On vacation models with bulk arrivals

Abstract

Forthe bulk arrival M/G/1 queueing model with a general exhaustive service vacation policy, we proved in our recent paper mentionedin 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. We here give an expression which holds in the general case, when this assumption is not necessarily satisfied.