Infinite-horizon average optimality of the N-network in the halfin-whitt regime

Ari Arapostathis, Guodong Pang

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


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 diffusionscaled state process to the corresponding values of the controlled diffusion limit. We also present a simple state-dependent priority scheduling policy under which the diffusionscaled state process is geometrically ergodic in the Halfin-Whitt regime, and some results on convergence of mean empirical measures, which facilitate the proofs.

Original languageEnglish (US)
Pages (from-to)838-866
Number of pages29
JournalMathematics of Operations Research
Issue number3
StatePublished - Aug 2018

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Computer Science Applications
  • Management Science and Operations Research


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