Equilibrium routing under uncertainty

We provide a brief introduction to the basic models used to describe traffic on congested networks, both in urban transport and telecommunications. We discuss traffic equilibrium models, covering atomic and non-atomic routing games, with emphasis on situations where the travel times are subject to random fluctuations. We use convex optimization to present the models in a unified framework that stresses the common underlying structures. As a prototypical example of traffic equilibrium with elastic demands, we discuss some models for routing and congestion control in telecommunications. We also describe a class of stochastic dynamics that model the adaptive behavior of agents and which provides a plausible micro-foundation for the equilibrium. Finally we present some recent ideas on how risk-averse behavior might be incorporated in the equilibrium models.