Further delay moment results for FIFO multiserver queues

Using a new family of service disciplines, we provide weaker su cient conditions for nite stationary delay moments in FIFO multiserver queues. This extends the work in Sigman and Scheller-Wolf[1997] to GI=GI=s queues with = E[S]=E[T ] < s 1, where S and T are generic service and interarrival times, respectively. Thus, only when > s 1 are the familiar Kie er and Wolfowitz conditions actually necessary. For the case when < 1, we provide su cient conditions for nite mean stationary delay which are a function of the number of servers in the system. As one would expect, these conditions approach the condition for nite mean stationary delay in a FIFO GI=GI=1 queue, E[S] <1, as s approaches in nity. Our results demonstrate the interplay between tra c intensity and service time distribution in determining the behavior of delay moments in multiserver queues. This is a relationship previously overlooked in the literature.