Resource congestion price (${\mu }_j$)

A resource congestion price signals scarcity at a capacity-constrained link. Under multiplicative resource-price dynamics, its increase indicates excess demand and its decrease indicates spare capacity. A route pays the sum of these prices, its route congestion price. A zero resource congestion price at an optimum satisfies complementary slackness with possible spare capacity.

The total price seen by a route is the sum of resource congestion prices on its links. With weighted logarithmic utility $w_r\log x_r$, maximizing utility minus linear expenditure gives the demand $x_r=w_r/p_r$. This relation links user decisions to multiplicative resource-price dynamics.