= Stability conditions for a two-resource linear flow network
{title2=$\rho_1+\rho_0<1,\quad\rho_2+\rho_0<1$}
The <stationary law of a two-resource linear flow network> is normalizable exactly when
$$
\rho_1+\rho_0<1,\qquad\rho_2+\rho_0<1.
$$
These are the strict offered-load constraints on the two unit-capacity resources. Summing first over the through-route count reduces normalization to two <geometric series>, which diverge at equality. With positive arrival rates, the nonexplosive <continuous-time Markov chain> is then positive recurrent.
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