On The Microscopic Modeling of Vehicular Traffic on General Networks
Physics and Society
2020-02-25 v1 Analysis of PDEs
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.
Keywords
Cite
@article{arxiv.2002.09512,
title = {On The Microscopic Modeling of Vehicular Traffic on General Networks},
author = {Rinaldo M. Colombo and Helge Holden and Francesca Marcellini},
journal= {arXiv preprint arXiv:2002.09512},
year = {2020}
}
Comments
15 pages