A model for lane-less traffic with local control laws

In this paper, a new model for traffic on roads with multiple lanes is developed, where the vehicles do not adhere to lane discipline. Assuming identical vehicles, the dynamics is split along two independent directions - the Y-axis representing the direction of the traffic and the X-axis representing the lateral or the direction perpendicular to the traffic direction. Different influence graphs are used to model the interaction between the vehicles in these two directions. The instantaneous accelerations of each vehicle, in both X and Y directions, are functions of the measurements from the neighbouring vehicles according to these influence graphs. Under time invariant influence structure, expected for example, in dense traffic, the collection converges to a layered formation with fixed inter-vehicle distances. In general, the formation is BIBO stable with the velocity and inter vehicle separations oscillating between a finite number of equilibrium points.