Boltzmann-type description with cutoff of Follow-the-Leader traffic models

Andrea Tosin; Mattia Zanella

doi:10.1007/978-3-030-67104-4_8

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arXiv · 1912.07417

Boltzmann-type description with cutoff of Follow-the-Leader traffic models

Andrea Tosin·Mattia Zanella

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Abstract

In this paper we consider a Boltzmann-type kinetic description of Follow-the-Leader traffic dynamics and we study the resulting asymptotic distributions, namely the counterpart of the Maxwellian distribution of the classical kinetic theory. In the Boltzmann-type equation we include a non-constant collision kernel, in the form of a cutoff, in order to exclude from the statistical model possibly unphysical interactions. In spite of the increased analytical difficulty caused by this further non-linearity, we show that a careful application of the quasi-invariant limit (an asymptotic procedure reminiscent of the grazing collision limit) successfully leads to a Fokker-Planck approximation of the original Boltzmann-type equation, whence stationary distributions can be explicitly computed. Our analytical results justify, from a genuinely model-based point of view, some empirical results found in the literature by interpolation of experimental data.

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Andrea Tosin, Mattia Zanella. 2020-04-14. Boltzmann-type description with cutoff of Follow-the-Leader traffic models. https://doi.org/10.1007/978-3-030-67104-4_8

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