In this talk, we discuss an optimal-control framework for determining a driver’s optimal braking / acceleration behavior in the face of a green traffic light with unknown duration. We interpret this as a control problem where the driver aims to minimize an expected cost based on their fuel use, discomfort from rapid velocity changes, and time to destination. Treating the problem with dynamic programming, we show that the probability distribution on green phase durations gives rise to a sequence of Hamilton-Jacobi-Bellman (HJB) PDEs. We then propose a numerical method to solve the resulting equations and obtain optimal acceleration/braking policy in feedback form. Finally, we present a selection of examples solved with realistic driving parameters which highlight the roles that conflicting optimization objectives and traffic signal uncertainty play in shaping drivers’ behavior. Joint work with Alex Vladimirsky.