A Queueing System with Vacations after N Services

Onno Boxma, Dieter Claeys, Lennart Gulikers, Offer Kella

Research output: Contribution to journalArticlepeer-review


This article is devoted to the study of an M/G/1 queue with a particular vacation discipline. The server is due to take a vacation as soon as it has served exactly N customers since the end of the previous vacation. N may be either a constant or a random variable. If the system becomes empty before the server has served N customers, then it stays idle until the next customer arrival. Such a vacation discipline arises, for example, in production systems and in order picking in warehouses. We determine the joint transform of the length of a visit period and the number of customers in the system at the end of that period. We also derive the generating function of the number of customers at a random instant, and the Laplace-Stieltjes transform of the delay of a customer.

Original languageAmerican English
Pages (from-to)646-658
Number of pages13
JournalNaval Research Logistics
Issue number8
StatePublished - 1 Dec 2015


  • M/G/1 queue
  • delay
  • order picking
  • queue length
  • vacation discipline

All Science Journal Classification (ASJC) codes

  • Modelling and Simulation
  • Ocean Engineering
  • Management Science and Operations Research


Dive into the research topics of 'A Queueing System with Vacations after N Services'. Together they form a unique fingerprint.

Cite this