The main purpose of this work is to generate optimal trajectories for vehicles crossing a signalized junction, with traffic signals operated in either fixed-time or real-time (adaptive) mode. In the latter case, the next switching time is decided in real time based on the prevailing traffic conditions and is therefore uncertain in advance. The GLOSA (Green Light Optimal Speed Advisory) problem is addressed by using traffic lights information and calculating a trajectory and velocity profile for the vehicle based on the vehicle’s initial state (position and speed) and a fixed final destination state. At first, an appropriate optimal control problem is formulated and solved analytically via Pontryagin’s minimum principle (PMP) for the case of known switching times. Subsequently, for the case of real-time signals, availability of a time-window of possible signal switching times, along with the corresponding probability distribution, is assumed, and the problem is cast in the format of a stochastic optimal control problem and is solved numerically using stochastic dynamic programming (SDP) techniques. Application results, for various driving scenarios, of the deterministic approach, which considers the case of known switching times, and a comprehensive comparison of the stochastic GLOSA approach with a sub-optimal approach are presented. In particular, it is demonstrated that the proposed SDP approach achieves better average performance compared with the sub-optimal approach because of the better (probabilistic) information on the traffic light switching time.
Flood routing with real-time stage correction method for flash flood forecasting in the Tanshui River, Taiwan
