Minimality of SRPT Networks With Resource Sharing

Ageneral 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. Key-Words: Queuing, resource sharing, SRPT, minimality, residual file sizes, partial ordering, service protocols