= Fluid scaling proof of multiple Erlang fixed points
Let $G_N(B)=E(20N[1+2B(1-B)],21N)-B$. The <proportional scaling limit of the Erlang loss formula> makes its limits at $B=1/100$ and $B=1/8$ respectively $-1/100$ and $7/520$. Since $G_N(0)>0$ and $G_N(1)<0$, sufficiently large $N$ give alternating signs at these four points. The <intermediate value theorem> supplies three distinct zeros in the intervening intervals. These are multiple solutions of the <Erlang fixed point approximation>, not multiple stationary laws of an exact finite <irreducible Markov chain>.
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