Sensitivity analysis of the LWR model for traffic forecast on large networks using Wasserstein distance

TL;DR

This paper analyzes how sensitive the LWR traffic flow model is to network parameters and structure by measuring Wasserstein distances between solutions, revealing high sensitivity to junction traffic, network size, and topology.

Contribution

It introduces a numerical method to approximate Wasserstein distance on networks and applies it to quantify the LWR model's sensitivity to various factors.

Findings

High sensitivity to junction traffic distribution

Significant impact of network size and topology

Wasserstein distance effectively quantifies sensitivity

Abstract

In this paper we investigate the sensitivity of the LWR model on network to its parameters and to the network itself. The quantification of sensitivity is obtained by measuring the Wasserstein distance between two LWR solutions corresponding to different inputs. To this end, we propose a numerical method to approximate the Wasserstein distance between two density distributions defined on a network. We found a large sensitivity to the traffic distribution at junctions, the network size, and the network topology.