Alternative-routing triangle with three Erlang fixed points ($B=E(C,v[1+2B(1-B)])$)

On a three-node loss network, each pair offers direct calls of load $v$ to its link of capacity $C$. If blocked, the call tries the two-link path through the remaining node. The symmetric reduced-load approximation gives a link its direct load and two overflow contributions $vB(1-B)$, hence the displayed equation. For $C=1000$, $v=940$, its residual has alternating signs at $B=0,0.01,0.10,0.25$, giving at least three distinct roots. This multiplicity belongs to the Erlang fixed point approximation, not to the exact stationary law of a finite reachable Markov chain.