Scandinavian Working Papers in Economics

Discussion Papers of Business and Economics,
University of Southern Denmark, Department of Business and Economics

No 3/2017: Equilibrium Arrival Times to Queues: The Case of Last-Come First-Serve Preemptive-Resume

Jesper Breinbjerg () and Lars Peter Østerdal ()
Additional contact information
Jesper Breinbjerg: Department of Business and Economics, Postal: University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark
Lars Peter Østerdal: Department of Economics, Postal: Copenhagen Business School, Porcelænshaven 16A, 2000 Frederiksberg, Denmark

Abstract: We consider a non-cooperative queueing environment where a finite number of customers independently choose when to arrive at a queueing system that opens at a given point in time and serves customers on a last-come first-serve preemptive-resume (LCFS-PR) basis. Each customer has a service time requirement which is identically and independently distributed according to some general probability distribution, and they want to complete service as early as possible while minimizing the time spent in the queue. In this setting, we establish the existence of an arrival time strategy that constitutes a symmetric (mixed) Nash equilibrium, and show that there is at most one symmetric equilibrium. We provide a numerical method to compute this equilibrium and demonstrate by a numerical example that the social efficiency can be lower than the efficiency induced by a similar queueing system that serves customers on a first-come first-serve (FCFS) basis.

Keywords: Queueing; strategic arrival times to a queue; non-cooperative games

JEL-codes: C72; D62; R41

22 pages, March 17, 2017

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