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.