Further delay moment results for FIFO multiserver queues

Abstract

Using a new family of service disciplines, we provide weaker sufficient conditions for finite stationary delay moments in FIFO multiserver queues. This extends the work in Sigman and Scheller-Wolf [6] to GI/GI/s queues with ρ = E[S]/E[T] <s-1, where S and T are generic service and interarrival times, respectively. Thus, only when ρ > s-1 are the familiar Kiefer and Wolfowitz conditions actually known to be necessary. For the case when ρ< 1, we provide sufficient conditions for finite mean stationary delay, expressed as a function of the number of servers in the system. The limit of these conditions as s→∞ is the requirement that E[S] < ∞, which is the condition for finite mean stationary delay in a FIFO GI/GI/∞ queue. Both of these results highlight the interplay between traffic intensity and service time distribution in determining the behavior of delay moments in multiserver queues.