Bayesian Dynamic Pricing in Queueing Systems with Unknown Delay Cost Characteristics

Philipp Afèche () and Barış Ata ()
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Philipp Afèche: Rotman School of Management, University of Toronto, Toronto, Ontario M5S 3E6, Canada
Barış Ata: Kellogg School of Management, Northwestern University, Evanston, Illinois 60208

Manufacturing & Service Operations Management, 2013, vol. 15, issue 2, 292-304

Abstract: The revenue management literature for queues typically assumes that providers know the distribution of customer demand attributes. We study an observable M/M/1 queue that serves an unknown proportion of patient and impatient customers. The provider has a Bernoulli prior on this proportion, corresponding to an optimistic or pessimistic scenario. For every queue length, she chooses a low or a high price, or turns customers away. Only the high price is informative. The optimal Bayesian price for a queue state is belief-dependent if the optimal policies for the underlying scenarios disagree at that queue state; in this case the policy has a belief-threshold structure. The optimal Bayesian pricing policy as a function of queue length has a zone (or, nested-threshold) structure. Moreover, the price convergence under the optimal Bayesian policy is sensitive to the system size, i.e., the maximum queue length. We identify two cases: prices converge (1) almost surely to the optimal prices in either scenario or (2) with positive probability to suboptimal prices. Only Case 2 is consistent with the typical incomplete learning outcome observed in the literature.

Keywords: Bayesian learning; delay; dynamic pricing; revenue management; queueing (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormsom:v:15:y:2013:i:2:p:292-304

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