A general multi-resource network with users requiring service from a number of shared resources simultaneously is considered. It is demonstrated that the Shortest Remaining Processing Time (SRPT) service protocol minimizes, in a suitable sense, the system resource idleness with respect to customers with residual service times not greater than any threshold value on every network route. Our arguments are pathwise, with no assumptions on the model stochastic primitives and the network topology.

We consider a general network with arbitrary topology and node capacities, in which users require simultaneous service from a number of shared resources. We study pathwise minimality of the shortest remaining processing time protocol with respect to suitable criteria based on the system’s cumulative transmission times of flows with residual service requirements not greater than any threshold value on the network routes. No distributional assumptions are made on the underlying stochastic primitives.