Communications in Mathematical Sciences

Volume 16 (2018)

Number 1

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

Pages: 123 – 144

DOI: https://dx.doi.org/10.4310/CMS.2018.v16.n1.a6

Authors

Maya Briani (Istituto per le Applicazioni del Calcolo, Consiglio Nazionale delle Ricerche, Roma, Italy)

Emiliano Cristiani (Istituto per le Applicazioni del Calcolo, Consiglio Nazionale delle Ricerche, Roma, Italy)

Elisa Iacomini (Dipartimento di Scienze di Base e Applicate per l’Ingegneria, Sapienza – Università di Roma, Italy)

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.

Keywords

LWR model, networks, traffic, uncertainty quantification, Wasserstein distance, earth mover’s distance, godunov scheme, multi-path model, linear programming

2010 Mathematics Subject Classification

35L50, 35R02, 90B20, 90C05

Full Text (PDF format)

Received 13 August 2016

Accepted 15 October 2017

Published 29 March 2018