A thesis submitted in the Partial Fulfillment for the Award of Master of Science Degree in Applied Mathematics in the School of Pure & Applied Sciences of Meru University of Science and Technology.

In this thesis, we outline the Kerner's 3-phase traffic flow theory, which states that traffic flow occurs in three phases and these are free flow,synchronized flow and wide moving jam phases. A macroscopic traffic flow model that is factoring dreiver aggressiveness is developed and its features discussed. By construction of the solution to the Riemann problem, the Aggressive model is written in conservative form and solves through numerical method.Using the Godunov numerical method we go ahead to stimulate traffic flow on a multilane road with a lane-drop bottleneck and the diagrams showing the results are given. The diagrammatic results of the model are compared with those of the Aw-Rascle model and features of the Aggressive model are shown to reproduce the features od a three phase traffic flow which the Aw-Rascle model cannot reproduce.It is also shown that the model respects aspects of traffic by responding to frontal stimuli only and it does not produce negative travel.