Criteria for convective versus absolute string instability in car-following models

Jonathan A. Ward*, R. Eddie Wilson

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

23 Citations (Scopus)

Abstract

The linear stability properties of car-following models of highway traffic are analysed. A general family of models is introduced and the subsequent analysis developed in terms of its partial derivatives. Two measures of wave propagation, namely (i) the group velocity and (ii) the signal velocity, are introduced and computed. These measures are used to classify how instability propagates disturbances, measured relative to the frame of the road along which the vehicles drive. Detector data suggest that disturbances should propagate only in an upstream direction (convective upstream instability), and it is shown how to parametrize models to agree with data and avoid unrealistic downstream propagation (absolute and convective downstream instability).

Original languageEnglish
Pages (from-to)2185-2208
Number of pages24
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume467
Issue number2132
DOIs
Publication statusPublished - 8 Aug 2011

Keywords

  • CONGESTED TRAFFIC STATES
  • highway traffic
  • FLOW
  • car-following models
  • PROPAGATION
  • instability
  • PHASE
  • STABILITY
  • LIGHT
  • DYNAMICS
  • wave propagation

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