Control of End-to-End Delay Tails in a Multiclass Network: LWDF Discipline Optimality

We consider a multiclass queueing network with N customer classes, each having an arbitrary fixed route through the network. (Thus, the network is not necessarily feedforward). We show that the Largest Weighted Delay First (LWDF) discipline [30] is an optimal scheduling discipline in the network in the following sense. Let w sub i be the (random) instantaneous largest end-to-end delay of a class i customer in the network in stationary regime.