Analytical and numerical investigations of refined macroscopic
traffic flow models
Michael Herty - RWTH Aachen, Mathematik, Templergraben 55, D-52056 Aachen, Germany (email)
Abstract: We continue research on generalized macroscopic models of conservation type as started in . In this paper we keep the characteristic (for traffic) non-locality removed in  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.
Received: June 2009; Revised: September 2009; Available Online: May 2010.
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