Journal
MATHEMATICS OF OPERATIONS RESEARCH
Volume 43, Issue 3, Pages 838-866Publisher
INFORMS
DOI: 10.1287/moor.2017.0886
Keywords
parallel-server network; N-network; reneging/abandonment; Halfin-Whitt (QED) regime; diffusion scaling; long-time average control; ergodic control; ergodic control with constraints; geometric ergodicity; stable Markov optimal control; asymptotic optimality
Funding
- Army Research Office [W911NF-17-1-0019]
- Office of Naval Research [N00014-14-1-0196]
- Marcus Endowment Grant at the Harold and Inge Marcus Department of Industrial and Manufacturing Engineering at Penn State
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We study the infinite-horizon optimal control problem for N-network queueing systems, which consists of two customer classes and two server pools, under average (ergodic) criteria in the Halfin-Whitt regime. We consider three control objectives: (1) minimizing the queueing (and idleness) cost, (2) minimizing the queueing cost while imposing a constraint on idleness at each server pool, and (3) minimizing the queueing cost while requiring fairness on idleness. The running costs can be any nonnegative convex functions having at most polynomial growth. For all three problems, we establish asymptotic optimality; namely, the convergence of the value functions of the diffusion-scaled state process to the corresponding values of the controlled diffusion limit. We also present a simple state-dependent priority scheduling policy under which the diffusion-scaled state process is geometrically ergodic in the Halfin-Whitt regime, and some results on convergence of mean empirical measures, which facilitate the proofs.
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