= Poisson effective bandwidth
{c}
{title2=$\alpha(\theta)=\nu(e^\theta-1)/\theta$}
For independent <Poisson> arrival counts of mean $\nu$ per slot, with one unit of work per arrival, the <cumulant-generating function> is $\nu(e^\theta-1)$. Its <effective bandwidth> is the displayed expression. If $c>\nu$, the equation $\nu(e^\theta-1)=c\theta$ has a unique positive root: strict <convexity>, negative initial derivative after subtracting $c\theta$, and divergence to infinity prove existence and uniqueness. Independent Poisson streams combine by replacing $\nu$ with the sum of their intensities.
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