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Kinetic and Related Models (KRM)
 

Analytical and numerical investigations of refined macroscopic traffic flow models

Pages: 311 - 333, Volume 3, Issue 2, June 2010      doi:10.3934/krm.2010.3.311

 
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Michael Herty - RWTH Aachen, Mathematik, Templergraben 55, D-52056 Aachen, Germany (email)
Reinhard Illner - University of Victoria, Department of Mathematics and Statistics, PO Box 3045 STN CSC, Victoria, B.C., Canada (email)

Abstract: We continue research on generalized macroscopic models of conservation type as started in [15]. In this paper we keep the characteristic (for traffic) non-locality removed in [15] by Taylor expansion and discuss the merits and problems of such an expansion. We observe that the models satisfy maximum principles and conclude that "triggers'' are needed in order to cause traffic jams (braking waves) in traffic guided by such models. Several such triggers are introduced and discussed. The models are refined further in order to properly address non-monotonic (in speed) traffic regimes, and the inclusion of an individual reaction time is discussed in the context of a braking wave. A number of numerical experiments are conducted to exhibit our findings.

Keywords:  Traffic Flow, Fokker-Planck Models, Mathematical Modeling.
Mathematics Subject Classification:  Primary: 90B20; Secondary: 35L65.

Received: June 2009;      Revised: September 2009;      Available Online: May 2010.