Theoretical approach to 2-dimensional traffic flow models



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Molera, Juan M. and Martínez, Froilán C. and Cuesta, José A. and Brito, Ricardo (1995) Theoretical approach to 2-dimensional traffic flow models. Physical Review E, 51 (1). pp. 175-187. ISSN 1063-651X

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In this paper we present a theoretical analysis of a recently proposed two-dimensional cellular automata model for traffic flow in cities with the ingredient of a turning capability. Numerical simulations of this model show that there is a transition between a freely moving phase with high velocity to a jammed state with low velocity. We study the dynamics of such a model, starting with the microscopic evolution equation, which will serve as a basis for further analysis. It is shown that a kinetic approach, based on the Boltzmann assumption, is able to provide a reasonably good
description of the jamming transition. We further introduce a space-time continuous phenomenological model, leading to two partial differential equations whose preliminary results agree rather well with the numerical simulations.

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©1995 The American Physical Society. We are indebted to Professor J. B. Keller for a careful reading of the manuscript and valuable suggestions. We also want to thank H. Bussemaker for his interesting comments on the Boltzmann approximation, J. L. Velázquez, M. A. Herrero, and A. Carpio for helpful discussions concerning the continuous model, and A. Sánchez for discussions and collaboration in the early stages of this work. Finally, we acknowledge financial support from the Dirección General de Investigación Científica y Técnica (Spain) through the Projects No. PB92-0248 (F.C.M. and J.M.M.) and No. PB91-0378 (J.A.C. and R.B.).

Uncontrolled Keywords:Lattice-gas automata; Jamming transition; Hydrodynamics
Subjects:Sciences > Physics > Thermodynamics
ID Code:22077
Deposited On:04 Jul 2013 10:42
Last Modified:24 Jul 2018 11:52

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