Optimal Average Cost Operating Policy for an M/G/1 Queueing System with Removable Server and Several Priority Classes

摘要

An optimal operating policy is characterized for the infinite horizon average cost case of a queueing 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 S(sub 1) and S(sub 2) for turning the server on and off respectively. It is shown that a stationary optimal policy exists which either (1) 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 when the state reaches a boundary and this boundary is a hyperplane of dimension N-1. (Author)