Abstract
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 language | English (US) |
|---|---|
| Pages (from-to) | 1748-1767 |
| Number of pages | 20 |
| Journal | SIAM Journal on Applied Mathematics |
| Volume | 79 |
| Issue number | 5 |
| DOIs | |
| State | Published - 2019 |
| Externally published | Yes |
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. https://doi.org/10.1137/18M1217000 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 ([email protected], [email protected]). \ddagger Rutgers University, Camden, NJ 08102 ([email protected]). \S Vanderbilt University, Nashville, TN 37212 ([email protected], [email protected]).
Publisher Copyright:
© 2019 Society for Industrial and Applied Mathematics
Keywords
- Density reconstruction
- PDE-ODE systems
- Scalar conservation laws
- Traffic flow models