This work deals with optimal or near-optimal operation of traffic lights in an urban area, e.g. a town or a neighborhood. The goal is on-line optimization of traffic light schedule in real time, so as to take into account variable traffic demands, with the objective of obtaining a better use of the road infrastructure. More precisely, we aim at maximizing total travel distance within the network, while also ensuring good servicing of demands of incoming cars in the network from other areas.
One way to address the complexity of the resulting optimization problem is to use a simplified averaged model for the traffic variables, and to optimize only the duty-cyles of traffic lights, i.e., the fractions of green time. This, together with a one-step optimization horizon, allows us to turn the problem into a simple linear program. Another approach is to include as optimization variables both duty-cycles and phases of the traffic lights. We show how to turn the resulting problem into a mixed-integer linear program (MILP). Then, to overcome its complexity, we propose a sub-optimal distributed solution, while the global MILP can be used off-line for performance comparison.
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