Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2020; 57(4): 987-1004

Online first article January 9, 2020      Printed July 1, 2020

https://doi.org/10.4134/JKMS.j190488

Copyright © The Korean Mathematical Society.

Traffic flow models with nonlocal looking ahead-behind dynamics

Yongki Lee

Georgia Southern University

Abstract

Motivated by the traffic flow model with Arrhenius look-ahead relaxation dynamics introduced in \cite{SK06}, this paper proposes a traffic flow model with look ahead relaxation-behind intensification by inserting look behind intensification dynamics to the flux. Finite time shock formation conditions in the proposed model with various types of interaction potentials are identified. Several numerical experiments are performed in order to demonstrate the performance of the modified model. It is observed that, comparing to other well-known macroscopic traffic flow models, the model equipped with look ahead relaxation-behind intensification has both enhanced dispersive and smoothing effects

Keywords: Nonlocal conservation law, shock formation, traffic flow, global flux

MSC numbers: Primary 35L65; Secondary 35L67

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