TY - JOUR

T1 - Infinite-horizon average optimality of the N-network in the halfin-whitt regime

AU - Arapostathis, Ari

AU - Pang, Guodong

N1 - Funding Information:
Funding:This research was supported in part by the Army Research Office [Grant W911NF-17-1-0019]. The work of the first author was also supported in part by the Office of Naval Research [Grant N00014-14-1-0196]. The work of the second author is also supported in part by the Marcus Endowment Grant at the Harold and Inge Marcus Department of Industrial and Manufacturing Engineering at Penn State.

PY - 2018/8

Y1 - 2018/8

N2 - 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.

AB - 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.

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U2 - 10.1287/moor.2017.0886

DO - 10.1287/moor.2017.0886

M3 - Article

AN - SCOPUS:85051494758

VL - 43

SP - 838

EP - 866

JO - Mathematics of Operations Research

JF - Mathematics of Operations Research

SN - 0364-765X

IS - 3

ER -