Multiscale analysis of a spatially heterogeneous microscopic traffic model

JA Ward, RE Wilson, Peter K Berg

Research output: Working paper

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The microscopic Optimal Velocity (OV) model is posed on an inhomogeneous ring-road, consisting of two spatial regimes which differ by a scaled OV function. Parameters are chosen throughout for which all uniform flows are linearly stable. The large-time behaviour of this discrete system is stationary and exhibits three types of macroscopic traffic pattern, each consisting of plateaus joined together by sharp interfaces. At a coarse level, these patterns are determined by simple flow and density balances, which in some cases have non-unique solutions. The theory of characteristics for the classical Lighthill-Whitham PDE model is then applied to explain which pattern the OV model selects. A global analysis of a second order PDE model is then performed in an attempt to explain some qualitative details of interface structure. Finally, the full microscopic model is analysed at the linear level to explain features which cannot be described by the present macroscopic approaches.
Original languageEnglish
Publication statusPublished - Apr 2007

Bibliographical note

Additional information: Preprint submitted to Elsevier Science


  • wave patterns
  • multiscale analysis
  • phase-plane analysis
  • optimal velocity model
  • bottlenecks
  • traffic modelling


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