Optimal control of the workload in an m/g/1 queueing system with removable server

This paper considers an M/G/! queueing system in which the server may be either turned on or turned off. The system can be controlled at the arrival epochs by taking an action to change the current position of the server or not. The control is based on the total amount of work remaining to be done in the system. The costs consist of a linear holding cost for the workload and a fixed cost for turning the server on. In this paper it will be shown that among a wide class of policies there is an average cost optimal policy which belongs to the subclass of the so-called D-policies where a D-policy is a stationary policy that turns the server off only when the system is empty and turns the server on only when the workload exceeds the level D. Also, an alternative derivation of the formula for the average cost of a D-policy will be given.