期刊
SIAM JOURNAL ON APPLIED MATHEMATICS
卷 82, 期 5, 页码 1661-1679出版社
SIAM PUBLICATIONS
DOI: 10.1137/21M1443650
关键词
car-following model; traffic control; transportation networks; stability of linear systems; methods of the complex variable
We investigate the transfer function resulting from the linearization of a car-following model for human drivers, considering their reaction time. The findings reveal nontrivial stability conditions and distinguish between stability, string stability, and partial string stability.
We investigate the transfer function emanating from the linearization of a car-following model for human drivers when taking into account their reaction time, which is known to be a cause of the stop-and-go traffic phenomenon. This leads to a nonrational transfer function, implying nontrivial stability conditions which are explicitly given. They are in particular satisfied whenever string stability holds. We also show how this reaction time can introduce a partial string stability, where the transfer function modulus remains smaller than 1 up to some critical frequency. We explore conditions in the parameter space discriminating between 3 different regimes (stability, string stability, and partial string stability).
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