Optimal pricing for a GI/M/k/N queue with several customer types and holding costs

This paper studies optimal pricing for a GI/M/k/N queueing system with several types of customers. An arrival joins the queue if the price of service is not higher than the maximum amount that the arrival is willing to pay, and this maximum amount is defined by the customer type. A system manager chooses a price depending on the number of customers in the system. In addition, the system incurs holding costs when there are customers waiting in the queue for their services. Service times and holding costs do not depend on customer types. The holding costs are nondecreasing and convex with respect to the number of customers in the queue. This paper describes average reward optimal, canonical, bias optimal, and Blackwell optimal policies for this pricing problem.