Anisotropic Continuum Model for Urban Traffic: An Evolutionary Formulation
DOI:
https://doi.org/10.70567/mc.v41i16.82Keywords:
Urban traffic, Congestion, Evolutionary continuum model, Finite elementsAbstract
This paper presents a continuous model to determine the distribution of vehicles in an urban vehicular network under congestion conditions. The formulation leads to an evolutionary system of partial differential equations that can be conveniently solved using the finite element method. The characteristics of the street network are encoded in system parameters similar to the conductivities in a diffusion equation. The asymptotic solution of such a system (for sufficiently high times) converges to the vehicular flows and travel times corresponding to Wardrop's equilibrium. The problem formulation is presented, and the efficiency of the model is studied through a comparison of results with those determined by the traditional detailed discrete approach.
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