Remark on ‘On vacation models with bulk arrivals’

For the bulk arrival M/G/1 queueing model with a general exhaustive service vacation policy, it was proved in the recent paper mentioned in the title that the steady-state queue length generating function-at a post-departure epoch and at an arbitrary epoch-is the product of the corresponding generating function in the bulk arrival model without server vacations and another generating function. The expression given for the latter, however, is valid only under the assumption that the number of groups arriving in an inactive phase is independent of the sizes of the groups. An expression is given here which holds in the general case, when this assumption is not necessarily satisfied.