Equilibrium arrivals to a last-come first-served preemptive-resume queue

Jesper Breinbjerg, Trine Tornøe Platz, Lars Peter Østerdal*

*Corresponding author af dette arbejde

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Abstract

We consider a queueing system which opens at a given point in time and serves a finite number of users according to the last-come first-served discipline with preemptive-resume (LCFS-PR). Each user must decide individually when to join the queue. We allow for general classes of user preferences and service time distributions and show existence and uniqueness of a symmetric Nash equilibrium. Furthermore, we show that no continuous asymmetric equilibrium exists, if the population consists of only two users, or if arrival strategies satisfy a mild regularity condition. For an illustrative example, we implement a numerical procedure for computing the symmetric equilibrium strategy based on our constructive existence proof for the symmetric equilibrium. We then compare its social efficiency to that obtained if users are instead served on a first-come first-served (FCFS) basis.

OriginalsprogEngelsk
TidsskriftAnnals of Operations Research
Vol/bind336
Sider (fra-til)1551–1572
Antal sider22
ISSN0254-5330
DOI
StatusUdgivet - 2024

Bibliografisk note

Funding Information:
The authors thank Refael Hassin, Liron Ravner, Galit Yom-Tov, and conference, workshop and seminar participants at EAGT2015 (Tokyo), GEM 7 (Odense), Copenhagen Business School, and SING15 (Turku) for helpful comments. We are also grateful to the Guest Editors, Ricardo Martínez, Ruud Hendrickx, Marco Slikker, and Izabella Stach, as well as to two anonymous referees, for useful comments and suggestions. Financial support from the Independent Research Fund Denmark Social Sciences (Grant ID: DFF-1327-00097 and DFF-6109-000132) is gratefully acknowledged. Special thanks are due to Agnieszka Rusinowska and the Paris School of Economics of the Université Paris 1 Panthéon-Sorbonne for the warm hospitality provided during research visits of JB and LPØ. This paper subsumes an earlier working paper circulated as “Equilibrium Arrival Times to Queues: The Case of Last-Come First-Serve Preemptive-Resume”, Discussion Papers on Business and Economics No. 3/2017, SDU.

Publisher Copyright:
© 2023, The Author(s).

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