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In this paper we consider a mean field approach to modeling the agents flowover a transportation network. In particular, beside a standard framework ofmean field games, with controlled dynamics by the agents and costsmass-distribution dependent, we also consider a path preferences dynamicsobtained as a generalization of the so-called noisy best response dynamics.Such a preferences dynamics says the agents choose their path having access toglobal information about the network congestion state and based on theobservation of the decision of the agents that have preceded. We prove theexistence of a mean field equilibrium obtained as a fixed point of a map over asuitable set of time-varying mass-distributions, defined edge by edge in thenetwork. We also address the case where the admissible set of controls issuitably bounded depending on the mass-distribution on the edge itself.

Origin-to-destination network flow with path preferences and velocity controls: a mean field game-like approach