Vacation policies for machine repair problem with two type spares

This paper studies the machine repair problem consisting of M operating machines with two types of spare machines (S = S₁ + S₂), and R servers (repairmen) who leave for a vacation of random length when there are no failed machines queuing up for repair in the repair facility. At the end of the vacation the servers return and operate two vacation policies. First, the servers take vacations repeatedly until they find the repair facility has at least one waiting failed machine in the queue. Second, the servers do not take a vacation again and remain idle until the first arriving failed machine arrives, which starts a busy period in the repair facility. For both policies, the servers have two service rates for repair-slow and fast. The matrix geometric theory is used to find the steady-state probabilities of the number of failed machines in the system as well as the performance measures. Some special cases are given. A direct search algorithm is used to simultaneously determine the optimal values of the number of two types of spares and the number of servers while maintaining a minimum specified level of system availability.