Eigenvalue and Eigenvector Analysis of Stability for a Line of Traffic

Many authors have recognized that traffic under the traditional car‐following model (CFM) is subject to flow instabilities. A recent model achieves stability using bilateral control (BCM)—by looking both forward and backward [1]. (Looking back may be difficult or distracting for human drivers, but i...

Full description

Saved in:
Bibliographic Details
Published inStudies in applied mathematics (Cambridge) Vol. 138; no. 1; pp. 103 - 132
Main Authors Wang, Liang, Horn, Berthold K. P., Strang, Gilbert
Format Journal Article
LanguageEnglish
Published Cambridge Blackwell Publishing Ltd 01.01.2017
Subjects
Applied mathematics
Differential equations
Eigenvalues
Simulation
Studies
Traffic flow
Online AccessGet full text

Cover

More Information
Summary:Many authors have recognized that traffic under the traditional car‐following model (CFM) is subject to flow instabilities. A recent model achieves stability using bilateral control (BCM)—by looking both forward and backward [1]. (Looking back may be difficult or distracting for human drivers, but is not a problem for sensors.) We analyze the underlying systems of differential equations by studying their eigenvalues and eigenvectors under various boundary conditions. Simulations further confirm that bilateral control can avoid instabilities and reduce the chance of collisions.
ISSN:0022-2526
1467-9590
DOI:10.1111/sapm.12144