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

Journal Article · · International Journal of Non-Linear Mechanics
 [1];  [2];  [3]
  1. Politecnico di Torino (Italy); OSTI
  2. Rutgers University, Camden, NJ (United States)
  3. Politecnico di Torino (Italy)
+ Show Author Affiliations
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, Journal Name: International Journal of Non-Linear Mechanics Journal Issue: C Vol. 137; ISSN 0020-7462
Publisher:
ElsevierCopyright Statement
Country of Publication:
United States
Language:
English

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Related Subjects

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