A Traffic Model Aware of Real Time Data

TL;DR

This paper introduces a new traffic model that incorporates real-time data, such as GPS information, to better predict traffic flow and effects of accidents, supported by mathematical proofs and numerical simulations.

Contribution

It presents a novel traffic model integrating real-time data and proves its well-posedness, addressing limitations of traditional models like LWR.

Findings

The model effectively captures the impact of accidents on traffic flow.

Numerical simulations demonstrate qualitative agreement with real traffic behavior.

The inverse problem for the LWR model is shown to be ill-posed.

Abstract

Nowadays, traffic monitoring systems have access to real time data, e.g. through GPS devices. We propose a new traffic model able to take into account these data and, hence, able to describe the effects of unpredictable accidents. The well posedness of this model is proved and numerical integrations show qualitative features of the resulting solutions. As a further motivation for the use of real time data, we show that the inverse problem for the Lighthill-Whitam and Richards (LWR) model is ill posed.