  Optimizing passengers routes is crucial to design efficient transportation
networks. Recent results show that optimal transport provides an efficient
alternative to standard optimization methods. However, it is not yet clear if
this formalism has empirical validity on engineering networks. We address this
issue by considering different response functions -- quantities determining the
interaction between passengers -- in the dynamics implementing the optimal
transport formulation. Particularly, we couple passengers' fluxes by taking
their sum or the sum of their squares. The first choice naturally reflects
edges occupancy in transportation networks, however the second guarantees
convergence to an optimal configuration of flows. Both modeling choices are
applied to the Paris metro. We measure the extent of traffic bottlenecks and
infrastructure resilience to node removal, showing that the two settings are
equivalent in the congested transport regime, but different in the branched
one. In the latter, the two formulations differ on how fluxes are distributed,
with one function favoring routes consolidation, thus potentially being prone
to generate traffic overload. Additionally, we compare our method to Dijkstra's
algorithm to show its capacity to efficiently recover shortest-path-like
graphs. Finally, we observe that optimal transport networks lie in the Pareto
front drawn by the energy dissipated by passengers, and the cost to build the
infrastructure.
