Diffusion Approximation for G^X /G^ Y /r+s Machine Repair Problem (MRP) with Mixed Spares, Balking, Reneging and Additional Removable Repairmen

In this paper we consider machine repair problem (MRP) with mixed spares, balking, reneging and additional removable repairmen. The operating and spare units are subject to failure and repair in batches. The inter-failure and repair times are assumed to be general identical and independently distributed. The failed units are subject to balk or renege when all permanent servers are busy. In order to maintain the regular production of the machining system, there is a provision of two types of warm spares and additional removable repairmen. By applying diffusion approximation approach and using elementary return boundaries, we obtain probability density function for the queue size. Furthermore, we provide expressions for some performance measures, which may be useful for improving the grade of service. We facilitate a comparison of results obtained by diffusion approximation and existing exact/simulation results in special case. The sensitivity analysis has also been carried out by taking numerical examples.