Theoretical approach to 2-dimensional traffic flow models
| dc.contributor.author | Molera, Juan M. | |
| dc.contributor.author | Martínez, Froilán C. | |
| dc.contributor.author | Cuesta, José A. | |
| dc.contributor.author | Brito López, Ricardo | |
| dc.date.accessioned | 2023-06-20T18:46:53Z | |
| dc.date.available | 2023-06-20T18:46:53Z | |
| dc.date.issued | 1995-01 | |
| dc.description | ©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.). | |
| dc.description.abstract | 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. | |
| dc.description.department | Depto. de Estructura de la Materia, Física Térmica y Electrónica | |
| dc.description.faculty | Fac. de Ciencias Físicas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | Dirección General de Investigación Científica y Técnica (Spain) | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/22077 | |
| dc.identifier.doi | 10.1103/PhysRevE.51.175 | |
| dc.identifier.issn | 1063-651X | |
| dc.identifier.officialurl | http://dx.doi.org/10.1103/PhysRevE.51.175 | |
| dc.identifier.relatedurl | http://pre.aps.org/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/58597 | |
| dc.issue.number | 1 | |
| dc.journal.title | Physical Review E | |
| dc.language.iso | eng | |
| dc.page.final | 187 | |
| dc.page.initial | 175 | |
| dc.relation.projectID | PB92-0248 | |
| dc.relation.projectID | PB91-0378 | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 536 | |
| dc.subject.keyword | Lattice-gas automata | |
| dc.subject.keyword | Jamming transition | |
| dc.subject.keyword | Hydrodynamics | |
| dc.subject.ucm | Termodinámica | |
| dc.subject.unesco | 2213 Termodinámica | |
| dc.title | Theoretical approach to 2-dimensional traffic flow models | |
| dc.type | journal article | |
| dc.volume.number | 51 | |
| dcterms.references | [1] D. L. Gerlough and M. J. Huber, Traffic Flour Theory (NRC, Washington, DC, 1975); Y. Sheffi, Urban Transportation Networks: Equilibrium Analysis with Mathematical Programming Methods (Prentice-Hall, Englewood Cliffs, NJ, 1985); Transportation and Traffic Theory, edited by N. H. Gartner and N. H. M. Wilson (Elsevier, New York, 1987); W. Leutzbach, Introduction to the Theory of Traffic Flow (Springer, Berlin, 1988). [2] M. J. Lighthill and G. B. Whitham, Proc. R. Soc. London Ser. A 229, 317 (1955); R. Haberman, Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow (Prentice-Hall, Englewood Cliffs, NJ, 1977); R. Herman and I. Prigogine, Science 204, 148 (1979); I. Prigogine, Kinetic Theory of Vehicular Traffic (Elsevier, New York, 1971); B. S. Kerner and P. Konhauser, Phys. Rev. E 48, R2335 (1993). [3] R. Kühne, in Highway Capacity and Level of Service, edited by U. Brannolte (Balkema, Rotterdam, 1991); K. Nagel and M. Schreckenberg, J. Phys. I (France) 2, 2221 (1992); K. Nagel and H. J. Herrmann, Physica A 199/192, 254 (1993); A. Schadschneider and M. Schreckenberg, J. Phys. A 26, L679 (1993). [4] K. Nagel (private communication). [5] O. Biham, A. A. Middleton, and D. Levine, Phys. Rev. A 46, R6124 (1992). [6] J. A. Cuesta, F. C. Martínez, J. M. Molera, and A. Sánchez, Phys. Rev. E 48, R4175 (1993). [7] T. Nagatani, Physica A 198, 108 (1993); J. Phys. A 26, L1015 (1993). [8] H. J. Bussemaker and M. H. Ernst, J. Stat. Phys. 68, 432 (1992). [9] T. Nagatani, Phys. Rev. E 48, 3290 (1993). [10] In principle, by virtue of the traffic lights, which introduce a time inhomogeneity, there might be two diferent steady states: one for even and one for odd time steps. In that case, Eq. (5) would be the average of the mean velocity in those two steady states. [11] In Ref. [6] this contradiction led us to suggest that the transition in Ref. [5] might fall to n = 0 in an infinite system. With the new analysis this claim can no longer be made and so it remains an open question. [12] F. C. Martínez, J. A. Cuesta, J. M. Molera, and R. Brito, Universidad Carlos III Report No. MA/UC3M/09/94, 1994 (unpublished). [13] P. Resibois and M. de Leener, Classical Kinetic Theory of Fluids (John Wiley & Sons, New York, 1977). [14] R. Balescu, Equilibrium and Non-equilibrium Statistical Thermodynamics (John Wiley 4 Sons, New York, 1975). [15] S. P. Das, H. J. Bussemaker, and M. H. Ernst, Phys. Rev. E 48, 245 (1993). [16] U. Frisch, D. d'Humières, B. Hasslacher, P. Lallemand, Y. Pomeau, and J. P. Rivet, Complex Syst. 1, 649 (1987). [17] M. H. Ernst and H. J. Bussemaker, in Pattern For motion and Lattice Gas Automata (Proceedings of the NATO Workshop, Waterloo, Canada, 1993), edited by A. Lawniczak and R. Kapral (American Mathematical Society, Providence, in press). [18] P. G. Grosfils, J. P. Boon, R. Brito, and M. H. Ernst, Phys. Rev. E 48, 2655 (1993). [19] M. Gerits, M. H. Ernst, and D. Frenkel, Phys. Rev. E 48, 988 (1993). [20] H. J. Bussemaker and M. H. Ernst, Physica A 184, 147 (1993). [21] M. H. Protter and H. F. Weinberger, Maximum Principles in Differential Equations (Springer-Verlag, New York, 1984). [22] V. S. Vladimirov, Equations of Mathematical Physics (Marcel Dekker, New York, 1971). | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | b5d83e4b-6cf5-4cfc-9a1e-efbf55f71f87 | |
| relation.isAuthorOfPublication.latestForDiscovery | b5d83e4b-6cf5-4cfc-9a1e-efbf55f71f87 |
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