A queueing system with vacations after N services. (24th December 2015)

• Record Type: Journal Article
• Authors: Boxma, Onno; Claeys, Dieter; Gulikers, Lennart; Kella, Offer
• Is Part Of: Naval research logistics. Volume 62:Number 8(2015:Dec.)
• Page Start: 646
• Page End: 658
• Publication Date: 2015-12-24
• Subjects: M/G/1 queue -- vacation discipline -- order picking -- queue length -- delay; Logistics, Naval -- Periodicals; Supplies and stores -- Periodicals; 359.07
• DOI: 10.1002/nav.21669
• Languages: English
• ISSNs: 0894-069X

Abstract

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. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 646–658, 2015