Yiannis Dimitrakopoulos and Apostolos Burnetas. Dynamic Admission and Service Control in the M|M|1 queue

Abstract. We consider the problem of joint admission and service rate control in an M|M|1 queue. Admission or rejection decisions are made at arrival epochs. A choice between high and low service rate is made at arrival and departure epochs. Admitted customers generate a fixed revenue and the holding cost rate is increasing and convex in the number of customers in the system. Also there is a service cost rate, depending on the server speed, and no cost for switching between service rates.
We formulate a Markov Decision Process model for maximization of the infinite horizon expected discounted net profit. We explore several properties of the value function and the optimal policy. In particular we consider the interaction between service rate and admission decisions.