Traffic reconstruction using autonomous vehicles

Maria Laura Delle Monache, Thibault Liard, Benedetto Piccoli, Raphael Stern, Dan Work

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


We consider a partial differential equation - ordinary differential equation system to describe the dynamics of traffic flow with autonomous vehicles. In the model the bulk flow is represented by a scalar conservation law, while each autonomous vehicle is described by a car following model. The autonomous vehicles act as tracer vehicles in the flow and collect measurements along their trajectories to estimate the bulk flow. The main result is to both prove theoretically and show numerically how to reconstruct the correct traffic density using only the measurements from the autonomous vehicles.

Original languageEnglish (US)
Pages (from-to)1748-1767
Number of pages20
JournalSIAM Journal on Applied Mathematics
Issue number5
StatePublished - 2019
Externally publishedYes

Bibliographical note

Funding Information:
\ast Received by the editors September 26, 2018; accepted for publication (in revised form) June 19, 2019; published electronically September 12, 2019. Funding: The work of the first author was supported by the IDEX-IRS 2018 project ``MAVIT--Modeling autonomous vehicles in traffic flow"" and by the support of Inria associated team ``MEMENTO."" This material is based upon work supported by the National Science Foundation under grants CNS-1837652 (D.W.) and CNS-1837481 (B.P.) \dagger Univ. Grenoble Alpes, Inria, CNRS, Grenoble INP, GIPSA-Lab, 38000 Grenoble, France (, \ddagger Rutgers University, Camden, NJ 08102 ( \S Vanderbilt University, Nashville, TN 37212 (,

Publisher Copyright:
© 2019 Society for Industrial and Applied Mathematics


  • Density reconstruction
  • PDE-ODE systems
  • Scalar conservation laws
  • Traffic flow models


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