Traffic regulation via controlled speed limit

TL;DR

This paper investigates optimal control strategies for traffic regulation using variable speed limits within the LWR model, demonstrating that gradient-based methods outperform random exploration in minimizing flow error.

Contribution

It introduces an analytical framework for optimal speed limit control, compares different strategies, and shows the efficiency of gradient-based optimization in traffic flow management.

Findings

Gradient method achieves within 10% of the minimum cost.

Analytical expressions for control variations are derived.

Gradient approach outperforms random exploration in efficiency.

Abstract

We study an optimal control problem for traffic regulation via variable speed limit. The traffic flow dynamics is described with the Lighthill-Whitham-Richards (LWR) model with Newell-Daganzo flux function. We aim at minimizing the $L^2$ quadratic error to a desired outflow, given an inflow on a single road. We first provide existence of a minimizer and compute analytically the cost functional variations due to needle-like variation in the control policy. Then, we compare three strategies: instantaneous policy; random exploration of control space; steepest descent using numerical expression of gradient. We show that the gradient technique is able to achieve a cost within 10% of random exploration minimum with better computational performances.