 Primal congestion potential

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 ${\dot{x}}_r={\kappa }_r{x}_r{\partial }_{r}U$ increases it strictly away from equilibrium.