Machine interference problem with warm spares, server vacations and exhaustive service

We consider the machine interference problem with warm spares in which the server takes a vacation of random duration every time the repair facility becomes empty. We address the cases of multiple vacations, single vacation and hybrid multiple/single vacation schemes with exhaustive service. Vacation models that have been studied in the past generally assume infinite population. In this paper, we provide new, transform free, closed form expressions for the probability distribution of the number of machines in the repair facility and the performance measures for machine interference problem with warm spares and server vacations. By adjusting the parameters, closed form expressions for machine interference problem with cold spares, machine interference problem without spares, finite capacity and infinite capacity vacation models can also be derived. An extremely powerful and efficient algorithm is presented to determine the steady state probability distribution of the number of customers in the system as well as the performance measures for all these models. An example is considered and some insight is also provided.