We develop a new model for traffic with on roads with multiple lanes but where the vehicles do not quite adhere to a lane discipline. To study the system the dynamics is split along two independent directions-the y-axis representing the direction of motion and and the x-axis representhe the lateral or the direction perpendicular to the direction of motion. Different influence graphs are used to model the interaction between the vehicles in these two directions.
The model allows more than one `layer’ ahead to influence the dynamics of a car thus allowing for mutliple cars in its visible range to affect its motion. The stability of the dynamical system models are analyzed. Conditions are provided under which all cars can converge to constant spacing. The spacing will refer to distance among cars in two levels along the direction of motion and between the cars in the same level.