%0 Journal Article
%T Scheduling parallel servers in the nondegenerate slowdown diffusion regime: Asymptotic optimality results
%A Rami Atar
%A Itai Gurvich
%J Mathematics
%D 2014
%I arXiv
%R 10.1214/13-AAP935
%X We consider the problem of minimizing queue-length costs in a system with heterogenous parallel servers, operating in a many-server heavy-traffic regime with nondegenerate slowdown. This regime is distinct from the well-studied heavy traffic diffusion regimes, namely the (single server) conventional regime and the (many-server) Halfin-Whitt regime. It has the distinguishing property that waiting times and service times are of comparable magnitudes. We establish an asymptotic lower bound on the cost and devise a sequence of policies that asymptotically attain this bound. As in the conventional regime, the asymptotics can be described by means of a Brownian control problem, the solution of which exhibits a state space collapse.
%U http://arxiv.org/abs/1403.5399v1