Optimal Operation of an M/G/1 Priority Queue with Removable Server

An optimal operating policy is characterized for the infinite-horizon average-cost case of a queuing control problem with the following properties: N priority classes of customers each arriving according to an independent Poisson process, a holding charge of h_i, per customer of class i per unit time, and a single server who provides independent identically distributed service times and who may be turned on at arrival epochs or off at departure epochs. The server costs w per unit time to operate and there are fixed charges of S₁ and S₂ for turning the server on and off, respectively. This paper shows that a stationary optimal policy exists that either (l) leaves the server on at all times or (2) turns the server off when the system is empty. In the latter case, if the state of the system is represented as a point in N-dimensional Euclidean space, the server is turned on at the first time that the state reaches a boundary and this boundary is a hyperplane of dimension N − 1.