On optimality gaps in the Halfin--Whitt regime

Details On optimality gaps in the Halfin--Whitt regime On optimality gaps in the Halfin--Whitt regime

2012-03-08

arxiv.org/abs/1203.1723v1

Annals of Applied Probability 2012, Vol. 22, No. 1, 407-455

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/11-AAP777 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst

Scientific paper

10.1214/11-AAP777

We consider optimal control of a multi-class queue in the Halfin--Whitt regime, and revisit the notion of asymptotic optimality and the associated optimality gaps. The existing results in the literature for such systems provide asymptotically optimal controls with optimality gaps of $o(\sqrt{n})$ where $n$ is the system size, for example, the number of servers. We construct a sequence of asymptotically optimal controls where the optimality gap grows logarithmically with the system size. Our analysis relies on a sequence of Brownian control problems, whose refined structure helps us achieve the improved optimality gaps.

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