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

We consider a queueing system where a single server opens and serves users according to the last-come first-served discipline with preemptive-resume (LCFS-PR). A finite number of strategic users must choose individually when to arrive at the server. 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 asymmetric equilibrium exists, if the population consists of only two users, or if arrival strategies satisfy a mild regularity condition. Based on the constructive existence proof for the symmetric equilibrium, we provide a numerical example in which we compute the symmetric equilibrium strategy and compare the resulting social efficiency to that obtained if users are instead served on a first-come first-served (FCFS) basis.