## 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 effciency can be lower than the effciency induced by a similar queueing system that serves customers on a first-come first-serve (FCFS) basis.

equilibrium and demonstrate by a numerical example that the social effciency can be lower than the effciency induced by a similar queueing system that serves customers on a first-come first-serve (FCFS) basis.

Original language | English |
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Place of Publication | Odense |

Publisher | Syddansk Universitet |

Number of pages | 22 |

Publication status | Published - 2017 |

Series | Discussion Papers on Business and Economics |
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Number | 3/2017 |

## Keywords

- Queueing
- Strategic arrival times to a queue
- Non-cooperative games