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

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