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**1 - 1**of**1**### ERGODIC CONTROL OF MULTI-CLASS M/M/N +M QUEUES IN THE HALFIN-WHITT REGIME

"... Abstract. 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 criter ..."

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Abstract. 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, i.e., the number of servers n and the total offered load r scale like n ≈ r + ρ̂√r for some constant ρ̂. This problem was proposed in [6, Section 5.2]. The optimal solution of this control problem can be approximated by that of the cor-responding 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 queue-ing 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