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

Author

Listed:
  • Baris Ata
  • Peter W. Glynn

    (Huang Engineering Center 357)

  • Xiaoshan Peng

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.

Suggested Citation

  • Baris Ata & Peter W. Glynn & Xiaoshan Peng, 2017. "An equilibrium analysis of a discrete-time Markovian queue with endogenous abandonments," Queueing Systems: Theory and Applications, Springer, vol. 86(1), pages 141-212, June.
    • Handle: RePEc:spr:queues:v:86:y:2017:i:1:d:10.1007_s11134-017-9521-6
    DOI: 10.1007/s11134-017-9521-6
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    References listed on IDEAS

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    Cited by:

    1. David Lingenbrink & Krishnamurthy Iyer, 2019. "Optimal Signaling Mechanisms in Unobservable Queues," Operations Research, INFORMS, vol. 67(5), pages 1397-1416, September.

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