= Moderate deviation scales of a clipped Poisson aggregate
{title2=$K_\beta(y)=y^2/(2\lambda)\ (y\le C),\quad K_\beta(y)=\infty\ (y>C)$}
Clip <Poisson> input of mean $L\lambda$ at $L\lambda+C L^{(1+\beta)/2}$. The <Poisson moderate deviation principle> and <contraction principle for large deviations> give the displayed output rate at the clipping scale. At smaller exponents the output retains the original rate by <moderate deviations below a bufferless queue cap>. At larger positive-deviation scales every overflow event is eventually impossible because the requested threshold exceeds the cap.
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