Optimal Priority-Purchasing and Pricing Decisions in Nonmonopoly and Monopoly Queues

An M/M/1 service station (computer center) consists of M separate queues. The ith (i = 1, 2, …, M) queue has priority over the jth iff i < j. Upon arrival, a customer receives all the information regarding the state of the system and accordingly makes an irrevocable decision as to which queue to join, or rather to balk (leave) and go to a competitor. The higher the priority of the queue, the higher the toll fee to join it but the shorter the time spent in the system. This paper considers nonmonopoly and monopoly cases, and optimal priority-purchasing or balking rules for the newly arrived customer, as well as optimal pricing policies for the service station for both preemptive-resume and non-preemptive-priority disciplines.