We consider a single server exponential queue with infinite waiting room and state dependent service rates. The server is unreliable and wears down when active and additionally may break down randomly. Repair times are random as well. The system is controlled with the possibility of preventive maintenance after a fixed number of services. This number is subject of optimization under a prescribed general cost structure. In case of breakdown (i.e. under repair) or during preventive maintenance no service is possible and no new customers are admitted.

We determine explicitly the stationary distribution of the queueing-availability process and how that the system is separable, i.e. the steady state is of product form.