An anisotropic diffusion model for the study of the urban traffic

作者：Cortinez V H^*; Dominguez P N

来源：Revista Internacional de Metodos Numericos Para Calculo y Diseno en Ingenieria, 2013, 29(1): 1-11.

DOI：10.1016/j.rimni.2011.10.005

• Urban traffic
• Anisotropic diffusion
• Continuum traffic model

In order to design or redesign urban transportation networks, the employment of mathematical models is very useful for predicting the effects of possible modifications of implementing. Such models allow the determination of vehicular flows and travel times for every link of the network from the knowledge of its inherent features and the corresponding traffic demand. They are based on a phenomenological law of the social collective behavior of the drivers called Wardrop principle. It is an optimization problem, in general, very demanding from the computational point of view.
In order to accelerate the computation process, in this paper, a continuum model for the urban traffic is proposed. The fundamental assumption behind this theory is that the variation of network properties is small in close regions when compared with the full system. Accordingly, it is possible to use continuous functions for representing travel times or vehicular flows. Essentially, the problem is formulated as a system of non-linear anisotropic diffusion (differential) equations that can be conveniently solved by means of the finite element method. The efficiency of the proposed model is studied by means of a comparison with results obtained with the classical optimization approach. As shown, the results are similar although the computation times are significantly reduced.

• 出版日期2013