  We study a novel approach to information design in the standard traffic model
of network congestion games. It captures the natural condition that the demand
is unknown to the users of the network. A principal (e.g., a mobility service)
commits to a signaling strategy, observes the realized demand and sends a
(public) signal to agents (i.e., users of the network). Based on the induced
belief about the demand, the users then form an equilibrium. We consider the
algorithmic goal of the principal: Compute a signaling scheme that minimizes
the expected total cost of the induced equilibrium. We concentrate on
single-commodity networks and affine cost functions, for which we obtain the
following results. First, we devise a fully polynomial-time approximation
scheme (FPTAS) for the case that the demand can only take two values. It relies
on several structural properties of the cost of the induced equilibrium as a
function of the updated belief about the distribution of demands. We show that
this function is piecewise linear for any number of demands, and monotonic for
two demands. Second, we give a complete characterization of the graph
structures for which it is optimal to fully reveal the information about the
realized demand. This signaling scheme turns out to be optimal for all cost
functions and probability distributions over demands if and only if the graph
is series-parallel. Third, we propose an algorithm that computes the optimal
signaling scheme for any number of demands whose time complexity is polynomial
in the number of supports that occur in a Wardrop equilibrium for some demand.
Finally, we conduct a computational study that tests this algorithm on
real-world instances.
