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equilibrium and learning in traffic network games

Congestion is a common characteristic in modern telecommunication networks  as well as in transportation systems of large urban areas. In this talk we  review  some recent developments in modeling traffic equilibrium in congested networks. Starting from the classical models of Wardrop Equilibrium and Stochastic  User Equilibrium, we will present in more detail the notion of Markovian Traffic Equilibrium as well as numerical methods for computing it. We will show how  all these equilibrium models admit a unified reformulation in terms of a strictly  convex mathematical program. From these static equilibrium notions we move  on to present a recent attempt to model the dynamic behavior of travelers by  using a stochastic adaptive-learning process, and describe its asymptotic  convergence  towards equilibrium.