The purpose of the research is to analyze the new Spanish law of Traffic, which no longer permits exceeding by up to 20 km/hour the generic speed limits when overtaking on conventional roads. In this research, deterministic and random models are developed to analyze the associated safety risks. The deterministic model highlights the importance of dimensional analysis and provides dimensionless abacuses to analyze the problem. Next, Bayesian networks and Bayesian models are used to build a random model from the previous one, providing a general method to convert deterministic into random models. In addition, the problems of ignoring the dimensions of the variables and parameters are discussed, a common mistake to be corrected. Some examples and multidimensional graphics illustrate the huge reduction in safety and the need to review the existing end of prohibition signs, most of which must be removed. Shortly, the research results show that the distance required for overtaking with safety increases drastically.
KeywordsBayesian NetworkModellingOpenBUGSWeibull Distribution
Decreto Aprobación Ley de Tráfico. BOE número 261, de 31 de octubre de 2015, Referencia: BOEA201511722.
Ley 18/2021, por la que se modifica el texto refundido de la Ley sobre Tráfico, Circulación de Vehículos a Motor y Seguridad Vial, aprobado por el Real Decreto Legislativo 6/2015, de 30 de octubre, en materia del permiso y licencia de conducción por puntos.
Manou-Abi, S.M., Dabo-Nian, S. and Salone, J.J. (2020) Mathematical Modeling of Random and Deterministic Phenomena. ISTE, Wiley, Berlin. https://doi.org/10.1002/9781119706922
Goicolea, T., et al. (2021) Deterministic, Random, or in between? Inferring the Randomness Level of Wildlife Movements. Movement Ecology, 9, 33. https://doi.org/10.1186/s40462-021-00273-7
Castillo, E. and Duato, J. (2022) Los riesgos de la nueva normativa de Tráfico para adelantar. The Conversation, 178930.
Buckingham, E. (1915) The Principle of Similitude. Nature, 96, 396-397. https://doi.org/10.1038/096396d0
Barenblatt, G.I., et al. (1996) Cambridge Texts in Applied Mathematics. 1em plus 0.5em minus 0.4em. Cambridge University Press, Cambridge.
Castillo. E., O’Connor, A., Nogal, M. and Calviño, A. (2014) On the Physical and Probabilistic Consistency of Some Engineering Random Models. Structural Safety, 51, 1-12. https://doi.org/10.1016/j.strusafe.2014.05.003
Castillo, E., Grande, Z. and Calviño, A. (2016) Bayesian Networks-Based Probabilistic Safety Analysis for Railway Lines. Computer-Aided Civil and Infrastructure Engineering, 31, 681-700. https://doi.org/10.1111/mice.12195
Grande, Z., Castillo, E., Mora, E. and Lo, H. (2017) Highway and Road Probabilistic Safety Assessment Based on Bayesian Network Models. Computer Aided Civil and Infrastructure Engineering, 32, 379-396. https://doi.org/10.1111/mice.12248
Pearl, J. (1988) Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann Publishers Inc., San Francisco.
Castillo, E., Gutiérrez, J.M. and Hadi, A.S. (2012) Expert Systems and Probabilistic Network Models, ser. Monographs in Computer Science. Springer, Berlin.
Castillo, E., Gutiérrez, J.M. and Hadi, A.S. (1997) Sistemas expertos y modelos de redes probabilísticas. Real Academia de Ingeniería, Madrid.
Bielza, C., Li, G. and Larrañaga, P. (2011) Multi-Dimensional Classification with Bayesian Networks. International Journal of Approximate Reasoning, 52, 705-727. https://doi.org/10.1016/j.ijar.2011.01.007
Castillo, E., Menéndez, J. and Sánchez-Cambronero, S. (2008) Predicting Traffic Flow Using Bayesian Networks. Transportation Research Part B: Methodological, 42, 482-509. https://doi.org/10.1016/j.trb.2007.10.003
Bielza, C., Moral, S. and Salmerón, A. (2015) Recent Advances in Probabilistic Graphical Models. International Journal of Intelligent Systems, 30, 207-208. https://doi.org/10.1002/int.21697
Castillo, E., Gutiérrez, J.M. and Hadi, A.S. (1996) A New Method for Efficient Symbolic Propagation in Discrete Bayesian Networks. Networks, 28, 31-43. https://doi.org/10.1002/(SICI)1097-0037(199608)28:1 3.0.CO;2-E
Larrañaga, P. and Moral, S. (2011) Probabilistic Graphical Models in Artificial Intelligence. Applied Soft Computing, 11, 1511-1528. https://doi.org/10.1016/j.asoc.2008.01.003
Castillo, E., Gutiérrez, J.M., Hadi, A.S. and Solares, C. (1997) Symbolic Propagation and Sensitivity Analysis in Gaussian Bayesian Networks. Application to Damage Assessment. Artificial Intelligence in Engineering, 11, 173-181. https://doi.org/10.1016/S0954-1810(96)00030-1
Arnold, B., Castillo, E. and Sarabia, J.M. (1992) Conditionally Specified Distributions, ser. Lecture Notes in Statistics, Vol. 73, Springer-Verlag, Berlin.
Arnold, B., Castillo, E. and Sarabia, J. (1996) Specification of Distributions by Combinations of Marginal and Conditional Distributions. Statistics and Probability Letters, 26, 153-157. https://doi.org/10.1016/0167-7152(95)00005-4
Arnold, B., Castillo, E. and Sarabia, J. (2002) Exact and Near Compatibility of Discrete Conditional Distributions. Computational Statistics and Data Analysis, 40, 231-252. https://doi.org/10.1016/S0167-9473(01)00111-6
Castillo, E., Calviño, A., Nogal, M. and Lo, H.K. (2014) On the Probabilistic and Physical Consistency of Traffic Random Variables and Models. Computer-Aided Civil and Infrastructure Engineering, 29, 496-517. https://doi.org/10.1111/mice.12061
Arnold, B., Castillo, E. and Sarabia, J. (2004) Compatibility of Partial or Complete Conditional Probability Specifications. Journal of Statistical Planning and Inference, 123, 133-159. https://doi.org/10.1016/S0378-3758(03)00137-X
Nogal, M., Castillo, E., Calviño, A. and O’Connor, A. (2015) Coherent and Compatible Statistical Models in Structural Analysis. International Journal of Computational Methods, 13, Article ID: 1640008. https://doi.org/10.1142/S0219876216400089
Girón, J. (2021) Bayesian Testing of Statistical Hypotheses. Real Academia de Ciencias Exactas, Físicas y Naturales, Málaga.
Pearl, J. (2009) Causality: Models, Reasoning and Inference. 2nd Edition, Cambridge University Press, Cambridge.
Pearl, J. and Mackenzie, D. (2018) The Book of Why: The New Science of Cause and Effect. Basic Books, Inc., New York.
Lunn, D., Thomas, A., Best, N. and Spiegelhalter, D. (2000) WinBUGS a Bayesian Modelling Framework: Concepts, Structure, and Extensibility. Statistics and Computing, 10, 325-337. https://doi.org/10.1023/A:1008929526011