Equilibrium Arrivals to a Last-come First-served Preemptive-resume Queue

Jesper Breinbjerg, Trine Tornøe Platz, Lars Peter Østerdal*

*Corresponding author for this work

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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.
Original languageEnglish
JournalAnnals of Operations Research
Number of pages22
Publication statusPublished - 15 May 2023

Bibliographical note

Epub ahead of print. Published online: 15 May 2023


  • Queueing
  • Strategic arrivals
  • Nash equilibrium
  • FCFS

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