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Analytical and numerical investigations of refined macroscopic traffic flow models. (English) Zbl 1200.90044
Summary: We continue research on generalized macroscopic models of conservation type as started in [M. Herty and R. Illner, Kinet. Relat. Models 1, No. 3, 437–452 (2008; Zbl 1165.90374) ($☆$)]. In the present 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.
##### MSC:
 90B20 Traffic problems 35L65 Conservation laws
##### Keywords:
traffic flow; Fokker-Planck models; mathematical modeling