ABSTRACTThis article introduces a new formulation for modeling and evaluating the effects of traffic signal timing over arterial roads, based on the Lighthill Whitham Richards model. We introduce a Hamilton–Jacobi formulation of the traffic model, in which the red phases of the traffic signals are described as internal conditions corresponding to a zero flow (fixed bottlenecks). With this approach, it is possible to model and evaluate the traffic signal timings accurately and efficiently. We then integrate this fast simulation scheme into an optimization framework for computing the optimal signal timing strategy associated with a given set of initial and boundary conditions, over a transportation network. A numerical implementation is shown for a single link case and for a more complex signalized intersection.