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This paper examines a doubly controlled process of servicing  machines. The classical system treated by TakÃƒÂ¡cs is equipped with  m+1 unreliable machines served by one repairman. In the present  modification of this model, the failure rates and the repair time may be  controlled with respect to the state of the system. The process  describing the number of intact machines is considered. To derive its  steady state distribution in the form of a simple explicit formula, the  author introduces an auxiliary model with m unreliable machines and a  single repairman who keeps working even when all machines are intact.  This result is based on a duality principle applied to the process above

On a duality principle in processes of servicing machines with double control