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.
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Acknowledgements
Yu.G. acknowledges a Guest Professorship funded by Civilingeniør Frederik Christiansens Almennyttige Fond and partial financial support from the National Academy of Sciences of Ukraine. He thanks the Department of Physics, Technical University of Denmark for its hospitality. J.G. C. received support from the Region of Normandy through the program Xterm.
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Gaididei, Y.B., Caputo, JG., Christiansen, P.L., Rasmussen, J.J., Sørensen, M.P. (2017). A General Microscopic Traffic Model Yielding Dissipative Shocks. In: Quintela, P., et al. Progress in Industrial Mathematics at ECMI 2016. ECMI 2016. Mathematics in Industry(), vol 26. Springer, Cham. https://doi.org/10.1007/978-3-319-63082-3_59
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DOI: https://doi.org/10.1007/978-3-319-63082-3_59
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