Optimal Operating Policy for an M/G/1 Exhaustive Server-Vacation Model

We consider an M/G/1 queueing system controlled by an exhaustive server–vacation policy, i.e, the server is turned off whenever the system becomes empty and it is turned on after a random time with at least a customer present in the system. In this paper, it is proved that there exists an exhaustive optimal policy which is of the form X + a(T - X)⁺, where, starting with the server off, X represents the time for the first arrival and T and a are non-negative real numbers. Using a classical average cost structure, the optimization problem is treated under the asymptotic average criterion. A structured definition of exhaustive policy is also derived.