Many researchers have described the nature of traffic flows using partial differential equations (PDE’s) and ordinary differential equations (ODE’s). Most of them use the concept of the conservation laws in fluid mechanics. For example, the model introduced by Lighthill-Whitman-Richards (LWR Model) is formulated as a nonlinear partial differential equation, derived by using the conservation of vehicles on a single road. This project describes the nature of traffic flow using a three- dimensional nonlinear dynamical system called the FBDF model. The well posedness of the model was established and the local stability analysis of the equilibrium points has been carried out using the retardation number while the global stability analysis has been performed using LaSalle’s invariance principle. The numerical simulations were carried out using Python. Furthermore the sensitivity analysis of the parameters has been performed via two methods: a derivative-based local method and algorithmic differentiation.