Purchasing Priorities in Queues

A class of queueing problems is introduced in which each customer can purchase preferential treatment by making a payment. Each customer is assumed to select his payment so as to minimize his own expected cost, without regard for global considerations. A payment policy determines a customer's payment as a function of the information available. A payment policy is said to be stable if no one customer can reduce his expected cost by deviating from it, provided that all other customers follow it. The existence of stable payment policies which are not globally optimal is demonstrated in examples based on the M/M/1 queue.