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                                SEEM-DOT Joint Seminar

                        The Chinese University of Hong Kong

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Date: Friday, January 30, 2026, 15:25 pm to 16:25 pm HKT

Venue: ERB 602, The Chinese University of Hong Kong

Title: When Strategic Customers Meet Strategic Servers: Individual and

Social Optimization in Many-Server Queueing Systems

Speaker: Prof. Amy Ward, The University of Chicago Booth School of Business

Abstract:

We initiate the study of joint strategic behavior of customers and

servers in many-server queueing systems. We model customers as strategic

agents who decide whether to join the system by weighing reward from

service against cost of waiting, following the seminal works of Naor

(1969) and Knudsen (1972). In those works, customers use a threshold

equilibrium joining strategy based on the number of customers already in

the system (whereas servers operate at fixed exogenous rates). Moreover,

customers "over-join" (that is, induce a higher threshold) compared to

the socially optimal threshold, a result known as Naor's inequality.

Although Naor's inequality is known to hold widely in queueing systems

with strategic customers, no work has considered whether or not it holds

when servers are also strategic (specifically, in choosing how fast to

work). We investigate this question within a large-system asymptotic

framework when servers choose service rates to balance reward and effort

cost.

We show that at equilibrium, customers may either over-join or

under-join the system (that is, induce a higher or lower threshold than

the socially optimal one), an observation that challenges the

universality of Naor's inequality. Next, we compare the welfare of

customers and servers under the social optimum and an individual

equilibrium and find the following imbalance: While customers always

benefit when moving from an equilibrium to the social optimum, servers

may end up experiencing reduced and even negative utility. Finally, we

propose an incentive scheme that charges an entry fee from customers and

offers a performance-based compensation for servers, which realigns

individual incentives with social optimum. The incentive scheme is

feasible (that is, does not require external subsidy) when the number of

servers is sufficiently small. Surprisingly, under the optimal incentive

scheme, the welfare distribution remains imbalanced but towards the

opposite party: Servers always benefit, while customers sometimes incur

welfare losses.

Biography:

Amy Ward's research focuses on the approximation and control of

stochastic systems, with applications to the service industry. Much of

her past work has focused on the impact of customer impatience and

abandonments on performance. Her more recent work investigates the

interactions between behavioral incentives and operational efficiency in

service systems.

Ward is a fellow of the INFORMS Manufacturing and Service Operations

Management (MSOM) Society (elected 6/2023), and is the Editor-in-Chief

for the journal Operations Research (term began 1/1/2024).  In the past,

she was Editor-in-Chief for the journal Operations Research Letters

(term 4/1/2021-12/31/2023), and earlier held the position of Chair of

the Applied Probability Society (term 11/2016-11/2018).

Prior to joining Booth, Ward was Professor of Data Sciences and

Operations at the University of Southern California Marshall School of

Business. She has also been a Visiting Associate Professor in the

Computing and Mathematical Sciences Department at Cal Tech, and an

Assistant Professor in Industrial and Systems Engineering at the Georgia

Institute of Technology. Outside of academia, during her doctoral

studies, she spent several summers at AT&T Laboratories. Ward earned

both a PhD and MA from Stanford University, and she holds a BA from

Claremont McKenna College.

Everyone is welcome to attend the talk!