title: Linear stability analysis of first-order delayed car-following models on a ring.
abstract: The evolution of a line of vehicles on a ring is modeled by means of first-order car-following models. Three generic models describe the speed of a vehicle as a function of the spacing ahead and the speed of the predecessor. The first model is a basic one with no delay. The second is a delayed car-following model with a strictly positive parameter for the driver and vehicle reaction time. The last model includes a reaction time parameter with an anticipation process by which the delayed position of the predecessor is estimated. Explicit conditions for the linear stability of homogeneous configurations are calculated for each model. Two methods of calculus are compared: an exact one via Hopf bifurcations and an approximation by second-order models. The conditions describe stable areas for the parameters of the models that we interpret. The results notably show that the impact of the reaction time on the stability can be palliated by the anticipation process.
authors.affiliation: Institut Français des Sciences et Technologies des Transports de l'Aménagement et des Réseaux, Génie des Réseaux de Transports Terrestres et Informatique Avancée, Descartes II, 2 rue de la Butte Verte, 93166 Noisy le Grand, France. sylvain.lassarre@ifsttar.fr
authors.forename: Sylvain
authors.initials: S
authors.lastname: Lassarre
authors.forename: Michel
authors.initials: M
authors.lastname: Roussignol
authors.forename: Antoine
authors.initials: A
authors.lastname: Tordeux
mesh_terms: D001336:Automobiles; D003198:Computer Simulation; D016014:Linear Models