Optimal Driving Under Traffic Signal Uncertainty

TL;DR

This paper develops a dynamic programming framework to determine optimal driving strategies under traffic signal duration uncertainty, balancing fuel efficiency, comfort, and travel time.

Contribution

It introduces a novel approach using Hamilton-Jacobi-Bellman PDEs to model and solve driver behavior under green light duration uncertainty.

Findings

Optimal policies depend on the probability distribution of green durations.

Uncertainty influences drivers to adopt more conservative acceleration strategies.

Numerical solutions demonstrate the impact of conflicting goals on driving behavior.

Abstract

We study driver's optimal trajectory planning under uncertainty in the duration of a traffic light's green phase. We interpret this as an optimal control problem with an objective of minimizing the expected cost based on the fuel use, discomfort from rapid velocity changes, and time to destination. Treating this in the framework of dynamic programming, we show that the probability distribution on green phase durations gives rise to a sequence of Hamilton-Jacobi-Bellman PDEs, which are then solved numerically to obtain optimal acceleration/braking policy in feedback form. Our numerical examples illustrate the approach and highlight the role of conflicting goals and uncertainty in shaping drivers' behavior.