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 α = α1 αN . We show that under the LWDF discipline the sequence of scaled stationary distributions of the delay ŵi of each flow satisfies a large deviation principle with the rate function given by a finitedimensional optimization problem. We also prove that the LWDF discipline is optimal in the sense that it maximizes the quantity