Equilibrium in a customer choice between observable and unobservable queues with heterogeneous servers

Bara Kim; Jeongsim Kim; Chia Li Wang

doi:10.1007/s11134-025-09957-y

Equilibrium in a customer choice between observable and unobservable queues with heterogeneous servers

Bara Kim
, Jeongsim Kim^*
, Chia Li Wang

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We consider a system with two servers, each with its own queue: one observable and the other unobservable. Upon arrival, customers choose which queue to join. It is known that a unique threshold-type equilibrium strategy exists when the service rates of the two servers are equal. Dvir, Hassin, and Haviv (2022) demonstrated that such a strategy does not always exist when the service rates differ. However, through extensive numerical experiments, they observed that a unique threshold-type equilibrium strategy exists whenever the service rate of the unobservable queue is greater than or equal to that of the observable queue. In this paper, we rigorously prove this observation.

Original language	English
Article number	28
Journal	Queueing Systems
Volume	109
Issue number	4
DOIs	https://doi.org/10.1007/s11134-025-09957-y
Publication status	Published - 2025 Dec

Bibliographical note

Publisher Copyright:
© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.

Keywords

Censored Markov chain
Nash equilibrium
Threshold-type strategy

ASJC Scopus subject areas

Statistics and Probability
Computer Science Applications
Management Science and Operations Research
Computational Theory and Mathematics

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Cite this

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abstract = "We consider a system with two servers, each with its own queue: one observable and the other unobservable. Upon arrival, customers choose which queue to join. It is known that a unique threshold-type equilibrium strategy exists when the service rates of the two servers are equal. Dvir, Hassin, and Haviv (2022) demonstrated that such a strategy does not always exist when the service rates differ. However, through extensive numerical experiments, they observed that a unique threshold-type equilibrium strategy exists whenever the service rate of the unobservable queue is greater than or equal to that of the observable queue. In this paper, we rigorously prove this observation.",

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AU - Kim, Bara

AU - Kim, Jeongsim

AU - Wang, Chia Li

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.

PY - 2025/12

Y1 - 2025/12

N2 - We consider a system with two servers, each with its own queue: one observable and the other unobservable. Upon arrival, customers choose which queue to join. It is known that a unique threshold-type equilibrium strategy exists when the service rates of the two servers are equal. Dvir, Hassin, and Haviv (2022) demonstrated that such a strategy does not always exist when the service rates differ. However, through extensive numerical experiments, they observed that a unique threshold-type equilibrium strategy exists whenever the service rate of the unobservable queue is greater than or equal to that of the observable queue. In this paper, we rigorously prove this observation.

AB - We consider a system with two servers, each with its own queue: one observable and the other unobservable. Upon arrival, customers choose which queue to join. It is known that a unique threshold-type equilibrium strategy exists when the service rates of the two servers are equal. Dvir, Hassin, and Haviv (2022) demonstrated that such a strategy does not always exist when the service rates differ. However, through extensive numerical experiments, they observed that a unique threshold-type equilibrium strategy exists whenever the service rate of the unobservable queue is greater than or equal to that of the observable queue. In this paper, we rigorously prove this observation.

KW - Censored Markov chain

KW - Nash equilibrium

KW - Threshold-type strategy

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DO - 10.1007/s11134-025-09957-y

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VL - 109

JO - Queueing Systems

JF - Queueing Systems

IS - 4

M1 - 28

ER -

Equilibrium in a customer choice between observable and unobservable queues with heterogeneous servers

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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