On vacation models with bulk arrivals

The paper considers a single server infinite 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. It is concerned with the steady-state distributions of the queue length at a post-departure epoch and at an arbitrary epoch. The paper gives a probabilistic proof of a relation between each of these distributions and the corresponding one in the bulk arrival model without server vacations. Specific types of vacation policies are then considered.