Offset optimization for a network of signalized intersections via semidefinite relaxation

We consider the problem of coordinating the traffic signals in a network of signalized intersections to reduce accumulated queues of vehicles throughout the network. We assume that all signals have a common cycle time and a fixed actuation plan, and we propose an approach for optimizing the relative phase offsets. Unlike existing techniques, our approach accommodates networks with arbitrary topology and scales well. This is accomplished by proposing a sinusoidal approximation of the queueing processes in the network, which enables a semidefinite relaxation of the offset optimization problem that is easily solved. We demonstrate the result in a case study of a traffic network in Arcadia, California.