A heterogeneous multiclass traffic flow model with creeping

Shimao Fan, Daniel B. Work

Research output: Contribution to journalArticlepeer-review


A heterogeneous traffic model with two vehicle classes is developed to capture overtaking and creeping in highly heterogeneous traffic flows. Creeping is a special case of overtaking that occurs when small vehicles continue to advance in congestion even though larger vehicles have completely stopped. To motivate the new model, it is shown that a two class homogeneous multiclass model is equivalent to a class of second order models originally proposed by Aw, Rascle, and Zhang (ARZ). Based on the properties of the ARZ model, homogeneous models do not allow overtaking or creeping. The new creeping model is a phase transition model which applies a system of conservation laws in the noncreeping phase and a system equivalent to a scalar model in the creeping phase. The solution to the Riemann problem is obtained by investigating the elementary waves, particularly for the cases when one vehicle class is absent, as well as in the presence of a phase transition. Based on the proposed Riemann solver, the solution to the Cauchy problem is constructed using wavefront tracking. Numerical tests are carried out using a Godunov scheme to illustrate the creeping phenomenon. Source code for the numerical simulations is available at https://github.com/shimaof/ heterogeneous-traffic-model.

Original languageEnglish (US)
Pages (from-to)813-835
Number of pages23
JournalSIAM Journal on Applied Mathematics
Issue number2
StatePublished - 2015


  • Heterogeneous flow
  • Hyperbolic system of conservation laws
  • Macroscopic traffic flow model
  • Multiclass traffic model
  • Phase transition
  • Riemann solver

ASJC Scopus subject areas

  • Applied Mathematics


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