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...

Priority rules that are mixtures of pre-emption and postponable rules are analyzed. Whether a pre-emption occurs is made to depend on some factor in addition to priority class. A lower priority customer is pre-empted if and only if the queue length of higher priority customers is N, a decision...