Una revisión de modelos de tráfico automotor usando autómatas celulares
DOI:
https://doi.org/10.37135/unach.ns.001.04.01Palabras clave:
Autómata Celular, flujo vehicular, modelo de NaSch, modelo microscópico, modelos de tráficoResumen
Los autómatas celulares son un modelo matemático utilizado para estudiar y representar sistemas dinámicos, adecuados para modelar sistemas naturales como la evolución de virus y bacterias, así como el flujo de gases, líquidos y del tráfico vehicular y peatonal. El primer modelo probabilístico no trivial fue presentado por Nagel y Schreckenberg y cada vez son más los investigadores que se suman a su aplicación en la vida diaria. En este artículo se plantea una revisión del comportamiento del flujo vehicular (FV) para vías de uno y varios carriles, considerando las modificaciones de los modelos ya existentes y los cambios en la forma de conducir con la finalidad de conocer el enfoque de los diversos investigadores sobre el estudio de tráfico vehicular. El estudio revela que el FV se adapta a las condiciones del tráfico del momento y que el modelo, por su propiedad, permite modificar reglas de interacción y considerar la infraestructura de la vía para el modelo de un carril mientras que los modelos con carriles múltiples son más complejos.
Descargas
Referencias
Benjamin, S., Johnson, N., & Hui, P. (1996). Cellular automata models of traffic flow along a highway containing a junction. Journal of Physics A: Mathematical and General, 29(12), 3119–3127. https://doi.org/10.1088/0305-4470/29/12/018
Biham, O., Middleton, A., & Levine, D. (1992). Self-organization and a dynamical transition in traffic-flow models. Physical Review A, 46(10), R6124–R6127. https://doi.org/10.1103/PhysRevA.46.R6124
Chandler, R., Herman, R., & Montroll, E. (1958). Traffic Dynamics: Studies in Car Following. Operations Research, 6(2), 165–184. https://doi.org/10.1287/opre.6.2.165
De camino, T. (2016). La matemática de las congestiones de tráfico. Recuperado de https://medium.com/@TomasDeCamino/la-matem%C3%A1tica-de-las-congestiones-de-tr%C3%A1fico-29681db8dbc0
Gazis, D. C., Herman, R., & Rothery, W. R. (1961). Nonlinear follow-the-leader models of traffic flow. Operations Research, 9(4), 545–567. https://doi.org/10.1287/opre.9.4.545
Greenshields, B. D., Bibbins, J. R., Channing, W. S., & Miller, H. H. (1935). A study of traffic capacity. In Proceedings of the 14th Annual Meeting of the Highway Research Board, (pp. 448–477). Washington D.C., USA: The National Academy of Science, Engineering, and Medicine.
Greenshields, B. D., Thompson, J. T., Dickinson, H. C., & Swinton, R. S. (1934). The photographic method of studying traffic behavior. In Proceedings of the 13th Annual Meeting of the Highway Research Board (pp. 382–399). Washington D.C., USA: The National Academy of Science, Engineering, and Medicine
Guzmán, H. A., Lárraga, M. E., Alvarez-Icaza, L., & Carvajal, J. (2018). A cellular automata model for traffic flow based on kinetics theory, vehicles capabilities and driver reactions. Physica A: Statistical Mechanics and Its Applications, 491, 528–548.
https://doi.org/10.1016/j.physa.2017.09.094
Hedlund, G. A. (1969). Endomorphisms and automorphisms of the shift dynamical system. Math. Systems Theory, 3(4), 320–375. https://doi.org/https://doi.org/10.1007/BF01691062
Jia, B., Jiang, R., Wu, Q., & Hu, M. (2005). Honk effect in the two-lane cellular automaton model for traffic flow. Physica A: Statistical Mechanics and Its Applications, 348, 544–552. https://doi.org/10.1016/j.physa.2004.09.034
Lárraga, M. E., & Alvarez-Icaza, L. (2010). A Cellular Automaton Model for Traffic Flow with Safe Driving Policies. Journal of Cellular Automata, 5(6), 421-429.
Li, X., Jia, B., Gao, Z., & Jiang, R. (2006). A realistic two-lane cellular automata traffic model considering aggressive lane-changing behavior of fast vehicle. Physica A: Statistical Mechanics and Its Applications, 367, 479–476. https://doi.org/10.1016/j.physa.2005.11.016
Maerivoet, S., & De Moor, B. (2005). Cellular automata models of road traffic. Physics Reports, 419(1), 1–64.
https://doi.org/10.1016/j.physrep.2005.08.005
Maglaras, L., Al-Bayatti, A., He, Y., Wagner, I., & Janicke, H. (2016). Social Internet of Vehicles for Smart Cities. Journal of Sensor and Actuator Networks, 5(1), 1-22. https://doi.org/10.3390/jsan5010003
Mallikarjuna, C., & Rao, K. R. (2011). Heterogeneous traffic flow modelling: a complete methodology. Transportmetrica, 7(5), 321–345. https://doi.org/10.1080/18128601003706078
Meng, J., Dai, S., Dong, L., & Zhang, J. (2007). Cellular automaton model for mixed traffic flow with motorcycles. Physica A: Statistical Mechanics and Its Applications, 380, 470–480. https://doi.org/10.1016/j.physa.2007.02.091
Nagel, K. (1994). Life times of simulated traffic jams. International Journal of Modern Physics C, 05(03), 567–580.
