Communications - Scientific Letters of the University of Zilina 2021, 23(2):A80-A93 | DOI: 10.26552/com.C.2021.2.A80-A93

The Viscosity Effect on Velocity of a Macroscopic Vehicular Traffic Model

Erick Javier Lopez-Sanchez ORCID...1, Norma Yanet Sanchez-Torres ORCID...2, Patricia Eugenia Olivera Martinez ORCID...3
1 Faculty of Philosophy and Letters, National Autonomous University of Mexico, Coyoacan, Mexico
2 Faculty of Sciences, National Autonomous University of Mexico, Coyoacan, Mexico
3 Critical Urban Studies Seminar, Geography Department, Faculty of Philosophy and Letters, National Autonomous University of Mexico, Coyoacan, Mexico

Traffic in Mexico City poses a serious problem of vehicle saturation that causes a decrease in speed and increased transport time in the streets that suffer mobility collapses. A macroscopic model of vehicular traffic is used to show the effect of viscosity on the vehicular variables (speed and vehicle density), applied to two avenues in Mexico City, is studied. The input parameters were calculated following the Greenberg model. As the original model presents numerical divergences, the two assumptions corresponding to conservation of the vehicle's mass and the viscous term are modified. The results suggest that the viscosity depends on time and that it can be adapted to recommend modifications in urban mobility parameters, or even to implement the public planning policies in construction of infrastructure for urban transport, to make vehicle flow more efficient.

Keywords: Greenberg traffic model; viscosity; vehicular density; vehicular velocity; numerical simulations

Received: May 15, 2020; Accepted: August 11, 2020; Prepublished online: December 18, 2020; Published: April 1, 2021  Show citation

ACS AIP APA ASA Harvard Chicago Chicago Notes IEEE ISO690 MLA NLM Turabian Vancouver
Lopez-Sanchez, E.J., Yanet Sanchez-Torres, N., & Martinez, P.E.O. (2021). The Viscosity Effect on Velocity of a Macroscopic Vehicular Traffic Model. Communications - Scientific Letters of the University of Zilina, 23(2), A80-93. doi: 10.26552/com.C.2021.2.A80-A93
Share...
Download citation
  • BibTeX (.bib)
  • Bookends (.ris)
  • EasyBib (.ris)
  • EndNote (.enw)
  • EndNote 8 (.xml)
  • ISI WoS (.isi)
  • Medlars (.medlars)
  • Mendeley (.ris)
  • MODS (.xml)
  • Papers (.ris)
  • RefWorks (.txt)
  • RefManager (.ris)
  • RIS (.ris)
  • MS Word (.xml)
  • Zotero (.ris)
    • Open full article

