= Alternative-routing triangle with three Erlang fixed points
{title2=$B=E(C,v[1+2B(1-B)])$}
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>.
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