Optimal scheduling of a large-scale multiclass parallel server system with ergodic cost

We consider the optimal scheduling problem for a large-scale parallel server system with one large pool of statistically identical servers and multiple classes of jobs under the expected long-run average (ergodic) cost criterion. Jobs of each class arrive as a Poisson process, are served in the FCFS discipline within each class and may elect to abandon while waiting in their queue. The service and abandonment rates are both class-dependent. Assume that the system is operating in the Halfin-Whitt regime, where the arrival rates and the number of servers grow appropriately so that the system gets critically loaded while the service and abandonment rates are fixed. The optimal solution is obtained via the ergodic diffusion control problem in the limit, which forms a new class of problems in the literature of ergodic controls. A new theoretical framework is provided to solve this class of ergodic control problems. The proof of the convergence of the values of the multiclass parallel server system to that of the diffusion control problem relies on a new approximation method, spatial truncation, where the Markov policies follow a fixed priority policy outside a fixed compact set.