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This paper develops a conservation-based approach to model traffic dynamicsand alleviate traffic congestion in a network of interconnected roads (NOIR).We generate a NOIR by using the Simulation of Urban Mobility (SUMO) softwarebased on the real street map of Philadelphia Center City. The NOIR is thenrepresented by a directed graph with nodes identifying distinct streets in theCenter City area. By classifying the streets as inlets, outlets, and interiornodes, the model predictive control (MPC) method is applied to alleviate thenetwork traffic congestion by optimizing the traffic inflow and outflow acrossthe boundary of the NOIR with consideration of the inner traffic dynamics as astochastic process. The proposed boundary control problem is defined as aquadratic programming problem with constraints imposing the feasibility oftraffic coordination, and a cost function defined based on the traffic densityacross the NOIR.

Conservation-Based Modeling and Boundary Control of Congestion with an Application to Traffic Management in Center City Philadelphia