  We study optimal information provision in transportation networks when users
are strategic and the network state is uncertain. An omniscient planner
observes the network state and discloses information to the users with the goal
of minimizing the expected travel time at the user equilibrium. Public signal
policies, including full-information disclosure, are known to be inefficient in
achieving optimality. For this reason, we focus on private signals and restrict
without loss of generality the analysis to signals that coincide with path
recommendations that satisfy obedience constraints, namely users have no
incentive in deviating from the received recommendation according to their
posterior belief. We first formulate the general problem and analyze its
properties for arbitrary network topologies and delay functions. Then, we
consider the case of two parallel links with affine delay functions, and
provide sufficient conditions under which optimality can be achieved by
information design. Interestingly, we observe that the system benefits from
uncertainty, namely it is easier for the planner to achieve optimality when the
variance of the uncertain parameters is large. We then provide an example where
optimality can be achieved even if the sufficient conditions for optimality are
not met.
