Network Traffic Signal Control with Nonconvex Alternating Direction Method of Multipliers Formulations

This paper considers the distributed solution of the online network traffic signal control problem. Toward systemwide optimality, the problem is modeled as a large-scale mixed-integer linear program with the traffic dynamics captured by the cell transmission model. The alternating direction method of multipliers (ADMM) is used to achieve spatial problem decomposition and to design an iterative approach that achieves networkwide solution under a fully distributed architecture, where computation, communication, and control are performed locally at individual intersections. Two ADMM-based algorithms were developed on the basis of appropriate problem reformulations; these algorithms resulted in the solution of convex–nonconvex subproblems with distinct properties. The performance of the algorithms was demonstrated to be close to global optimality and comparative to that of genetic algorithms. Each algorithm offers a different trade-off between communication and computation complexity.