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

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