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

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.

18 pages, 7 figures

References in corpus (5)

• Kinetic-controlled hydrodynamics for traffic models with driver-assist vehicles
• Model-based assessment of the impact of driver-assist vehicles using kinetic theory
• Uncertainty damping in kinetic traffic models by driver-assist controls
• Moment analysis of highway-traffic clearance distribution
• Non-Maxwellian kinetic equations modeling the evolution of wealth distribution

Cited by in corpus (3)

• Model-based assessment of the impact of driver-assist vehicles using kinetic theory
• Multiscale control of generic second order traffic models by driver-assist vehicles
• Macroscopic limits of non-local kinetic descriptions of vehicular traffic