Continuous-time link-based kinematic wave model: formulation, solution existence, and well-posedness

Ke Han, Benedetto Piccoli, W. Y. Szeto

Research output: Contribution to journalArticlepeer-review

44 Scopus citations


We present a continuous-time link-based kinematic wave model (LKWM) for dynamic traffic networks based on the scalar conservation law model. Derivation of the LKWM involves the variational principle for the Hamilton–Jacobi equation and junction models defined via the notions of demand and supply. We show that the proposed LKWM can be formulated as a system of differential algebraic equations (DAEs), which captures shock formation and propagation, as well as queue spillback. The DAE system, as we show in this paper, is the continuous-time counterpart of the link transmission model. In addition, we present a solution existence theory for the continuous-time network model and investigate continuous dependence of the solution on the initial data, a property known as well-posedness. We test the DAE system extensively on several small and large networks and demonstrate its numerical efficiency.

Original languageEnglish (US)
Pages (from-to)187-222
Number of pages36
JournalTransportmetrica B
Issue number3
StatePublished - Sep 1 2016

All Science Journal Classification (ASJC) codes

  • Software
  • Modeling and Simulation
  • Transportation


  • continuous-time traffic flow model
  • differential algebraic equations
  • kinematic wave model
  • link transmission model
  • well-posedness


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