Simulations suggest that navigation software may not be as efficient as expected for city traffic.

We suggest a theoretical framework to study the dynamics of an open city, with cars entering at a certain rate and leaving as they reach their destinations. In particular, we assess through simulations some unexpected consequences of the massive use of GPS (global positioning system) navigation systems in the overall dynamics. One of our main interest is to identify what type of measurements would be the most relevant for an experimental study of this system, specifically, the ones useful for city traffic administrators. To do so, we solve the microdynamics using a cellular automaton model considering three different navigation strategies based on the minimization of the individual paths (unweighted strategy) or travel times (weighted strategies). Although the system is inherently stochastic, we found in our simulations an equivalent saddle-node bifurcation for all strategies where the input rate acts as a bifurcation parameter. There is also evidence of additional bifurcations for travel time minimization based strategies. Although we found that weighted strategies are more efficient in terms of car motion, there is a destabilization phenomenon that makes, in an unexpected way, a variation of the unweighted strategy more optimal at certain densities from the fuel efficiency of the overall city traffic point of view. These results bring new insight into the intrinsic dynamics of cities and the perturbations that individual traffic routing can produce on the city as a whole.