A queueing system with vacations after N services

A queueing system with vacations after N services

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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: , , ,
Keywords: simulation
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.

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