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Erschienen in:
2017 | OriginalPaper | Buchkapitel
A General Microscopic Traffic Model Yielding Dissipative Shocks
verfasst von : Yuri Borissovich Gaididei, Jean-Guy Caputo, Peter Leth Christiansen, Jens Juul Rasmussen, Mads Peter Sørensen
Erschienen in: Progress in Industrial Mathematics at ECMI 2016
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Abstract
We consider a general microscopic traffic model with a delay. An algebraic traffic function reduces the equation to the Aw-Rascle microscopic model while a sigmoid function gives the standard “follow the leader”. For zero delay we prove that the homogeneous solution is globally stable. For a positive delay, it becomes unstable and develops dispersive and dissipative shocks. These are followed by a finite time singularity for the algebraic traffic function and by kinks for the sigmoid function.