Infinite Horizon Average Optimality of the N-network Queueing Model in the Halfin-Whitt Regime
This work provides theoretical foundations for optimal control of multi-class multi-server queues in the heavy-traffic regime, relevant to operations research and queueing theory.
The paper establishes asymptotic optimality for infinite horizon average cost control of N-network queues in the Halfin-Whitt regime, proving convergence of value functions to a diffusion limit for three control objectives with convex costs. It also provides a geometrically ergodic priority policy and convergence results for mean empirical measures.
We study the infinite horizon optimal control problem for N-network queueing systems, which consist 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.