A tracking algorithm for car paths on road networks

Gabriella Bretti, Benedetto Piccoli

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


In this paper we introduce a computation algorithm to trace car paths on road networks, whose load evolution is modeled by conservation laws. This algorithm is composed of two parts: computation of solutions to conservation equations on each road and localization of car position resulting by interactions with waves produced on roads. Some applications and examples to describe the behavior of a driver traveling in a road network are shown. Moreover, a convergence result for wave front tracking approximate solutions, with BV initial data on a single road, is established.

Original languageEnglish (US)
Pages (from-to)510-531
Number of pages22
JournalSIAM Journal on Applied Dynamical Systems
Issue number2
StatePublished - 2008
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Modeling and Simulation


  • Conservation laws
  • Discontinuous ordinary differential equations
  • Finite difference schemes
  • Fluid-dynamic models
  • Traffic flow

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