{"paper":{"title":"Multi-Anticipative Piecewise-Linear Car-Following Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.DS","math.MP"],"primary_cat":"math.OC","authors_text":"Habib Haj-Salem, Jean-Patrick Lebacque, Nadir Farhi","submitted_at":"2013-02-01T11:53:44Z","abstract_excerpt":"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, a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.0153","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}