Offset optimization in signalized traffic networks via semidefinite relaxation

- An approach for optimizing intersection offsets in arterial networks is proposed.
- The optimization approach is posed as a convex program for reducing link queues.
- The approach can accommodate networks with arbitrary topology and scales well with network size.
- Two supporting case studies are provided.

We study the problem of selecting offsets of the traffic signals in a network of signalized intersections to reduce queues of vehicles at all intersections. The signals in the network have a common cycle time and a fixed timing plan. It is assumed that the exogenous demands are constant or periodic with the same period as the cycle time and the intersections are under-saturated. The resulting queuing processes are periodic. These periodic processes are approximated by sinusoids. The sinusoidal approximation leads to an analytical expression of the queue lengths at every intersection as a function of the demands and the vector of offsets. The optimum offset vector is the solution of a quadratically constrained quadratic program (QCQP), which is solved via its convex semidefinite relaxation. Unlike existing techniques, our approach accommodates networks with arbitrary topology and scales well with network size. We illustrate the result in two case studies. The first is an academic example previously proposed in the literature, and the second case study consists of an arterial corridor network in Arcadia, California.