  In this paper, we address the problem of modeling the traffic flow of a
heritage city whose streets are represented by a network. We consider a mean
field approach where the standard forward backward system of equations is also
intertwined with a path preferences dynamics. The path preferences are
influenced by the congestion status on the whole network as well as the
possible hassle of being forced to run during the tour. We prove the existence
of a mean field equilibrium as a fixed point, over a suitable set of
time-varying distributions, of a map obtained as a limit of a sequence of
approximating functions. Then, a bi-level optimization problem is formulated
for an external controller who aims to induce a specific mean field
equilibrium.
