An Equilibrium Analysis of a Discrete-Time Markovian Queue with Endogenous Abandonments

72 Pages Posted: 3 Apr 2017

See all articles by Baris Ata

Baris Ata

University of Chicago - Booth School of Business

Peter Glynn

Stanford University

Xiaoshan Peng

Indiana University - Kelley School of Business

Date Written: April 1, 2017

Abstract

This paper studies a Geo/Geo/1 GI 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

Ata, Baris and Glynn, Peter and Peng, Xiaoshan, An Equilibrium Analysis of a Discrete-Time Markovian Queue with Endogenous Abandonments (April 1, 2017). Available at SSRN: https://ssrn.com/abstract=2944797 or http://dx.doi.org/10.2139/ssrn.2944797

Baris Ata

University of Chicago - Booth School of Business ( email )

5807 S. Woodlawn Avenue
Chicago, IL 60637
United States

Peter Glynn

Stanford University ( email )

Stanford, CA 94305
United States

Xiaoshan Peng (Contact Author)

Indiana University - Kelley School of Business ( email )

1309 East Tenth Street
Bloomington, IN 47405-1701
United States

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