  Stability of Wardrop equilibria is analyzed for dynamical transportation
networks in which the drivers' route choices are influenced by information at
multiple temporal and spatial scales. The considered model involves a continuum
of indistinguishable drivers commuting between a common origin/destination pair
in an acyclic transportation network. The drivers' route choices are affected
by their, relatively infrequent, perturbed best responses to global information
about the current network congestion levels, as well as their instantaneous
local observation of the immediate surroundings as they transit through the
network. A novel model is proposed for the drivers' route choice behavior,
exhibiting local consistency with their preference toward globally less
congested paths as well as myopic decisions in favor of locally less congested
paths. The simultaneous evolution of the traffic congestion on the network and
of the aggregate path preference is modeled by a system of coupled ordinary
differential equations. The main result shows that, if the frequency of updates
of path preferences is sufficiently small as compared to the frequency of the
traffic flow dynamics, then the state of the transportation network ultimately
approaches a neighborhood of the Wardrop equilibrium. The presented results may
be read as a further evidence in support of Wardrop's postulate of equilibrium,
showing robustness of it with respect to non-persistent perturbations. The
proposed analysis combines techniques from singular perturbation theory,
evolutionary game theory, and cooperative dynamical systems.
