  This paper proposes a new physics-based approach to effectively control
congestion in a network of interconnected roads (NOIR). The paper integrates
mass flow conservation and diffusion-based dynamics to model traffic
coordination in a NOIR. The mass conservation law is used to model the traffic
density dynamics across the NOIR while the diffusion law is applied to include
traffic speed and motion direction into planning. This paper offers an analogy
between traffic coordination in a transportation system and heat flux in a
thermal system to define a potential filed over the NOIR. The paper also
develops an interactive light-based and boundary control to manage traffic
congestion through optimizing the traffic signal operations and controlling
traffic flows at the NOIR boundary nodes. More specifically, a model predictive
boundary control optimizes the NOIR inflow traffic while a receding horizon
optimizer assigns the optimal movement phases at the NOIR intersections. For
simulation, the paper models traffic congestion in a heterogeneous NOIR with a
large number of interior and boundary nodes where the proposed interactive
control can successfully manage the congestion.
