The warm-standby M/M/R machine repair problem with balking, reneging and service pressure coefficient

This paper 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 − b) 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 constructed to determine the joint optimal values of the number of repairmen, the number of warm standbys, and the joint optimal values of the service rate and the balking rate simultaneously by using two‐stage optimisation method. Numerical results are provided to illustrate the effectiveness of the two‐stage optimisation algorithm. Sensitivity analysis is also investigated.