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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
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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.
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