 Marginal external cost toll

For a differentiable link delay $D_j(y)$, the toll $T_j(y)=y{D}_j^{\prime }(y)$ charges a user for the additional delay imposed on the other users. Its perceived link cost is the derivative of $y{D}_j(y)$. The resulting Beckmann potential equals total travel delay. If total delay is convex, its Wardrop equilibria minimize that delay globally. Strict increase of $D_j$ alone does not imply this convexity; optimal-flow calibrated congestion tolling avoids that extra requirement.