    References

    1. GREENSHIELDS, D. B., BIDDINS, R. J., CHANNING, S. W., MILLER, H. H. A study in highway capacity. In: 14th Annual Meeting of the Highway Research Board: proceedings. Vol. 14. Highway Research Board, 1935. ISSN 0096-102, p. 448-477.
    2. LIGHTHILL, M. J., WHITMAN, G. B. On kinematic waves. II. A theory of traffic flow on long crowded roads. In: Royal Society of London: proceedings [online]. Vol. 229 A. 1955. ISSN 0080-4630, p. 317-345 Available from: https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.1955.0089 Go to original source...
    3. RICHARDS, P. I. Shock waves on the highway. Operations Research [online]. 1956, 4(1), p. 1-137. ISSN 0030-364X. Available from: https://doi.org/10.1287/opre.4.1.42 Go to original source...
    4. GREENBERG, H. An analysis of traffic flow. Operations Research [online]. 1959, 7(1), p. 79-85. ISSN 0030-364X. Available from: http://dx.doi.org/10.1287/opre.7.1.79 Go to original source...
    5. NEWELL, G. F. Nonlinear effects in the dynamics of car following. Operations Research [online]. 1961, 9(2), p. 209-229. ISSN 0030-364X. Available from: https://doi.org/10.1287/opre.9.2.209 Go to original source...
    6. PAVERI-FONTANA, S. L. On Boltzmann-like treatments for traffic flow: a critical review of the basic model and an alternative proposal for dilute traffic analysis. Transportation Research [online]. 1975, 9, p. 225-235. Available from: https://doi.org/10.1016/0041-1647(75)90063-5 Go to original source...
    7. HELBING, D. Gas-kinetic derivation of Navier-Stokes-like traffic equations. Physical Review E [online]. 1996, 53(3), p. 2366-2381. ISSN 2470-0045. Available from: https://doi.org/10.1103/PhysRevE.53.2366 Go to original source...
    8. PIPES, L. A. An operational analysis of traffic dynamics. Journal of Applied Physics [online]. 1953, 24, p. 274-281. ISSN 0021-8979. Available from: https://doi.org/10.1063/1.1721265 Go to original source...
    9. PRIGOGINE, I., ANDREWS, F. C. A Boltzmann-like approach for traffic flow. Operations Research [online]. 1960, 8(6), p. 789-797. ISSN 0030-364X. Available from: https://doi.org/10.1287/opre.8.6.789 Go to original source...
    10. DRAKE, J. S., SCHOFER, J. L., MAY, A. D. A statistical analysis of speed-density hypotheses. In: 45th Annual Meeting of the Highway Research Board: proceedings [online]. Vol. 154. Highway Research Board, 1967. ISSN 0096-102, p. 53-87. Available from: http://onlinepubs.trb.org/Onlinepubs/hrr/1967/154/154-004.pdf
    11. PAYNE, H. J. Models of freeway traffic and control. In: Mathematical Models of Public Systems. Vol. 1. La Jolla, USA: Simulation Councils, INC., 1971. p. 51-61.
    12. SMULDERS, S. Control of freeway traffic flow by variable speed signs. Transportation Research Part B: Methodological [online]. 1990, 24(2), p. 111-132. ISSN 0191-2615. Available from: https://doi.org/10.1016/0191-2615(90)90023-R Go to original source...
    13. DAGANZO, C. F. The cell transmission model: a dynamic representation of highway traffic consistent whit the hydrodynamic theory. Transportation Research Part B: Methodological [online]. 1994, 28(4), p. 269-287. ISSN 0191-2615. Available from: https://doi.org/10.1016/0191-2615(94)90002-7 Go to original source...
    14. NELSON, P. Synchronized traffic flow from a modified Lighthill-Whitman model. Physical Review E [online]. 2000, 61(6), R6052. ISSN 2470-0045. Available from: https://doi.org/10.1103/PhysRevE.61.R6052 Go to original source...
    15. ZHANG, H. M. A non-equilibrium traffic model devoid of gas-like behavior. Transportation Research Part B: Methodological [online]. 2002, 36(3), p. 275-290. ISSN 0191-2615. Available from: https://doi.org/10.1016/S0191-2615(00)00050-3 Go to original source...
    16. VELASCO, R. M., MARQUEZ, W. Navier-stokes-like equations for traffic flow. Physical Review E [online]. 2005, 72, 046102. ISSN 2470-0045. Available from: https://doi.org/10.1103/PhysRevE.72.046102 Go to original source...
    17. VAN WAGENINGEN-KESSELS, F., VAN LINT, H., VUIK, K., HOOGENDOORN, S. Genealogy of traffic flow models. EURO Journal on Transportation and Logistics [online]. 2015, 4, p. 445-473. ISSN 2192-4376, eISSN 2192-4384. Available from: https://doi.org/10.1007/s13676-014-0045-5 Go to original source...
    18. Origin destination survey of households in the Metropolitan Area of the Valley of Mexico / Encuesta origen destino en hogares de la Zona Metropolitana Valle de Mexico (in Spanish) - Inegi and Cdmx-Gov [online] [accessed 2019-10-02]. Available from: https://www.inegi.org.mx/contenidos/programas/eod/2017/doc/resultados_eod_2017.pdf
    19. ASUAD, N. E. The main challenges of the Mexico City conurbation and metropolitan transportation / Principales retos de la conurbacion de la Ciudad de Mexico y el transporte metropolitano (in Spanish) [online] [accessed 2019-04-10]. Available from: http://www.economia.unam.mx/cedrus/descargas/Retos%20transporte%20ZMCM.pdf
