An equilibrium analysis of a discrete-time Markovian queue with endogenous abandonments

Baris Ata (), Peter W. Glynn () and Xiaoshan Peng ()
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Peter W. Glynn: Huang Engineering Center 357

Queueing Systems: Theory and Applications, 2017, vol. 86, issue 1, No 5, 212 pages

Abstract: Abstract This paper studies a Geo/Geo/1 $$+GI$$ + G I queue in which the abandonments are endogenous. One crucial feature of this model is that the abandonment behavior is affected by the system performance and vice versa. Our model captures this interaction by developing two closely related models: an abandonment model and a queueing model. In the abandonment model, customers take the virtual waiting time distribution as given. They receive a reward r from service and incur a cost c per period of waiting. Customers are forward-looking and maximize their expected discounted utilities by making wait or abandon decisions dynamically as they wait in the queue. The queueing model takes the customers’ abandonment time distribution as an input and studies the resulting virtual waiting time distribution. In equilibrium, the customers’ abandonment behavior and the system performance must be consistent across the two models. Therefore, combining the two models and imposing this consistency requirement, we show that there exists a unique equilibrium. Lastly, we provide a computational scheme to calculate the equilibrium numerically.

Keywords: Invisible queue; Endogenous abandonment; Customer abandonment; Impatient customers; Single-class queue; 60K25; 90B22; 91G80 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11134-017-9521-6

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