 Boundary exclusion for elastic Wardrop demand

For nonnegative strictly increasing link delays and nonempty routes, let $M=B(0)$ and $L={\lim }_{\lambda \to \infty }B(\lambda )$. The inverse demand tends to infinity as flow decreases to $L$, so increasing flow slightly there gains more utility than the bounded link-cost increment. At $M$ the inverse demand is zero, whereas a used route has positive delay, so reducing flow improves the objective. A minimizer consequently has $L<f<M$ and satisfies the ordinary interior Wardrop equilibrium conditions. Lower-semicontinuous endpoint extensions permit minimization on the compact demand interval even when utility diverges at $L$.