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A queueing system with vacations after N services
Author(s) -
Boxma Onno,
Claeys Dieter,
Gulikers Lennart,
Kella Offer
Publication year - 2015
Publication title -
naval research logistics (nrl)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 68
eISSN - 1520-6750
pISSN - 0894-069X
DOI - 10.1002/nav.21669
Subject(s) - computer science , queueing system , queue , idle , operations research , variable (mathematics) , order (exchange) , constant (computer programming) , laplace transform , function (biology) , random variable , real time computing , computer network , mathematics , business , statistics , operating system , mathematical analysis , finance , evolutionary biology , biology , programming language
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