 Moderate-deviation queue scaling

For a bufferless queue with Poisson mean input $L\lambda$, place the service margin at $C{L}^{(1+\beta )/2}$, $0<\beta <1$. It exceeds the ordinary square-root fluctuation scale but is sublinear in total input. The Poisson moderate deviation principle gives the displayed overflow exponent. This interpolates between a central-limit safety margin and a fixed per-source excess capacity.