This paper examines a doubly controlled process of servicing
machines. The classical system treated by Takács 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.