On The Microscopic Modeling of Vehicular Traffic on General Networks

Rinaldo M. Colombo; Helge Holden; Francesca Marcellini

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arXiv · 2002.09512

On The Microscopic Modeling of Vehicular Traffic on General Networks

Rinaldo M. Colombo·Helge Holden·Francesca Marcellini

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Abstract

We introduce a formalism to deal with the microscopic modeling of vehicular traffic on a road network. Traffic on each road is uni-directional, and the dynamics of each vehicle is described by a Follow-the-Leader model. From a mathematical point of view, this amounts to define a system of ordinary differential equations on an arbitrary network. A general existence and uniqueness result is provided, while priorities at junctions are shown to hinder the stability of solutions. We investigate the occurrence of the Braess paradox in a time-dependent setting within this model. The emergence of Nash equilibria in a non-stationary situation results in the appearance of Braess type paradoxes, and this is supported by numerical simulations.

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Rinaldo M. Colombo, Helge Holden, Francesca Marcellini. 2020-02-21. On The Microscopic Modeling of Vehicular Traffic on General Networks. https://arxiv.org/abs/2002.09512

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