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

• Published in: Ingeniería y ciencia (Medellín, Colombia) Colombia), 2019-01, Vol.15 (29), p.127
• Main Authors: Mesa-Mazo, M.J, Valencia-Calvo, Johnny, Olivar-Tost, Gerard
• Format: Article
• Language: Spanish
• Subjects: Numerical analysis
• ISSN: 1794-9165
• DOI: 10.17230/ingciencia.15.29.5

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. Keywords: Vehicular traffic; stability; fuel consumption; dynamical systems; modeling and simulation; non-smooth dynamics; applied mathematics. En el siguiente articulo, se presenta un sistema suave por tramos que describe la dinamica de un vehiculo que se mueve a traves de una calle con semaforos que se encienden y apagan con una frecuencia especifica. El modelo presenta tres comportamientos dinamicos: acelerado, desacelerado y detenido. Ademas, se muestra la descripcion del modelo matematico utilizado para simular el sistema. La simulacion se desarrollo bajo un esquema basado en eventos y se implemento en Matlab. Para realizar el analisis numerico, se toma como parametro el ciclo de los semaforos, que mejora el sistema de trafico vehicular debido a que con su configuracion se logran implementar estrategias de optimizacion permitiendo que los vehiculos se desplacen en ola verde y reduzcan el tiempo de viaje, minimizando asi, el numero de paradas a lo largo del camino y reduciendo el consumo de combustible debido a las paradas y aceleradas. Ademas, se estudio la estabilidad de las orbitas periodicas uno y dos que presenta el modelo de simulacion, asi como sus implicaciones dinamicas. Finalmente, se presenta una propuesta para calcu