Queueing to learn

I study the efficient design of a queue to dynamically allocate a scarce resource to long-lived agents. Agents can be served multiple times, and their valuations fluctuate over time with some persistence. Each agent privately learns whether his prevailing valuation is high or low only when served. An agent can decide anytime whether to either join a queue of his choice or renege. I show that it is efficient to elicit agents' private information by offering a simple binary menu (i.e., two customer classes): a first-come, first-served queue, to attract low-value agents, and one in random order, to attract high-value agents. When queueing is costly, offering a single queue may be optimal because of the tradeoff between allocative efficiency and the cost of screening.