The steady increase in car ownership has made essential the development of macroscopic models of fine resolution changing dynamics of vehicles using different theories such as traffic signaling systems in the presence of signaling lights. The central objective of this study is to provide elements of knowledge needed to characterize the road traffic conditions on through the development of macroscopic modeling based on a lagrangian discretisation of the GSOM (generic second order model). Our research is to model the evolution of a line of vehicle packets and a distribution of microscopic variables by a system of differential equations while using an exponential law for the generation of vehicles. It’s a simulation study of the behavior of a queue of vehicle packets moving according to the GSOM model in lagrangian coordinates. We focused on a representation of real objects: segment, junction and vehicle. We showed how the distribution of vehicle packets varies according to different driving conditions. To assess the ability of our basic lagrangian GSOM model to correctly reproduce the observations of behavior common traffic, we have developed a traffic control model in the presence of signaling lights, while implementing an analysis of key results. The advantage of these signaling lights is that they can observe the creation of shock waves (deceleration waves) when the lights turn red and rarefaction waves (acceleration waves) when the lights turn green.