https://doi.org/10.1142/S012918319400074X
Nagel, K., & Schreckenberg, M. (1992). A cellular automaton model for freeway traffic. Journal de Physique I, 2(12), 2221–2229. https://doi.org/10.1051/jp1:1992277
Nagel, K., Wolf, D. E., Wagner, P., & Simon, P. (1998). Two-lane traffic rules for cellular automata: A systematic approach. Physical Review E, 58(2), 1425–1437.
https://doi.org/10.1103/PhysRevE.58.1425
Nassab, K., Schreckenberg, M., Ouaskit, S., & Boulmakoul, A. (2005). Impacts of different types of ramps on the traffic flow. Physica A: Statistical Mechanics and its Applications, 354(2–4), 601–611.
https://doi.org/10.1016/j.physa.2004.11.044
Pandey, G., Rao, K. R., & Mohan, D. (2015). A review of cellular automata model for heterogeneous traffic conditions. In M. Chraibi, M. Boltes, A. Schadschneider & A. Seyfried (Eds.), Traffic and Granular Flow'13 (pp. 471–478). https://doi.org/10.1007/978-3-319-10629-8_52
Rawat, K., Katiyar, V. K., & Gupta, P. (2012). Two-Lane Traffic Flow Simulation Model via Cellular Automaton. International Journal of Vehicular Technology, 2012, 1–6. https://doi.org/10.1155/2012/130398
Reis, L. G. (2008). Produção de monografias: da teoria à pratica o método educar pela pesquisa (MEP)(2nd ed.). Brasilia, Brasil: SENAC.
Rickert, M., Nagel, K., Schreckenberg, M., & Latour, A. (1996). Two lane traffic simulations using cellular automata. Physica A: Statistical Mechanics and Its Applications, 231(4), 534–550. https://doi.org/10.1016/0378-4371(95)00442-4
Romero, N. (2012). Dinámica Topológica y Autómata Celulares: conceptos y propiedades fundamentales. Germany: Editorial Académica Española.
Schadschneider, A. (1999). The Nagel-Schreckenberg model revisited. The European Physical Journal B, 10(3), 573–582.
https://doi.org/10.1007/s100510050888
Schadschneider, A. (2002). Traffic flow: a statistical physics point of view. Physica A: Statistical Mechanics and Its Applications, 313(1–2), 153–187.
https://doi.org/10.1016/S0378-371(02)01036-1
Schneider, B. (2018). Traffic's Mind-Boggling Economic Toll. Recuperado de la página web de Bloomberg CityLab:
https://www.citylab.com/transportation/2018/02/traffics-mind-boggling-economic-toll/552488/
Schrank, D., Turner, S., & Lomax, T. (1994). Trends in Urban Roadway Congestion – 1982 to 1991. Volume 1: Annual Report (Report No. FHWA/TX-94/1131-6). Recuperado de https://static.tti.tamu.edu/tti.tamu.edu/documents/1131-6-V1.pdf
Schreckenberg, M., Barlović, R., Knospe, W., & Klüpfel, H. (2002). Statistical Physics of Cellular Automata Models for Traffic Flow. K. H. Hoffmann, & M. Schreiber (Eds.). In Computational Statistical Physics (pp. 113–126). https://doi.org/10.1007/978-3-662-04804-7_7
Smartmotoris. (2019). What Cause Traffic Jams? The Physics Behind You Need To Know. Recuperado de
https://www.smartmotorist.com/traffic-jams
Tyagi, V., Darbha, S., & Rajagopal, K. R. (2009). A review of the mathematical models for traffic flow. International Journal of Advances in Engineering Sciences and Applied Mathematics, 1(1), 53–68. Recuperado de https://doi.org/10.1007/s12572-009-0005-8
Wagner, P., Nagel, K., & Wolf., D. E. (1997). Realistic multi-lane traffic rules for cellular automata. Physica A: Statistical Mechanics and its Applications, 234(3-4), 687–698.
https://doi.org/10.1016/S0378-4371(96)00308-1
Wolfram, S. (1983). Statistical mechanics of cellular automata. Reviews of Modern Physics, 55(3), 601–644. https://doi.org/10.1103/RevModPhys.55.601
Wolfram, S. (1984). Computation theory of cellular automata. Communications in Mathematical Physics, 96(1), 15–57.
https://doi.org/10.1007/BF01217347
Yang, L., Zheng, J., Cheng, Y., & Ran, B. (2019). An asymmetric cellular automata model for heterogeneous traffic flow on freeways with a climbing lane. Physica A: Statistical Mechanics and Its Applications, 535.
https://doi.org/10.1016/j.physa.2019.122277
Zhao, H. T., Liu, X.-R., Chen, X.-X., & Lu, J.-C. (2018). Cellular automata model for traffic flow at intersections in internet of vehicles. Physica A: Statistical Mechanics and Its Applications, 494, 40–51. https://doi.org/10.1016/J.PHYSA.2017.11.152
Zhu, H. B., Lei, L., & Dai, S. Q. (2009). Two-lane traffic simulations with a blockage induced by an accident car. Physica A: Statistical Mechanics and Its Applications, 388(14), 2903–2910. https://doi.org/10.1016/J.PHYSA.2009.01.040
Publicado
Versiones
- 2021-05-20 (5)
- 2021-05-20 (4)
- 2021-05-20 (3)
- 2021-05-20 (2)
- 2019-12-10 (1)
