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

Research output: Contribution to journalArticle

3 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)449-478
Number of pages30
JournalNetworks and Heterogeneous Media
Volume13
Issue number3
DOIs
StatePublished - Sep 1 2018

Fingerprint

Traffic Flow
Traveling Wave
Rough
Discontinuous Differential Equations
Discontinuous Flux
Vanishing Viscosity
Conservation
Differential equations
Local Stability
Viscosity
Fluxes
Delay Differential Equations
Conservation Laws
Jump
Existence and Uniqueness
Trace
Model
Alternatives
Approximation
Profile

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Engineering(all)
  • Computer Science Applications
  • Applied Mathematics

Cite this

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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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Traveling wave profiles for a Follow-the-Leader model for traffic flow with rough road condition. / Shen, Wen.

In: Networks and Heterogeneous Media, Vol. 13, No. 3, 01.09.2018, p. 449-478.

Research output: Contribution to journalArticle

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