The Mn/Gn/1 queue with vacations and exhaustive service

Binyamin Oz*, Ivo Adan, Moshe Haviv

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


We consider the Mn/Gn/1 queue with vacations and exhaustive service in which the server takes (repeated) vacations whenever it becomes idle, the service time distribution is queue length dependent, and the arrival rate varies both with the queue length and with the status of the server, being busy or on vacation. Using a rate balance principle, we derive recursive formulas for the conditional distribution of residual service or vacation time given the number of the customers in the system and the status of the server. We also derive a closed-form expression for the steady-state distribution as a function of the probability of an empty system. As an application of the above, we provide a recursive computation method for Nash equilibrium joining strategies to the observable M/G/1 queue with vacations.

Original languageAmerican English
Pages (from-to)945-952
Number of pages8
JournalEuropean Journal of Operational Research
Issue number3
StatePublished - 19 Sep 2019

Bibliographical note

Publisher Copyright:
© 2019 Elsevier B.V.


  • Nash equilibrium
  • Queueing
  • Rate balance
  • Residual lifetime
  • Server vacations


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