A Model of Rational Retrials in Queues

64 Pages Posted: 25 Oct 2013 Last revised: 9 Jan 2019

See all articles by Shiliang Cui

Shiliang Cui

Georgetown University - McDonough School of Business

Xuanming Su

University of Pennsylvania - Operations & Information Management Department

Senthil K. Veeraraghavan

University of Pennsylvania - The Wharton School - Operations, Information and Decisions

Date Written: January 1, 2014

Abstract

Customers often wait in queues before being served. Since waiting is undesirable, customers may come back later (i.e., retry) when the queue is too long. However, retrial attempts can be costly due to transportation fees and service delays. This paper introduces a framework for rational retrial decisions in stationary queues. Our approach accommodates retrials in queues by replicating the Naor (1969) model repeatedly over time periods. Within each period, similar to Naor (1969), we study an observable queue in which customers make rational state-dependent decisions to join, balk or retry in a future period. We focus on a stationary environment where all arrivals, including new and retrying customers, will face the steady-state distribution of the system in equilibrium. Equilibrium analysis on customers' decision making is necessary as they choose optimal strategies corresponding to the stationary queueing dynamics that are in turn determined by their decisions. We characterize the equilibria in both stable and overloaded systems. We find that (1) Compared to a system without retrials, the additional option to retry can hurt consumer welfare. (2) Compared to the socially optimal decisions, surprisingly, self-interested customers retry insufficiently (they join overly long queues) when the retrial cost is low, and retry too often when the retrial cost is high. (3) Self-interested (retrial) customers can generate positive externalities by smoothing workload over time.

Keywords: Retrials in Queues, Rational Customers, Queueing Games, Equilibrium vs. Social Optimum.

Suggested Citation

Cui, Shiliang and Su, Xuanming and Veeraraghavan, Senthil K., A Model of Rational Retrials in Queues (January 1, 2014). Available at SSRN: https://ssrn.com/abstract=2344510 or http://dx.doi.org/10.2139/ssrn.2344510

Shiliang Cui (Contact Author)

Georgetown University - McDonough School of Business ( email )

Washington, DC 20057
United States

Xuanming Su

University of Pennsylvania - Operations & Information Management Department ( email )

Philadelphia, PA 19104
United States

Senthil K. Veeraraghavan

University of Pennsylvania - The Wharton School - Operations, Information and Decisions ( email )

Philadelphia, PA 19104
United States

HOME PAGE: http://https://oid.wharton.upenn.edu/profile/senthilv/

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