Derivation of second order traffic flow models with time delays

Michael Burger; Simone Göttlich; Thomas Jung; Michael Burger; Simone Göttlich; Thomas Jung

doi:10.3934/nhm.2019011

Networks and Heterogeneous Media

2019, Volume 14, Issue 2: 265-288. doi: 10.3934/nhm.2019011

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Derivation of second order traffic flow models with time delays

1.
Fraunhofer Institute ITWM, 67663 Kaiserslautern, Germany
2.
University of Mannheim, Department of Mathematics, 68131 Mannheim, Germany

Received: 01 December 2017 Revised: 01 December 2018
Primary: 35L51, 90B20; Secondary: 65M06

Starting from microscopic follow-the-leader models, we develop hyperbolic delay partial differential equations to govern the density and velocity of vehicular traffic. The proposed models can be seen as an extension of the classical Aw-Rascle-Zhang model, where the reaction time of drivers appears as an additional term in the velocity equation. We propose numerical methods based on first principles and present a numerical study, where we focus on the impact of time delays in comparison to undelayed models.
- Traffic flow models,
- hyperbolic delay partial differential equation,
- numerical simulations,
- microscopic to macroscopic,
- data fitting
Citation: Michael Burger, Simone Göttlich, Thomas Jung. Derivation of second order traffic flow models with time delays[J]. Networks and Heterogeneous Media, 2019, 14(2): 265-288. doi: 10.3934/nhm.2019011

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Abstract

Starting from microscopic follow-the-leader models, we develop hyperbolic delay partial differential equations to govern the density and velocity of vehicular traffic. The proposed models can be seen as an extension of the classical Aw-Rascle-Zhang model, where the reaction time of drivers appears as an additional term in the velocity equation. We propose numerical methods based on first principles and present a numerical study, where we focus on the impact of time delays in comparison to undelayed models.

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