Priority Queues and Consumer Surplus
33 Pages Posted: 23 Sep 2018 Last revised: 26 Jun 2019
Date Written: June 25, 2019
We examine whether priority queues benefit or hurt customers in a setting in which customers are privately informed of their per-unit-time waiting cost. Implementing a priority queue thus means posting a menu of expected waits and out-of-pocket prices that are incentive compatible. Whether priorities increase or decrease consumer surplus relative to first- in, first-out service depends on the model of customer utility and on the distribution of customer waiting costs. If all customers have the same value of the service independent of their waiting costs, priorities essentially always lower consumer surplus. If a customer’s value of the service is an increasing function of her waiting cost, priorities lower surplus if the distribution of waiting costs has a decreasing mean residual life. If the mean residual life is increasing, then priorities make consumers better off. We show that the results across utility models are linked by an elasticity measure. If an appropriate measure of waiting cost is elastic, consumer surplus falls with priorities. We also explore how priorities impact individual customers and show that they potentially make all customers worse off. It is possible that low priority customers may pay a higher out-of-pocket price than they would under first-in, first-out service.
Keywords: Queues, Revenue Management, Consumer Surplus
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