Application of Neuts’ method to bulk queueing models with vacations

The paper studies a single server infinite capacity queueing system in which customers, arriving in groups according to a Poisson process, are served in batches under the usual bulk service rule. The server applies a general exhaustive service vacation policy. Computational results for the queue length at a post-departure or inactive phase termination epoch, at a post-departure epoch and at an arbitrary epoch are given. In particular, the paper considers a vacation model where the decision of whether to take a vacation or not, in a given inactive phase, is allowed to depend on the number of vacations already taken in this inactive phase and the number of customers waiting, compared to a specified number N. As special cases, it includes the (T(SV);N)-policy and the (T(MV);N)-policy. The paper discusses two applications in the analysis of production, computer and communication systems. A simple numerical example is also considered.