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Journal Articles SIAM Journal on Applied Mathematics Year : 2022

Stability and string stability of car-following models with reaction-time delay

Abstract

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 non rational 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, partial string stability).
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Dates and versions

hal-03697661 , version 3 (06-04-2020)
hal-03697661 , version 6 (28-04-2020)
hal-03697661 , version 7 (30-04-2020)
hal-03697661 , version 8 (04-12-2020)
hal-03697661 , version 9 (17-06-2022)

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Cite

Guy Fayolle, Jean-Marc Lasgouttes, Carlos Flores. Stability and string stability of car-following models with reaction-time delay. SIAM Journal on Applied Mathematics, 2022, 82 (5), pp.1661-1679. ⟨10.1137/21M1443650⟩. ⟨hal-03697661v9⟩
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