Application of Neuts’ method to vacation models with bulk arrivals

Application of Neuts’ method to vacation models with bulk arrivals

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Article ID: iaor19931590
Country: Belgium
Volume: 31
Start Page Number: 34
End Page Number: 48
Publication Date: Dec 1991
Journal: Belgian Journal of Operations Research, Statistics and Computer Science
Authors:
Keywords: vacation models
Abstract:

This paper studies a single server infinity capacity queueing system with Poisson arrivals of customers groups of random size and a general service time distribution, the server of which applies a general exhaustive service vacation policy. A computational method is applied to obtain the steady state distributions of the queue at a post-departure or inactive phase termination epoch, at a post-departure epoch and at an arbitrary epoch. Relations between these distributions are given. As special cases, two hybrid vacation models are considered: the (T(SV),N)-policy and the (T(MV);N)-policy. In particular, when the service time distribution is of phase type, explicit results can be obtained for the n-policy. This is shown by a simple example.

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