  Advanced traffic navigation systems, which provide routing recommendations to
drivers based on real-time congestion information, are nowadays widely adopted
by roadway transportation users. Yet, the emerging effects on the traffic
dynamics originating from the widespread adoption of these tools have remained
largely unexplored until now. In this paper, we propose a dynamic model where
drivers imitate the path preferences of previous drivers, and we study the
properties of its equilibrium points. Our model is a dynamic generalization of
the classical traffic assignment framework, and extends it by accounting for
dynamics both in the path decision process and in the network's traffic flows.
We show that when travelers learn shortest paths by imitating other travelers,
the overall traffic system benefits from this mechanism and transfers the
maximum admissible amount of traffic demand. On the other hand, we demonstrate
that when the travel delay functions are not sufficiently steep or the rates at
which drivers imitate previous travelers are not adequately chosen, the
trajectories of the traffic system may fail to converge to an equilibrium
point, thus failing asymptotic stability. Illustrative numerical simulations
combined with empirical data from highway sensors illustrate our findings.
