Analyses of Equilibrium Behaviour of Customers and Optimal Design for Queues under a Preemptive Priority Discipline

Abstract

The paper considers a classical M/M/1 queue with two priority classes under a preemptive priority discipline. Based on the performance measures of White and Christie [14], the paper studies the optimal pricing policy of the server who is an individual profit maximizer when the customers adopt their respective equilibrium arrival rate, then discusses the service rate control problem from the perspective of social welfare maximization. Because of the complexity of the model, it's intractable to theoretically analyze the queueing system in depth. In the section of example analyses, two numerical examples are presented, on the one hand to give the specifically optimal pricing policy and service rate control policy, and on the other hand to conduct some sensitivity analyses for some important parameters.