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Title: A statistical mechanics approach to macroscopic limits of car-following traffic dynamics

Journal Article · · International Journal of Non-Linear Mechanics
 [1]; ORCiD logo [2]; ORCiD logo [1]
  1. Politecnico di Torino (Italy)
  2. Rutgers University, Camden, NJ (United States)
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Herein we study the derivation of macroscopic traffic models from car-following vehicle dynamics by means of hydrodynamic limits of an Enskog-type kinetic description. We consider the superposition of Follow-the-Leader (FTL) interactions and relaxation towards a traffic-dependent Optimal Velocity (OV) and we show that the resulting macroscopic models depend on the relative frequency between these two microscopic processes. If FTL interactions dominate then one gets an inhomogeneous Aw–Rascle–Zhang model, whose (pseudo) pressure and stability of the uniform flow are precisely defined by some features of the microscopic FTL and OV dynamics. Conversely, if the rate of OV relaxation is comparable to that of FTL interactions then one gets a Lighthill–Whitham–Richards model ruled only by the OV function. We further confirm these findings by means of numerical simulations of the particle system and the macroscopic models. Unlike other formally analogous results, our approach builds the macroscopic models as physical limits of particle dynamics rather than assessing the convergence of microscopic to macroscopic solutions under suitable numerical discretisations.

Research Organization:
Univ. of California, Oakland, CA (United States)
Sponsoring Organization:
USDOE Office of Energy Efficiency and Renewable Energy (EERE), Office of Sustainable Transportation. Vehicle Technologies Office (VTO)
Grant/Contract Number:
EE0008872
OSTI ID:
1977211
Journal Information:
International Journal of Non-Linear Mechanics, Vol. 137, Issue C; ISSN 0020-7462
Publisher:
ElsevierCopyright Statement
Country of Publication:
United States
Language:
English

References (29)

Micro-Macro Limit of a Nonlocal Generalized Aw-Rascle Type Model journal January 2020
Dynamical model of traffic congestion and numerical simulation journal February 1995
Self-sustained nonlinear waves in traffic flow journal May 2009
Cluster effect in initially homogeneous traffic flow journal October 1993
Derivation of Continuum Traffic Flow Models from Microscopic Follow-the-Leader Models journal January 2002
Enskog-like kinetic models for vehicular traffic journal April 1997
Extensions and Amplifications of a Traffic Model of Aw and Rascle journal January 2002
A derivation of the Aw–Rascle traffic models from Fokker–Planck type kinetic models journal January 2009
A Boltzmann-Like Approach for Traffic Flow journal December 1960
Many particle approximation of the Aw-Rascle-Zhang second order model for vehicular traffic journal January 2017
On the micro-to-macro limit for first-order traffic flow models on networks journal August 2016
The Aw–Rascle Traffic Model: Enskog-Type Kinetic Derivation and Generalisations journal November 2019
Rigorous Derivation of Nonlinear Scalar Conservation Laws from Follow-the-Leader Type Models via Many Particle Limit journal January 2015
Fluid dynamic description of flocking via the Povzner–Boltzmann equation journal January 2011
Direct Simulation and the Boltzmann Equation journal January 1970
Some comments on wave propagation and shock wave structure with application to magnetohydrodynamics journal February 1959
On a simulation scheme for the Boltzmann equation journal January 1986
Kinetic Derivation of Macroscopic Anticipation Models for Vehicular Traffic journal January 2000
Nonlinear Follow-the-Leader Models of Traffic Flow journal August 1961
Resurrection of "Second Order" Models of Traffic Flow journal January 2000
Constructing set-valued fundamental diagrams from Jamiton solutions in second order traffic models journal January 2013
Direct Simulation Scheme Derived from the Boltzmann Equation. I. Monocomponent Gases journal November 1980
Traffic Dynamics: Studies in Car Following journal April 1958
An improved macroscopic model of traffic flow: Derivation and links with the Lighthill-Whitham model journal March 2002
On the Micro-Macro limit in traffic flow journal January 2014
Enskog-like discrete velocity models for vehicular traffic flow journal January 2007
A traffic flow model with non-smooth metric interaction: Well-posedness and micro-macro limit journal January 2017
A non-equilibrium traffic model devoid of gas-like behavior journal March 2002
Shock Waves on the Highway journal February 1956

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Related Subjects

97 MATHEMATICS AND COMPUTING
Mechanics
Non-local particle models
Follow-the-Leader
Optimal Velocity
Relative frequency
Inhomogeneous Aw-Rascle-Zhang model
Lighthill-Whitham-Richards model
Stability of the uniform flow