Optimal control of an M/G/1 queue with impatient priority customers (Q2741215)

The paper deals with optimal control of a single server with two classes of customers that arrive according to independent Poisson processes. Customers of class 1 are impatient, that is, they leave the system without being served if they cannot access the service upon arrival. The server may be turned on at arrival epochs or turned off at departure epochs and operates according to a nonpreemptive priority service discipline. The service times of customers are identically distributed and do not depend on the class of customers. There is a holding charge per unit waiting time for each 2-customer. When the server is off (on), it must be paid a dormant (running) rate per unit time. There are fixed charges for turning the server on and off. The planning horizon is infinite and the objective is to minimize the long-run average cost. It is proved that a stationary optimal policy exists such that either leaves the server on at all times or turns the server off when the system is empty. In the latter case the stationary optimal policy is a threshold strategy, determined by two thresholds instead of one as in most similar models.