On the fundamental diagram of traffic flow

Details On the fundamental diagram of traffic flow On the fundamental diagram of traffic flow

2005-03-11

arxiv.org/abs/cond-mat/0503290v1

Physics

Condensed Matter

Statistical Mechanics

7 pages, 6 figures, submitted to Phys. Rev. E

Scientific paper

We present a new fluid-dynamical model of traffic flow. This model generalizes the model of Aw and Rascle [SIAM J. Appl. Math. 60 916-938] and Greenberg [SIAM J. Appl. Math 62 729-745] by prescribing a more general source term to the velocity equation. This source term can be physically motivated by experimental data, when taking into account relaxation and reaction time. In particular, the new model has a (linearly) unstable regime as observed in traffic dynamics. We develop a numerical code, which solves the corresponding system of balance laws. Applying our code to a wide variety of initial data, we find the observed inverse-$\lambda$ shape of the fundamental diagram of traffic flow.

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