Traveling wave profiles for a Follow-the-Leader model for traffic flow with rough road condition

Wen Shen; Wen Shen

doi:10.3934/nhm.2018020

Networks and Heterogeneous Media

2018, Volume 13, Issue 3: 449-478. doi: 10.3934/nhm.2018020

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Traveling wave profiles for a Follow-the-Leader model for traffic flow with rough road condition

Wen Shen ^,

Mathematics Department, Pennsylvania State University, University Park, PA 16802, USA

Received: 01 November 2017 Revised: 01 January 2018
Primary: 65M20, 35L02, 35L65; Secondary: 34B99, 35Q99

We study a Follow-the-Leader (FtL) ODE model for traffic flow with rough road condition, and analyze stationary traveling wave profiles where the solutions of the FtL model trace along, near the jump in the road condition. We derive a discontinuous delay differential equation (DDDE) for these profiles. For various cases, we obtain results on existence, uniqueness and local stability of the profiles. The results here offer an alternative approximation, possibly more realistic than the classical vanishing viscosity approach, to the conservation law with discontinuous flux for traffic flow.
- Traffic flow,
- rough coefficient,
- traveling waves,
- microscopic models,
- delay differential equation,
- local stability
Citation: Wen Shen. Traveling wave profiles for a Follow-the-Leader model for traffic flow with rough road condition[J]. Networks and Heterogeneous Media, 2018, 13(3): 449-478. doi: 10.3934/nhm.2018020

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Abstract

We study a Follow-the-Leader (FtL) ODE model for traffic flow with rough road condition, and analyze stationary traveling wave profiles where the solutions of the FtL model trace along, near the jump in the road condition. We derive a discontinuous delay differential equation (DDDE) for these profiles. For various cases, we obtain results on existence, uniqueness and local stability of the profiles. The results here offer an alternative approximation, possibly more realistic than the classical vanishing viscosity approach, to the conservation law with discontinuous flux for traffic flow.

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