A queueing system with vacations after N services

O.J. Boxma, D. Claeys, L. Gulikers, O. Kella

Research output: Contribution to journalArticleAcademicpeer-review

5 Citations (Scopus)

Abstract

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 languageEnglish
Pages (from-to)646-658
Number of pages13
JournalNaval Research Logistics
Volume62
Issue number8
DOIs
Publication statusPublished - 1 Dec 2015

Keywords

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

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