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A derivation of the Aw-Rascle traffic models from Fokker-Planck type kinetic models
Author(s):
R.
Illner;
C.
Kirchner;
R.
Pinnau
Journal:
Quart. Appl. Math.
67
(2009),
39-45.
MSC (2000):
Primary 35Qxx, 82C31
Posted:
January 22, 2009
MathSciNet review:
2495070
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Abstract:
We show how the Aw-Rascle model, a hyperbolic system of PDEs modeling traffic flow, can be derived from a simplified Fokker-Planck type kinetic equation.
References:
-
- 1.
- A. Aw and M. Rascle.
Resurrection of ``second order'' models of traffic flow.
SIAM J. Appl. Math., Vol. 60(3), pp. 916-938, 2000. MR 1750085 (2001a:35111) - 2.
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The Mathematical Theory of Dilute Gases, Springer-Verlag, 1994. MR 1307620 (96g:82046) - 3.
- M. Herty, R. Illner, A. Klar, and V. Panferov.
Qualitative Properties of Solutions to Systems of Fokker-Planck equations for Multilane Traffic Flow.
Transport Theory and Statistical Physics, Vol. 35, pp. 31-54, 2006. MR 2284533 - 4.
- R. Illner, A. Klar and T. Materne.
On Vlasov-Fokker-Planck Type Kinetic Models for Multilane Traffic Flow.
Preprint, 2003. - 5.
- R. Illner, A. Klar and T. Materne.
Vlasov-Fokker-Planck Models for Multilane Traffic Flow.
Commun. Math. Sci., Vol. 1(1), pp. 1-12, 2003. MR 1979839 - 6.
- A. Klar and R. Wegener.
Kinetic Derivation of Macroscopic Anticipation Models for Vehicular Traffic.
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Moment Closure Hierarchies for Kinetic Theories.
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Additional Information:
R.
Illner
Affiliation:
Department of Mathematics and Statistics, University of Victoria, PO Box 3045 STN CSC, Victoria, B.C., Canada V8W 3P4
Email:
rillner@math.uvic.ca
C.
Kirchner
Affiliation:
Fachbereich Mathematik, TU Kaiserslautern, D-67653 Kaiserslautern, Germany
Email:
kirchner@mathematik.uni-kl.de
R.
Pinnau
Affiliation:
Fachbereich Mathematik, TU Kaiserslautern, D-67653 Kaiserslautern, Germany
Email:
pinnau@mathematik.uni-kl.de
PII:
S0033-569X-09-01075-7
Keywords:
Traffic flow,
kinetic equation,
Fokker--Planck,
Aw--Rascle model,
multilane traffic
Received by editor(s):
June 1, 2007
Posted:
January 22, 2009
Copyright of article:
Copyright
2009,
Brown University
The copyright for this article reverts to public domain after 28 years from publication.
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