= Stability region for the reversible four-cycle flow network
{title2=$\max(\rho_1,\rho_3)+\max(\rho_2,\rho_4)<1$}
Group the normalizing sum by its odd and even flow counts. The coefficient sums are $h_p(\rho_1,\rho_3)=\sum_{i=0}^p\rho_1^i\rho_3^{p-i}$ and the analogous $h_q$ for even routes. If $a$ and $b$ are the two maximum loads, then $a^p\leq h_p\leq(p+1)a^p$ and similarly for $b$. The generating identity $\sum_{p,q}\binom{p+q}{p}a^pb^q=(1-a-b)^{-1}$ proves necessity and sufficiency of the displayed strict inequality. It is equivalent to strictly subunit offered load on each of the four resources.
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