On the Role of Non-Localities in Fundamental Diagram Estimation

TL;DR

This paper investigates how non-local speed-density data, incorporating anticipated densities, can improve the classification of stationary and non-stationary traffic states, leading to more accurate fundamental diagram estimation.

Contribution

The paper introduces an enhanced cross entropy method that accounts for non-localities and equilibrium physics, improving fundamental diagram fitting over traditional local approaches.

Findings

Separating boundary is invariant across trajectory samples within the same region.

Anticipated densities enable clear classification of acceleration and deceleration regimes.

Proposed method outperforms traditional least squares estimation in accuracy.

Abstract

We consider the role of non-localities in speed-density data used to fit fundamental diagrams from vehicle trajectories. We demonstrate that the use of anticipated densities results in a clear classification of speed-density data into stationary and non-stationary points, namely, acceleration and deceleration regimes and their separating boundary. The separating boundary represents a locus of stationary traffic states, i.e., the fundamental diagram. To fit fundamental diagrams, we develop an enhanced cross entropy minimization method that honors equilibrium traffic physics. We illustrate the effectiveness of our proposed approach by comparing it with the traditional approach that uses local speed-density states and least squares estimation. Our experiments show that the separating boundary in our approach is invariant to varying trajectory samples within the same spatio-temporal region, providing further evidence that the separating boundary is indeed a locus of stationary traffic states.