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

The authors 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. The authors 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 the authors show in this paper, is the continuous-time counterpart of the link transmission model. In addition, they 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. The authors test the DAE system extensively on several small and large networks and demonstrate its numerical efficiency.


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  • Accession Number: 01669313
  • Record Type: Publication
  • Files: TRIS
  • Created Date: Apr 21 2018 3:01PM