Edge minimality of EDF resource sharing networks

We consider a general real-time network with soft customer deadlines, in which users require service from several shared resources simultaneously. We call the service protocol for such a network edge minimal (locally edge minimal) if it minimizes globally (resp., locally) in time, 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. We show that the preemptive Earliest-Deadline-First (EDF) service discipline is edge minimal. Moreover, we characterize the preemptive EDF policy as a protocol making the underlying network locally edge minimal. Our arguments are pathwise, independent on the network topology and requiring very mild assumptions, or even no assumptions, on the model stochastic primitives. Application of our characterization to fluid model analysis for EDF resource sharing networks is also discussed.