Largest Weighted Delay First Scheduling: Large Deviations and Optimality

We consider a single server system with N input flows. We assume that each flow has stationary increments and satisfies a sample path large deviation principle, and that the system is stable. We introduce the largest weighted delay first (LWDF) queueing discipline associated with any given weight vector .=(.1,...,.N). We show that under the LWDF discipline the sequence of scaled stationary distributions of the delay ^wi of each flow satisfies a large deviation principle with the rate function given by a finite- dimensional optimization problem. We also prove that the LWDF discipline is optimal in the sense that it maximizes the quantity mini=1, ..., N[.ilimn...1nlogP(^wi>n)], within a large class of work conserving disciplines.