Minimality of EDF networks with resource sharing

We consider a general real-time, multi-resource network with soft customer deadlines, in which users require service from several shared resources simultaneously. We show that the preemptive earliest-deadline-first scheduling strategy minimizes, in a suitable sense, the system resource idleness with respect to customers with lead times not greater than any given threshold value on all the routes of the network. Related methods of performance evaluation for such systems are also discussed. Our arguments are pathwise, requiring no assumptions on the network topology and very mild assumptions, or even no assumptions, on the model stochastic primitives.