A Model for the Formation and Evolution of Traffic Jams

In this paper, we establish and analyze a traffic flow model which describes the formation and dynamics of traffic jams. It consists of a pressureless gas dynamics system under a maximal constraint on the density and is derived through a singular limit of the Aw-Rascle model. From this analysis, we...

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Bibliographic Details
Published in:Archive for rational mechanics and analysis 2008-02, Vol.187 (2), p.185-220
Main Authors: Berthelin, F., Degond, P., Delitala, M., Rascle, M.
Format: Article
Language:English
Subjects:
Applied sciences
Classical Mechanics
Complex Systems
Exact sciences and technology
Fluid- and Aerodynamics
Ground, air and sea transportation, marine construction
Mathematical and Computational Physics
Physics
Physics and Astronomy
Physics of gases
Physics of gases, plasmas and electric discharges
Road transportation and traffic
Studies
Theoretical
Traffic flow
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Summary:In this paper, we establish and analyze a traffic flow model which describes the formation and dynamics of traffic jams. It consists of a pressureless gas dynamics system under a maximal constraint on the density and is derived through a singular limit of the Aw-Rascle model. From this analysis, we deduce the particular dynamical behavior of clusters (or traffic jams), defined as intervals where the density limit is reached. An existence result for a generic class of initial data is proved by means of an approximation of the solution by a sequence of clusters. Finally, numerical simulations are produced.
ISSN:0003-9527
1432-0673
DOI:10.1007/s00205-007-0061-9