Behavior-Aware Queueing: The Finite-Buffer Setting with Many Strategic Servers

87 Pages Posted: 15 Jul 2020 Last revised: 31 Aug 2020

See all articles by Yueyang Zhong

Yueyang Zhong

The University of Chicago Booth School of Business

Raga Gopalakrishnan

Smith School of Business at Queen's University

Amy Ward

The University of Chicago Booth School of Business

Date Written: June 22, 2020

Abstract

Service system design is often informed by queueing theory. Traditional queueing theory assumes that servers work at constant speeds. That is reasonable in computer science and manufacturing contexts. However, servers in service systems are people, and, in contrast to machines, systemic incentives created by design decisions influence their work speeds. We study how server work speed is affected by managerial decisions concerning (i) how many servers to staff and (ii) whether and when to turn away customers, in the context of a finite-buffer many-server queue (an M/M/N/k queue) in which the work speeds emerge as the solution to a noncooperative game.

We show that a symmetric equilibrium always exists in a loss system (N=k) and provide conditions for equilibrium existence in a single-server system (N=1). For the general M/M/N/k system, we provide a sufficient condition for the existence of a solution to the relevant first-order condition and bounds on such a solution; however, showing that it is an equilibrium is challenging due to the existence of multiple local maxima in the utility function. Nevertheless, in an asymptotic regime in which demand becomes large, the utility function becomes concave and the first-order condition simplifies to that for an infinite buffer (k=∞) system, allowing us to characterize "stable" prelimit equilibria.

Keywords: service systems; strategic servers; finite buffer; queueing game; equilibrium

Suggested Citation

Zhong, Yueyang and Gopalakrishnan, Ragavendran and Ward, Amy, Behavior-Aware Queueing: The Finite-Buffer Setting with Many Strategic Servers (June 22, 2020). Available at SSRN: https://ssrn.com/abstract=3633435 or http://dx.doi.org/10.2139/ssrn.3633435

Yueyang Zhong (Contact Author)

The University of Chicago Booth School of Business ( email )

5807 S. Woodlawn Avenue
Chicago, IL 60637
United States

Ragavendran Gopalakrishnan

Smith School of Business at Queen's University ( email )

143 Union Street
Kingston, Ontario K7L 3N6
Canada
+16135332340 (Phone)

HOME PAGE: http://https://smith.queensu.ca/faculty_and_research/faculty_list/gopalakrishnan-raga.php

Amy Ward

The University of Chicago Booth School of Business ( email )

5807 S Woodlawn Ave
Chicago, IL 60637
United States

HOME PAGE: http://www.chicagobooth.edu/faculty/directory/w/amy-ward

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