{"doi":"10.3390/axioms10010017","title":"A Three-Phase Fundamental Diagram from Three-Dimensional Traffic Data","abstract":"This paper uses empirical traffic data collected from three locations in Europe and the US to reveal a three-phase fundamental diagram with two phases located in the uncongested regime. Model-based clustering, hypothesis testing and regression analyses are applied to the speed–flow–occupancy relationship represented in the three-dimensional space to rigorously validate the three phases and identify their gaps. The finding is consistent across the aforementioned different geographical locations. Accordingly, we propose a three-phase macroscopic traffic flow model and a characterization of solutions to the Riemann problems. This work identifies critical structures in the fundamental diagram that are typically ignored in first- and higher-order models and could significantly impact travel time estimation on highways.","journal":"Axioms","year":2021,"id":200753,"datarank":0.0,"base_score":0.0,"endowment":0.0,"self_citation_contribution":0.0,"citation_network_contribution":0.0,"self_endowment_contribution":0.0,"citer_contribution":0.0,"corpus_percentile":null,"corpus_rank":null,"citation_count":7,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":0.91,"is_data_producer":false,"deposit_databanks":null,"is_oa":true,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":"2021-01-01","fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":779024,"name":"Karen Chi","orcid":null,"position":1,"is_corresponding":false},{"id":778575,"name":"Yong Chen","orcid":"0000-0003-4580-8655","position":2,"is_corresponding":false},{"id":778576,"name":"Paola Goatin","orcid":"0000-0001-5169-1751","position":3,"is_corresponding":false},{"id":778577,"name":"Ke Han","orcid":"0000-0003-3529-6246","position":4,"is_corresponding":false},{"id":778578,"name":"Jing‐Mei Qiu","orcid":"0000-0002-3462-188X","position":5,"is_corresponding":false},{"id":778579,"name":"Benedetto Piccoli","orcid":"0000-0002-6000-5394","position":6,"is_corresponding":false},{"id":778574,"name":"Maria Laura Delle Monache","orcid":"0000-0003-1355-8153","position":0,"is_corresponding":true}],"reference_count":22,"raw_metadata":null,"created_at":"2026-07-18T23:50:48.624274Z","pmid":null,"pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":null,"fair_a":null,"fair_i":null,"fair_r":null,"fair_zscore":null,"fair_rationale":null,"fair_model":null,"fair_agent_version":null,"fair_fulltext_source":null,"fair_has_llm":null,"fair_computed_at":null,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}