Data-driven Variable Speed Limit Design for Highways via Distributionally Robust Optimization

TL;DR

This paper develops a data-driven, distributionally robust optimization approach to design variable speed limits for highways, effectively managing traffic congestion under uncertain vehicle flow conditions with guaranteed out-of-sample performance.

Contribution

It introduces a tractable reformulation and efficient algorithm for a robust speed limit design problem using finite data samples, ensuring performance guarantees.

Findings

Method effectively manages traffic congestion under uncertainty

Reformulation ensures computational tractability

Simulation confirms practical effectiveness

Abstract

This paper introduces an optimization problem (P) and a solution strategy to design variable-speed-limit controls for a highway that is subject to traffic congestion and uncertain vehicle arrival and departure. By employing a finite data-set of samples of the uncertain variables, we aim to find a data-driven solution that has a guaranteed out-of-sample performance. In principle, such formulation leads to an intractable problem (P) as the distribution of the uncertainty variable is unknown. By adopting a distributionally robust optimization approach, this work presents a tractable reformulation of (P) and an efficient algorithm that provides a suboptimal solution that retains the out-of-sample performance guarantee. A simulation illustrates the effectiveness of this method.