Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/18711
標題: 具有阻礙,放棄及服務壓力係數之M/M/R暖備機器修理問題
The warm-standby M/M/R machine repair problem with balking, reneging and service pressure coefficient
作者: 商紓瑋
Shang, Shu-Wei
關鍵字: balk;阻礙;cost;renege;service pressure coefficient;direct search method;Newton-Quasi method;成本;放棄;服務壓力係數;直接尋找法;牛頓法
出版社: 統計學研究所
引用: [1] Jr. C.J. Ancker and A.V. Gafarian. Some queueing problems with balking and reneging: II. Operations Research 11 (1963): 928-937. [2] M.O. Abou-El-Ata and A.M.A. Hariri. The M/M/c/N queue with balking and reneging. Computers and Operations Research 19 (1992): 713-716. [3] M.O. Abou-El-Ata and A.I. Shawky. The single-server Markovian overflow queue with balking, reneging and an additional server for longer queues. Microelectronics and Reliability 32 (1992): 1389-1394. [4] F. Benson and D.R. Cox. The productivity of machine requiring attention at random intervals. Journal of the Royal Statistical Society 13 (1951): 65-82. [5] S. Drekic and D.G. Woolford. A preemptive priority queue with balking. European Journal of Operational Research 164 (2005): 387–401. [6] F.S. Hiller and G.J. Lieberman. Introduction to Operations Research, 6rd edn. McGraw Hill Higher Education (2001). [7] J.-C. Ke. Operating characteristic analysis on the M[x]/G/1 system with a variant vacation policy and balking. Applied Mathematical Modelling 31 (2007): 1321–1337. [8] J.-C. Ke and K.-H. Wang. Cost analysis of the M/M/R machine repair problem with balking, reneging, and server breakdowns. Journal of the Operational Research Society 50 (1999): 275-282. [9] M. Lozano and P. Moreno. A discrete time single-server queue with balking: economic applications. Applied Economics 40 (2008): 735–748. [10] A.I. Shawky. The single-server machine interference model with balking, reneging, and an additional server for longer queues. Microelectronics and Reliability 37 (1997): 355-357. [11] B.D. Sivazlian and K.-H. Wang. Economic analysis of the M/M/R machine repair problem with warm standbys. Microelectronics and Reliability 29 (1989): 25-35. [12] K.-H. Wang and Y.-Ch. Chang. Cost analysis of a finite M/M/R queueing system with balking, reneging, and server b reakdowns. Mathematical Methods of Operations Research 56 (2002): 169-180. [13] K.-H. Wang, J.-B. Ke, and 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. [14] K.-H. Wang and J.-C. Ke. The reliability analysis of balking and reneging in a repairable system. Quality and Reliability Engineering International 18 (2002): 467-478. [15] K.-H. Wang and J.-C. Ke. Probabilistic analysis of a repairable system with warm standbys plus balking and reneging. Applied Mathematical Modelling 27 (2003): 327-336. [16] D. Yue, W. Yue, and Y. Sun. Performance analysis of an M/M/c/N queueing system with balking, reneging and synchronous vacations of partial servers. International Symposium on OR and Iits Applications (2006): 128–143. [17] 藍俊雄和郭美貝.考慮服務壓力係數下M/M/s/k等候模式之建構 與推導.管理科學研究 第一屆管理與決策2005年學術研討會特 刊:151-159.
摘要: 
此篇論文研究了M/M/R暖備機器修理問題,包含阻礙、放棄以及服務壓力係數。失敗的機器具有(1-bn)的機率遇到阻礙(不進入排隊)以及放棄(進入排隊後卻離開)的時間根據指數分配。我們使用生與死(birth-and-death)結果去推導穩態的機率,而獲得不同的系統執行測度。接下來發展一個成本模型,用來決定在最小成本之下的聯合最佳解。我們運用直接尋找的方法來找尋最佳修理人員個數(R)和暖備備用機器(S)個數。當獲得最佳解R*和S*之後,我們利用數學上的牛頓法來獲得最佳服務率與阻礙率。同時,我們也研究了敏感度分析。

This thesis studies the warm-standby M/M/R machine repair problem with balking and reneging plus service pressure coefficient. Failed machines balk (do not enter) with a constant probability (1-bn) and renege (leave the queue after entering) according to a negative exponential distribution. We use the birth-and-death results to derive the steady-state probabilities, using which various system performance measures that can be obtained. A cost model is developed to determine the joint optimal values at the minimum cost. We use the direct search method to find the optimal values of the number of repairmen, R, and the number of warm standbys, S. Subsequently, we employ the Newton-Quasi method to obtain the optimal service rate μ and balking rate b after R* and S* are determined. Numerical results are provided in which various system performance measures are calculated under optimal operating conditions. Sensitivity analysis is also investigated.
URI: http://hdl.handle.net/11455/18711
Appears in Collections:統計學研究所

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