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Eigenvalue and Eigenvector Analysis of Stability for a Line of Traffic
Author(s) -
Wang Liang,
Horn Berthold K. P.,
Strang Gilbert
Publication year - 2017
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/sapm.12144
Subject(s) - eigenvalues and eigenvectors , stability (learning theory) , traffic flow (computer networking) , line (geometry) , boundary (topology) , mathematics , control theory (sociology) , differential equation , flow (mathematics) , computer science , boundary value problem , control (management) , mathematical analysis , physics , artificial intelligence , geometry , computer security , quantum mechanics , machine learning
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.