We consider a memoryless unobservable single-server queue where customers are homogeneous with respect to their reward (due to service completion) and with respect to their cost per unit of time of waiting. Left to themselves, it is well known that in equilibrium they will join the queue at a rate that is higher than it is socially optimal. We show that if customers draw a random preemptive priority parameter prior to deciding whether or not to join, the resulting equilibrium joining rate coincides with the socially optimal one. We also introduce some variations of this regulation scheme and review a few existing schemes from the literature. We suggest a classification of all these schemes, based on a few key properties, and use it to compare our new schemes with the existing ones.
