Optimality of the generalized $$\varvec{c\mu }$$ c μ rule in the moderate deviation regime

This paper studies a multiclass queueing system with an associated risksensitive cost observed in heavy traffic at the moderate deviation scale, accounting for convex queue length penalties. The main result is the asymptotic optimality of a dynamic index policy known from the diffusion-scale heavy traffic literature as the generalized cμ rule.