2013/02/01 by Nadir Farhi, Farhi, Nadir, Habib Haj-Salem +3
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Optimization and Control (math.OC) #math-ph #math.AP #math.DS #math.MP #math.OC
paper · pdf · doi:10.48550/arxiv.1302.0153
19 pages
arxiv created 2013/02/01 · arxiv updated 2013/02/04
We propose in this article an extension of the piecewise linear car-following model to multi-anticipative driving. As in the one-car-anticipative model, the stability and the stationary regimes are characterized thanks to a variational formulation of the car-dynamics. We study the homogeneous driving case. We show that in term of the stationary regime, the multi-anticipative model guarantees the same macroscopic behavior as for the one-car-anticipative one. Nevertheless, in the transient traffic, the variance in car-velocities and accelerations is mitigated by the multi-anticipative driving, and the car-trajectories are smoothed. A parameter identification of the model is made basing on NGSIM data and using a piecewise linear regression approach.