PMID: 11909164Mar 23, 2002Paper

Towards a macroscopic modeling of the complexity in traffic flow

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Stephan Rosswog, Peter Wagner

Abstract

Based on the assumption of a safe velocity U(e)(rho) depending on the vehicle density rho, a macroscopic model for traffic flow is presented that extends the model of the Kühne-Kerner-Konhäuser by an interaction term containing the second derivative of U(e)(rho). We explore two qualitatively different forms of U(e): a conventional Fermi-type function and, motivated by recent experimental findings, a function that exhibits a plateau at intermediate densities, i.e., in this density regime the exact distance to the car ahead is only of minor importance. To solve the fluid-like equations a Lagrangian particle scheme is developed. The suggested model shows a much richer dynamical behavior than the usual fluid-like models. A large variety of encountered effects is known from traffic observations, many of which are usually assigned to the elusive state of "synchronized flow." Furthermore, the model displays alternating regimes of stability and instability at intermediate densities. It can explain data scatter in the fundamental diagram and complicated jam patterns. Within this model, a consistent interpretation of the emergence of very different traffic phenomena is offered: they are determined by the velocity relaxation time, i.e., t...Continue Reading

References

Oct 1, 1993·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·B S Kerner, P Konhäuser
Nov 23, 2000·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·M TreiberD Helbing

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Citations

Oct 10, 2006·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Peng Zhang, S C Wong
Sep 21, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Ihor LubashevskySergey Kalenkov

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