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A Markovian queueing network is considered with d independent customer classes and d server pools in Halfin–Whitt regime. Class i customers has priority for service in pool i for i = 1, …, d, and may access some other pool if the pool has an idle server and all the servers in pool i are busy. We formulate an ergodic control problem where the running cost is given by a non-negative convex function with polynomial growth. We show that the limiting controlled diffusion is modelled by an action space which depends on the state variable. We provide a complete analysis for the limiting ergodic control problem and establish asymptotic convergence of the value functions for the queueing model.

An Ergodic Control Problem for Many-Server Multiclass Queueing Systems with Cross-Trained Servers