Vacation queuing model for a machining system with two unreliable repairmen

This investigation is concerned with multi‐component machining system having two types of warm standby units and two unreliable heterogeneous repairmen. The life time and repair time of the failed units are exponentially distributed. The first repairman is working according to N (N ≥ 1) policy whereas the second repairman has the privilege of going for a vacation of random length. Both repairmen may also fail while rendering the repair to the failed units either individually or simultaneously. Runge‐Kutta method is used to obtain the transient‐state probabilities of the system states for which Chapman‐Kolmogrov differential equations governing the model are constructed. We have established some indices for the system performance in terms of transient probabilities. The sensitivity analysis is carried out to examine the system efficiency and profitability as per requirements. The numerical results are provided in order to explore the sensitivity of the system descriptors on the performance measures more precisely.