Analytical Approximation of Fuel Consumption and Periodic Behaviors for a Vehicle that Travels Through a Traffic Light Series

Main Article Content

M J Mesa-Mazo
Johnny Valencia-Calvo
Gerard Olivar-Tost


modeling, simulation, vehicular traffic, fuel consumption, stability analysis, dynamical systems


In this paper, we present a piecewise smooth system, that describes the dynamics of a single vehicle moving through a street that has a sequence of lights that turn on and off with a specific frequency. The model presents three dynamic ways: accelerated, decelerated and zero state. Besides, we show the description of the mathematical model used to simulate the system. The simulation was developed under an event-based scheme and implemented in Matlab. To make the numerical analysis, we take as a parameter study the cycle traffic light, which provides benefits to vehicular traffic system due to its configuration is achieved implementing optimization strategies for the phenomenon of green wave and reduces the travel time as the vehicle minimizes the number of stops along the road. Also, the stability was studied for the periodic orbits one and two. Finally, we made an approximation of fuel consumption. We assume that this is proportional to the mechanical energy produced by the motor. From this point of view, it can be concluded that it is possible to apply modeling and simulation strategies based on dynamic systems to understand the complex behaviors associated with the travel of vehicles in a traffic controlled by traffic lights. 


Download data is not yet available.
Abstract 485 | PDF Downloads 393


[1] L. Lotero and A. Arenas, “Spreading Processes in Multiplex Metapopulations Containing Different Mobility Networks,” Physical Review X, vol. 8, no. 3, p. 31039, 2018. [Online]. Available: 55

[2] F. Espinosa, C. Gordillo, and O. Avilés, “Algoritmos de visión de máquina aplicados al control dinámico de intersecciones semáforizadas.” DYNA, vol. 80, no. 178, pp. 132–140, 2013. 55, 58

[3] M. Catalano and F. Galatioto, “Enhanced transport-related air pollution prediction through a novel metamodel approach,” Transportation Research Part D: Transport and Environment, vol. 55, pp. 262–276, 2017. [Online]. Available: 55, 58

[4] A. Matas, J.-L. Raymond, and A. Dominguez, “Changes in fuel economy: An analysis of the Spanish car market,” Transportation Research Part D: Transport and Environment, vol. 55, pp. 175–201, 2017. [Online]. Available: 55

[5] A. D. Marchi, M. Gerdts, and M. Matthias, “Traffic Flow on Single-Lane Road Networks : Multiscale Modelling and Simulation,” IFAC-PapersOnLine, vol. 51, no. 2, pp. 162–167, 2018. [Online]. Available: 55

[6] J. Mihelj, A. Kos, U. Sedlar, J. Mihelj, A. Kos, and U. Sedlar, “Source reputation assessment in an IoT-based vehicular traffic monitoring system monitoring system,” Procedia Computer Science, vol. 147, pp. 295–299, 2019. [Online]. Available: 55

[7] B. A. Toledo, V. Muñoz, J. Rogan, C. Tenreiro, and J. A. Valdivia, “Tráfico Vehicular como Sistema Complejo,” Physical Review, vol. 70, pp. 1–4, 2004. 55, 56, 60

[8] M. Mesa-Mazo, J. Valencia-Calvo, and G. Olivar-Tost, “Modelo para la dinámica de un vehículo a través de una secuencia de semáforos,” DYNA, vol. 81, no. 184, pp. 138–145, 2014. [Online]. Available: 55, 57, 60, 62, 64

[9] G. O. Tost, M. Mesa-Mazo, and J. Valencia, “Numerical Simulation Analysis of a Traffic Model,” Springer Proceedings in Mathematics and Statistics, vol. 121, 2015. [Online]. Available: 55

[10] B. A. Toledo, E. Cerda, J. Rogan, C. Tenreiro, R. Zarama, and J. A. Valdivia, “Universal and nonuniversal features in a model of city traffic,” pp. 1–10, 2007. [Online]. Available: 55, 72

[11] A. Varas, M. D. Cornejo, B. A. Toledo, V. Muñoz, J. Rogan, R. Zarama, and J. A. Valdivia, “Resonance, criticality, and emergence in city traffic investigated in cellular automaton models,” Phys. Rev. E, vol. 80, no. 5, p. 056108, 2009. [Online]. Available: 56

[12] M. J. Mesa-Mazo, “Bifurcaciones en un Sistema de Tráfico Vehicular,” Ph.D. Thesis, Departamento de Ingeniería Eléctrica, Electrónica y Computación. Universidad Nacional de Colombia, 2014. [Online]. Available: 56, 60, 64

[13] B. Palat and P. Delhomme, “A simulator study of factors influencing drivers’ behavior at traffic lights,” Transportation Research Part F: Traffic Psychology and Behaviour, vol. 37, pp. 107–118, 2016. [Online]. Available: 56

[14] M. Makys and S. Kozak, Effective method for design of traffic lights control. IFAC, 2011, vol. 44, no. 1. [Online]. Available: 56

[15] B. Davies, Exploring Chaos: Theory and Experiment., P. B. Publishing and . L.L.C., Eds. Perseus Books, 1999. 68, 79

[16] P. G. Lind, “Pattern Formation in Diffusive-Advective Networks of DiscreteTime Oscillators,” Ph.D. Tesis, Universidade de Lisboa 2003. 68, 71

[17] D. C. Lane and J. D. Sterman, “Profiles in Operations Research : JayWright Forrester. Chapter 20 in Profiles in Operations Research: Pioneers and Innovators. S.” Springer, pp. 363–386, 2011. 68

[18] J. a.C. Gallas, “Dissecting shrimps: results for some one-dimensional physical models,” Physica A: Statistical Mechanics and its Applications, vol. 202, no. 1-2, pp. 196–223, jan 1994. [Online]. Available: 71

[19] R. Serway and J. Jewett, FÍSICA para ciencias e ingeniería con Física Moderna, 7th ed., S. R. Cervantes González, Ed. México, D.F.: Cengage Learning Editores, 2008. 72

Most read articles by the same author(s)