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Zbl 1200.90044
Herty, Michael; Illner, Reinhard
Analytical and numerical investigations of refined macroscopic traffic flow models. (English)
[J] Kinet. Relat. Models 3, No. 2, 311-333 (2010). ISSN 1937-5093; ISSN 1937-5077/e

Summary: We continue research on generalized macroscopic models of conservation type as started in [{\it M. Herty} and {\it R. Illner}, Kinet. Relat. Models 1, No.~3, 437--452 (2008; Zbl 1165.90374) ($\star$)]. In the present paper we keep the characteristic (for traffic) non-locality removed in ($\star$) 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 2000:: *90B20 Highway traffic
35L65 Conservation laws

Keywords: traffic flow; Fokker-Planck models; mathematical modeling

Citations: Zbl 1165.90374

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