A convex formulation of traffic dynamics on transportation networks

Yanning Li, Christian G. Claudel, Benedetto Piccoli, Daniel B. Work*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


This article proposes a numerical scheme for c omputing the evolution of vehicular traffic on a road network over a finite time horizon. The traffic dynamics on each link is modeled by the Hamilton-Jacobi (HJ) partial differential equation (PDE), which is an equivalent form of the Lighthill-Whitham-Richards PDE. The main contribution of this article is the construction of a single convex optimization program which computes the traffic flow at a junction over a finite time horizon and decouples the PDEs on connecting links. Compared to discretization schemes which require the computation of all traffic states on a time-space grid, the proposed convex optimization approach computes the boundary flows at the junction using only the initial condition on links and the boundary conditions of the network. The computed boundary flows at the junction specify the boundary condition for the HJ PDE on connecting links, which then can be separately solved using an existing semi-explicit scheme for single link HJ PDE. As demonstrated in a numerical example of ramp metering control, the proposed convex optimization approach also provides a natural framework for optimal traffic control applications.

Original languageEnglish (US)
Pages (from-to)1493-1515
Number of pages23
JournalSIAM Journal on Applied Mathematics
Issue number4
StatePublished - 2017
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2017 Society for Industrial and Applied Mathematics.


  • Convex optimization
  • Junction solver
  • Networks
  • Traffic control
  • Traffic modeling

ASJC Scopus subject areas

  • Applied Mathematics


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