This paper studies the machine repair
problem consisting of M operating machines with S spare
machines, 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 to the repair facility and operate one of three
vacation policies: single vacation, multiple vacation, and hybrid
single/multiple vacation. The Markov process and the
matrix-geometric approach are used to develop the steady-state
probabilities of the number of failed machines in the system as
well as the performance measures. A cost model is developed to
obtain the optimal values of the number of spares and the number
of servers while maintaining a minimum specified level of system
availability. Some numerical experiments are performed and some
conclusions are drawn.