Applied Mathematical Modelling 31 (2007) 1701-1710. [3] U. Chatterjee, S.P. Mukherjee, GI/M/1 queue with server vacations. Journal of the Operational Research Society 41 (1990) 83-87. [4] B.T. Doshi, Queueing systems with vacations - a survey. Queueing Systems 1 (1986) 29-66. [5] S.W. Fuhrmann, R.B. Cooper, Stochastic decompositions in the M/G/1 queue with generalized vacations. Operations Research 33 (1985) 1117-1129. [6] F. Karaesmen, S.M. Gupta, The finite capacity GI/M/1 queue with server vacations. Journal of the Operational Research Society 47 (1996) 817-828. [7] J.-C. Ke, S.-L. Lee and C.-H. Liou, Machine Repair Problem in Production Systems with Spares and Server Vacations. RAIRO-Oper. Res. 43 (2009) 35-54. [8] J.-C. Ke, K.-H. Wang, Vacation policies for machine repair problem with two type spares. Applied Mathematical Modelling 31 (2007) 880-894. [9] T. Lee, The M/G/1/N queue with vacation and exhaustive service discipline. Operations Research 32 (1984) 774-784. [10] J.-H. Li, N.-S. Tian, Z.-Y. Ma, Performance analysis of GI/M/1 queue with working vacations and vacation interruption. Applied Mathematical Modelling 31 (2007) 880-894. [11] L.D. Servi, S.G. Finn, M/M/1 queues with working vacations (M/M/1/WV). Performance Evaluation 50 (2002) 41-52. [12] H. Takagi, Queueing analysis-A foundation of Performance Evaluation, Vacation and Priority Systems, vol. 1, North-Holland, New York, 1991. [13] N.-S. Tian, The GI/M//1 queueing system with a single exponential vacation. Journal of Systems and Mathematical Science 13 (1993) 1-9. [14] N.-S. Tian, The GI/M/1 queue with phase-type vacations. Acta Mathematicae Applicatae Sinica 16 (1993) 452-461. [15] N.-S Tian, D. Zhang, C. Cao, The GI/M/1 queue with exponential vacations. Queueing Systems 5 (1989) 331-344. [16] K.-H. Wang, J.-B. Ke, J.-C. Ke, Profit analysis of the M/M/R machine repair problem with balking, reneging, and standby switching failures. Computers and Operations Research 34 (2007) 835-847. [17] D.-A. Wu, H. Takagi, M/G/1 queue with multiple working vacations. Performance Evaluation 63 (2006) 654-681.
摘要: In this thesis, we study the M/M/R machine repair problem with working vacation which the servers work with slower repair rate rather than completely terminates repair during a vacation period. We assume that the servers begin a working vacation when they are free of work. The breakdown times, repair times and vacation times are all assumed to be exponentially distributed. We construct the transition rate matrix Q to compute steady-state probabilities and system performance measures by matrix analytic method. A cost model is derived to determine the optimal values of the number of servers and two different repair rates under some constraints. Two methods: Direct search method and Newton-Quasi method are used sequentially to find the minimal total expected cost value within a certain availability level. Some numerical examples are provided to explain the Newton-Quasi method.
URI: http://hdl.handle.net/11455/18139
其他識別: U0005-2506200914350600
文章連結: http://www.airitilibrary.com/Publication/alDetailedMesh1?DocID=U0005-2506200914350600
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