Path functional theory for optimal transport in steady state urban traffic networks

Path-choice problems in vehicular traffic in urban environments are dominated by an interplay of local decision-making and global optimization. With local routing uncertainties being taken account of by the introduction of an (repulsive) interaction of paths, a variational principle for the formation of the paths can be formulated. Theoretically, the shape of the resulting description bears strong resemblance to the density functional theory (DFT) introduced in 1964 for Coulomb systems. Some examples, together with thermodynamical implications, are discussed within the framework of this paper.