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Scheduling Parallel Servers in the Non-Degenerate Slowdown Diffusion Regime: Asymptotic Optimality Results, Annals of Applied Probability

Abstract

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 non-degenerate slowdown. This regime is distinct from the well-studied heavy traffic diusion 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.

Type

Article

Author(s)

Rami Atar, Itai Gurvich

Date Published

2014

Citations

Atar, Rami, and Itai Gurvich. 2014. Scheduling Parallel Servers in the Non-Degenerate Slowdown Diffusion Regime: Asymptotic Optimality Results. Annals of Applied Probability. 24(2): 760-810.

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