Article ID: | iaor201679 |
Volume: | 62 |
Issue: | 8 |
Start Page Number: | 646 |
End Page Number: | 658 |
Publication Date: | Dec 2015 |
Journal: | Naval Research Logistics (NRL) |
Authors: | Kella Offer, Boxma Onno, Claeys Dieter, Gulikers Lennart |
Keywords: | simulation |
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.