= Primal congestion potential
{title2=$U(x)=\sum_rw_r\log x_r-\sum_j\int_0^{(Ax)_j}p_j(u)\,du$}
This potential subtracts integrated resource prices from <weighted logarithmic utility>. Continuous nonnegative nondecreasing prices make it strictly concave on positive rates. If every route meets a resource with a nonzero price function, its superlevel sets are compact and its maximizer is unique. The rate adjustment $\dot x_r=\kappa_rx_r\partial_rU$ increases it strictly away from equilibrium.
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