The paper reviews the Kiefer-Wolfowitz conditions for finite delay moments at a GI/G/s queue, which are independent of moment conditions on the arrival process. Through examples, it shows that for nonrenewal arrivals, some additional conditions on the arrival process are necessary. The paper discusses the question of whether some known sufficient conditions for finite delay moments at ‘downstream’ stations in a tandem queue are really necessary. It then shows how to decouple conditions on the arrival process from conditions on service times. Finally, the paper obtains sufficient conditions for queues with regenerative arrivals.
