Ergodic Control of Multi-Class M/M/N+M Queues in the Halfin-Whitt Regime

Ari Arapostathis, Anup Biswas, Guodong Pang

Published 2014-04-07, updated 2014-08-23Version 2

We consider a dynamic scheduling problem for a multi-class queueing network with a large pool of statistically identical servers. The arrival processes are Poisson, and service times and patience times are assumed to be exponentially distributed and class dependent. The optimization criterion is the expected long time average (ergodic) of a general (non-linear) running cost function of the queue lengths. We consider this control problem in the Halfin-Whitt (QED) regime. The optimal solution of this control problem can be approximated by that of the corresponding ergodic diffusion control problem in the limit. We introduce a broad class of ergodic control problems for controlled diffusions, which includes a large class of queueing models in the diffusion approximation, and establish a complete characterization of optimality via the study of the associated HJB equation. We also prove the asymptotic convergence of the values for the multi-class queueing control problem to the value of the associated ergodic diffusion control problem. The proof relies on an approximation method by spatial truncation for the ergodic control of diffusion processes, where the Markov policies follow a fixed priority policy outside a fixed compact set.