# American Institute of Mathematical Sciences

2010, 3(2): 311-333. doi: 10.3934/krm.2010.3.311

## Analytical and numerical investigations of refined macroscopic traffic flow models

 1 RWTH Aachen, Mathematik, Templergraben 55, D-52056 Aachen 2 University of Victoria, Department of Mathematics and Statistics, PO Box 3045 STN CSC, Victoria, B.C., Canada

Received  June 2009 Revised  September 2009 Published  May 2010

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.
Citation: Michael Herty, Reinhard Illner. Analytical and numerical investigations of refined macroscopic traffic flow models. Kinetic & Related Models, 2010, 3 (2) : 311-333. doi: 10.3934/krm.2010.3.311
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