= Monotonicity of the Erlang blocking probability
{title2=$\partial_aE(a,C)=E(a,C)[C-m_C(a)]/a>0$}
For positive integer capacity $C$ and <offered load> $a>0$, let $m_C(a)$ be the <carried load of an Erlang loss resource>. Differentiating the <upper-truncated Poisson distribution> gives $m_C'(a)=\operatorname{Var}(N)/a>0$. Differentiating its probability at $C$ gives the displayed <derivative> of the <Erlang loss formula>; it is positive because $m_C(a)<C$. Thus blocking increases continuously from zero to one, and the carried load increases from zero to $C$. These properties justify the inverse blocking coordinates in the <convex potential for the Erlang fixed point>.
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