Application of Neuts’ method to vacation models with bulk arrivals

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.