Local edge minimality of SRPT networks with shared resources

Abstract

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.

Diffusion Limits for Shortest Remaining Processing Time Queues with Multiple Customer Types

“…The last term in (24) takes into account possible initial jobs with processing times greater than x * . Under the diffusion scaling Ŵ r Σ,L (t) = 1 r W r Σ,L (r 2 t) we have Ŵ r Σ,L = Ŵ r Σ − Ŵ r Σ,H and by ( 5) and (11),…”

“…Another related field of research involves studying resource sharing networks under the SRPT service discipline. In [10], [11], a notion of minimality, related to maximizing the corresponding cumulative transmission time with respect to jobs with residual service time not greater than a given threshold, was introduced and it was shown that SRPT is minimal in this sense. Moreover, in [11], another optimality criterion, local edge minimality, was proposed and it was proved that it characterizes a certain subclass of SRPT disciplines, named strong SRPT protocols.…”