This paper studies the machine repairproblem consisting of M operating machines with S sparemachines, and R servers (repairmen) who leave for a vacation ofrandom length when there are no failed machines queuing up forrepair in the repair facility. At the end of the vacation theservers return to the repair facility and operate one of threevacation policies: single vacation, multiple vacation, and hybridsingle/multiple vacation. The Markov process and thematrix-geometric approach are used to develop the steady-stateprobabilities of the number of failed machines in the system aswell as the performance measures. A cost model is developed toobtain the optimal values of the number of spares and the numberof servers while maintaining a minimum specified level of systemavailability. Some numerical experiments are performed and someconclusions are drawn.
