We develop a dynamic model for traffic on (Indian) roads with multiple lanes, where the vehicles do not adhere to lane discipline. Identical vehicles are assumed to influence each other based on proximity and visual feedback. This percolation of influence across suitably defined layers of vehicles, is modeled using weighted directed graphs. Drivers accelerate, decelerate or maneuver sideways with the objective of maintaining safe inter-vehicle distances between the cars. This target inter-vehicle distance may vary with the absolute velocity of the cars. When the influence structure is time invariant, e.g. in dense traffic, the collection converges to a layered formation with inter-vehicle distances based on vehicle velocities. In general, for a changing influence topology the inter-car distance can oscillate, while remaining uniformly bounded. The model is inspired by and validated with limited video-graphic evidence recorded on the road outside IITB main gate.
Debraj Chakraborty received his BE in Electrical Engineering from Jadavpur University, Kolkata, India in 2001, MTech in Electrical Engineering from IIT Kanpur, Kanpur, India in 2003 and PhD in Electrical and Computer Engineering from University of Florida Gainesville, USA in 2007 respectively. Thereafter he joined the Department of Electrical Engineering, Indian Institute of Technology Bombay where he is currently an Associate Professor. His research interests include optimal control, multi agent systems and control applications.