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A multi-class single-server system with general service time distributions isstudied in a moderate deviation heavy traffic regime. In the scaling limit, anoptimal control problem associated with the model is shown to be governed by adifferential game that can be explicitly solved. While the characterization ofthe limit by a differential game is akin to results at the large deviationscale, the analysis of the problem is closely related to the much studied areaof control in heavy traffic at the diffusion scale.

Control of the multiclass $G/G/1$ queue in the moderate deviation regime