Signaling quality via queues

We consider a firm’s choice of service rate in the following environment. The firm may have high or low quality, and sells a good to consumers who are heterogeneously informed. Consumers arrive according to a Poisson process and are serviced in a random period of time. If a consumer arrives when another consumer is being serviced, he must join a queue. Consumers observe the length of the queue before making their purchasing decision. The firm may choose a fast or slow service rate. A faster rate requires a costly investment in technology. We show that, in equilibrium, informed consumers join the queue if it is below a threshold. The threshold varies with the quality of the good, so an uninformed consumer updates her belief about quality on observing the length of the queue. The strategy of an uninformed consumer has a “hole”: she joins the queue at lengths both below and above the hole, but not at the hole itself. When all consumers are informed, the high-quality firm has a greater incentive to speed up than the low-quality firm. However, the high-quality firm selects a slower service rate than the low-quality firm if there are a lot of queue lengths between the hole in an uninformed consumer’s strategy and the threshold at which informed consumers balk from its queue. Strikingly, if the proportion of informed consumers is low, the high-quality firm may choose the slow service rate even if the technological cost of speeding up is zero. The queue can therefore be a valuable signaling device for a high-quality firm