Abstract
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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