Distributed Optimal Traffic Lights Design for Large-Scale Urban Networks

In this paper, we deal with the problem of dynamical assignment of traffic light schedules in large-scale urban networks. We present a model for signalized traffic networks, based on the cell transmission model, and then a simplified model based on averaging theory. The control objective is to improve traffic, optimizing traffic indexes such as total travel distance and density balancing. We design a scheme that decides the duty cycles of traffic lights, by solving a convex program. The optimization is done in real time, at each cycle of traffic lights, so as to take into account variable traffic demands. The scalability problem is tackled through the synthesis of a distributed optimization algorithm; this reduces the computational load significantly, since the large optimization problem is broken into small local subproblems, whose size does not grow with the size of the network, together with iterative exchanges of messages with few neighbor subproblems. The performance of the proposed approach is evaluated via numerical simulations in two different scenarios: a macroscopic (MATLAB-based) Manhattan grid and a microscopic scenario (based on Aimsun simulator) reproducing a portion of the city of Grenoble, France.