Multivalued fundamental diagrams of traffic flow in the kinetic Fokker-Planck limit

Abstract

Starting from interaction rules based on two levels of stochasticity we study the influence of the microscopic dynamics on the macroscopic properties of vehicular flow. In particular, we study the qualitative structure of the resulting flux-density and speed-density diagrams for different choices of the desired speeds. We are able to recover multivalued diagrams as a result of the existence of a one-parameter family of stationary distributions, whose expression is analytically found by means of a Fokker-Planck approximation of the initial Boltzmann-type model.

25 pages, 8 figures

References in corpus (1)

• A fully-discrete-state kinetic theory approach to traffic flow on road networks

Cited by in corpus (10)

• Opinion modeling on social media and marketing aspects
• Generalized collision-free velocity model for pedestrian dynamics
• Kinetic-controlled hydrodynamics for traffic models with driver-assist vehicles
• Model-based assessment of the impact of driver-assist vehicles using kinetic theory
• The Aw-Rascle traffic model: Enskog-type kinetic derivation and generalisations
• Hybrid stochastic kinetic description of two-dimensional traffic dynamics
• Reconstruction of traffic speed distributions from kinetic models with uncertainties
• An interface-free multi-scale multi-order model for traffic flow
• Macroscopic and multi-scale models for multi-class vehicular dynamics with uneven space occupancy: a case study
• Monte Carlo stochastic Galerkin methods for non-Maxwellian kinetic models of multiagent systems with uncertainties