Coverage, Coarseness and Classification: Determinants of Social Efficiency in Priority Queues

Abstract

Many service providers utilize priority queues. Many consumers revile priority queues. However, some form of priority service may be necessary to maximize social welfare. Consequently, it is useful to understand how the priority scheme chosen by a revenue-maximizing firm differs from the one a social planner would use. We examine this in a single server-queue with customers that draw their valuation from a continuous distribution and have a per-period waiting cost that is proportional to their realized valuation. The decision maker must post a menu offering a finite number of waiting time-price pairs. There are then three dimensions on which a revenue maximizer and social planner can differ: coverage (i.e., how many customer in total to serve), coarseness (i.e., how many classes of service to offer), and classification (i.e., how to map customers to priority levels).

We show that differences between the decision makers’ priority policies are all about classification. Both are content to offer very coarse schemes with just two priority levels, and they will have negligible differences in coverage. However, differences in classification are persistent. Further, a revenue maximizer may — relative to the social planner — have too few or too many high priority customers. Whether the revenue maximizer over- or under-stuffs the high priority class depends on a measure of consumer surplus that is captured by the mean residual life function of the valuation distribution. In addition we show that there is a large class of valuation distributions for which a move from first-in, first-out service to a priority scheme that places those with higher waiting costs at the front of the line reduces consumer surplus.

Keywords: queues, pricing, priorities

JEL Classification: M11