    20. MUNOZ, J. C., BATARCE, M., TORRES, I.) . Comparison of the level of public transport service in six Latin American cities / Comparacion del nivel de servicio del transporte publico en seis ciudades latinoamericanas (in Spanish). In: XVI Congreso Chileno de Ingenieria de Transporte: proceedings [online]. Vol. 18. 2013. p. 10-16. Available from: https://auroradechile.uchile.cl/index.php/CIT/article/view/28452/30173
    21. Inegi [online] [accessed 2019-11-25] Available from: https://www.inegi.org.mx
    22. MIRALLES-GUASH, C., CEBOLLADA, A. Mobility and transportation. Political options for the city / Movilidad y transporte. Opciones politicas para la ciudad (in Spanish) [online]. Madrid: Laboratorio de Alternativas, 2003. ISBN 84-96204-28-6. Available from: https://www.fundacionalternativas.org/public/storage/laboratorio_documentos_archivos/xmlimport-GVOoD4.pdf
    23. HELBING, D., HENNECKE, A., TREIBER, M., SHVETSOV, V. Master: macroscopic traffic simulation based on a gas-kinetic, non-local traffic model. Transportation Research Part B: Methodological [online]. 2001, 35, p. 183-211. ISSN 0191-2615. Available from: https://doi.org/10.1016/S0191-2615(99)00047-8 Go to original source...
    24. DELGADO, J., SAAVEDRA, P., VELASCO, R. M. Modeling of traffic flow problems / Modelacion de problemas de flujo vehicular (in Spanish) [online]. Iztapalapa, Mexico: CBI UAM, 2012. Available from: https://www.academia.edu/27515488/Modelaci%C3%B3n_de_problemas_de_flujo_vehicular
    25. FANG, J., YE, H., EASA, S. M. Modified traffic flow model with connected vehicle microscopic data for proactive variable speed limit control. Journal of Advanced Transportation [online]. 2019, 8151582, p. 1-11. ISSN 0197-6729. Available from: https://doi.org/10.1155/2019/8151582 Go to original source...
    26. GOMEZ-HERNANDEZ, E. Development of a vehicle simulation model to improve traffic light synchronization/Desarrollo de un modelo de simulacion vehicular para la mejora en la sincronizacion de semaforos (in Spanish). PhD thesis. Puebla, Mexico: INAOE, 2009. Available from: https://inaoe.repositorioinstitucional.mx/jspui/bitstream/1009/379/1/GomezHE.pdf
    27. ASMAR, N. H. Partial differential equations with Fourier series and boundary value problems. 2. Ed. USA: Pearson: Prentice-Hall, 2005. ISBN 0-13-148096-0.
    28. WEBER, H. J., ARFKEN, G. B. Essential mathematical methods for physicists. USA: Academic Press, 2003. ISBN 0-12-059877-9.
    29. BOAS, M. L. Mathematical methods in the physical sciences. 3. ed. USA: John Wiley & Sons., 2005. ISBN 978-0-471-19826-0.
    30. GUYON, E., HULIN, J.-P., PETIT, L. Hidrodynamique physique. Paris: EDP Sciences, CNRS Ed., 2001. ISBN 2-86883-502-3. Go to original source...
    31. TREIBER, M, A. KESTING, A. Traffic flow dynamics. data, models and simulation. Berlin Heidelberg: Springer-Verlag, 2013. ISBN 978-3-642-32460-4. Go to original source...
    32. BURDEN, R. L., FAIRES, J. D. Numerical analysis. 9. ed. USA: Cengage Learning, 2011. ISBN-13: 978-0-538-73351-9.
    33. MATTHEWS, J. H., FINK, K. D. Numerical methods: using Matlab. 3. edition. USA: Prentice-Hall, 1999. ISBN-13: 978-0132700429.
    34. ESI-OpenCFD. OpenFOAM. The open-source CFD toolbox. Programmer's guide. Version 3.0.1. [online] [accessed 2019-12-14]. Available from: http://foam.sourceforge.net/docs/Guides-a4/ProgrammersGuide.pdf
    35. KESSELS. F. Traffic flow modelling. Introduction to traffic flow theory through a genealogy of models. Cham, Switzerland: Springer, 2019. ISBN 978-3-319-78695-7. Go to original source...
    36. SMALL, K. A., VERHOEF, E. T. The economics of urban transportation. 2. ed. New York, USA: Taylor & Francis and Routledge, 2007. ISBN-13: 978-0415285155. Go to original source...
    37. KERNER, B. S., KONHAUSER, P. Structure and parameters of clusters in traffic flow. Physical Review E. 1994, 50(1), p. 54-83. ISSN 2470-0045. Go to original source...
    38. DELGADO, J. SAAVEDRA, P. Global bifurcation diagram for the Kerner and Konhauser traffic flow model. International Journal of Bifurcation and Chaos [online]. 2015, 25(5), 1550064. ISSN 0218-1274. Available from: https://doi.org/10.1142/S0218127415500649 Go to original source...
    39. HABERMAN, R. Mathematical models. Philadelphia, USA: Society for Industrial and Applied Mathematics, 1998. ISBN 0-89871408-7.

    This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International License (CC BY 4.0), which permits use, distribution, and reproduction in any medium, provided the original publication is properly cited. No use, distribution or reproduction is permitted which does not comply with these terms.


    Return to the content