Coverage, coarseness, and classification: Determinants of social efficiency in priority queues

Customers often resent priority queues even though priorities are often necessary to maximize either social welfare or revenue. Consequently, it is useful to consider the level of social inefficiency introduced when the design of a priority scheme is turned over to a revenue-maximizing firm. In this paper we study how the priority scheme chosen by a revenue-maximizing firm differs from the one a social planner would use. We study a single-server queue with customers who draw their valuations from a continuous distribution and have a per-period waiting cost that is proportional to their realized valuations. 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 customers 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 overstuffs or understuffs the high-priority class depends on a measure of consumer surplus that is captured by the mean residual life function of the valuation distribution.