0004. Multi-class model: PCE, extra costs, allowed links

Decision. A class has its own demand, a PCE, an optional per-link extra cost and an optional allowed-links mask. Delays depend on the PCE-weighted total volume. Only gradient projection supports classes.

Why this shape. It covers the usual needs (cars and trucks, tolls with different values of time, truck bans) with data the user already has, and without per-class delay functions. Extra costs are in time units so the core needs no value-of-time model.

Implementation. Disallowed links get infinite cost in that class's cost array, which the shortest-path search treats as unusable. The single-class functions are wrappers over the multi-class core, so the existing single-class tests are regression tests for it.

Asymmetry. With different PCEs, \(\partial g_k / \partial x_{k'} \ne \partial g_{k'} / \partial x_k\), so there is no objective to minimise. Gradient projection still works: shifting class-\(k\) flow changes volume by \(\mathrm{pce}_k\) times the shift, and the Newton step scales its slope accordingly. Convergence is judged by the relative gap, and Frank-Wolfe (which needs an objective for its line search) is not offered.

Validation. Identical classes reproduce the published single-class solution; tolls, bans and PCE match closed forms.