{"id":"https://openalex.org/W2760695377","doi":"https://doi.org/10.3934/nhm.2018018","title":"Follow-the-Leader models can be viewed as a numerical approximation to the Lighthill-Whitham-Richards model for traffic flow","display_name":"Follow-the-Leader models can be viewed as a numerical approximation to the Lighthill-Whitham-Richards model for traffic flow","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2760695377","doi":"https://doi.org/10.3934/nhm.2018018","mag":"2760695377"},"language":"en","primary_location":{"id":"doi:10.3934/nhm.2018018","is_oa":true,"landing_page_url":"https://doi.org/10.3934/nhm.2018018","pdf_url":"https://www.aimsciences.org/article/exportPdf?id=badc26c7-2aba-4fa7-ac1e-df5dd50f4a42","source":{"id":"https://openalex.org/S21752972","display_name":"Networks and Heterogeneous Media","issn_l":"1556-1801","issn":["1556-1801","1556-181X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks & Heterogeneous Media","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.aimsciences.org/article/exportPdf?id=badc26c7-2aba-4fa7-ac1e-df5dd50f4a42","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037337641","display_name":"Helge Holden","orcid":"https://orcid.org/0000-0002-8564-0343"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Helge Holden","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5081764581","display_name":"Nils Henrik Risebro","orcid":"https://orcid.org/0000-0003-4069-8282"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nils Henrik Risebro","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5037337641"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.1873,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.46332651,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"13","issue":"3","first_page":"409","last_page":"421"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10524","display_name":"Traffic control and management","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10524","display_name":"Traffic control and management","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11500","display_name":"Evacuation and Crowd Dynamics","score":0.9699000120162964,"subfield":{"id":"https://openalex.org/subfields/2212","display_name":"Ocean Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10698","display_name":"Transportation Planning and Optimization","score":0.9674999713897705,"subfield":{"id":"https://openalex.org/subfields/3313","display_name":"Transportation"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/conservation-law","display_name":"Conservation law","score":0.8068326711654663},{"id":"https://openalex.org/keywords/eulerian-path","display_name":"Eulerian path","score":0.6842743158340454},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.6216907501220703},{"id":"https://openalex.org/keywords/lagrangian","display_name":"Lagrangian","score":0.5691289901733398},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5485979318618774},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.5439825057983398},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5011289119720459},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.4786842465400696},{"id":"https://openalex.org/keywords/microscopic-traffic-flow-model","display_name":"Microscopic traffic flow model","score":0.4713525176048279},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.44063663482666016},{"id":"https://openalex.org/keywords/traffic-flow","display_name":"Traffic flow (computer networking)","score":0.4347856342792511},{"id":"https://openalex.org/keywords/computer-simulation","display_name":"Computer simulation","score":0.43442779779434204},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4309898018836975},{"id":"https://openalex.org/keywords/numerical-approximation","display_name":"Numerical approximation","score":0.42352089285850525},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4181652367115021},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.3444845676422119},{"id":"https://openalex.org/keywords/simulation","display_name":"Simulation","score":0.22594726085662842},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21610555052757263},{"id":"https://openalex.org/keywords/traffic-generation-model","display_name":"Traffic generation model","score":0.14673978090286255},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11969545483589172},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10373115539550781},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.07498058676719666}],"concepts":[{"id":"https://openalex.org/C3445786","wikidata":"https://www.wikidata.org/wiki/Q205805","display_name":"Conservation law","level":2,"score":0.8068326711654663},{"id":"https://openalex.org/C43058520","wikidata":"https://www.wikidata.org/wiki/Q624580","display_name":"Eulerian path","level":3,"score":0.6842743158340454},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.6216907501220703},{"id":"https://openalex.org/C53469067","wikidata":"https://www.wikidata.org/wiki/Q505735","display_name":"Lagrangian","level":2,"score":0.5691289901733398},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5485979318618774},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.5439825057983398},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5011289119720459},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.4786842465400696},{"id":"https://openalex.org/C205269179","wikidata":"https://www.wikidata.org/wiki/Q17144160","display_name":"Microscopic traffic flow model","level":3,"score":0.4713525176048279},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.44063663482666016},{"id":"https://openalex.org/C207512268","wikidata":"https://www.wikidata.org/wiki/Q3074551","display_name":"Traffic flow (computer networking)","level":2,"score":0.4347856342792511},{"id":"https://openalex.org/C500300565","wikidata":"https://www.wikidata.org/wiki/Q925667","display_name":"Computer simulation","level":2,"score":0.43442779779434204},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4309898018836975},{"id":"https://openalex.org/C2986878899","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical approximation","level":3,"score":0.42352089285850525},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4181652367115021},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.3444845676422119},{"id":"https://openalex.org/C44154836","wikidata":"https://www.wikidata.org/wiki/Q45045","display_name":"Simulation","level":1,"score":0.22594726085662842},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21610555052757263},{"id":"https://openalex.org/C176715033","wikidata":"https://www.wikidata.org/wiki/Q2080768","display_name":"Traffic generation model","level":2,"score":0.14673978090286255},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11969545483589172},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10373115539550781},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.07498058676719666},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.3934/nhm.2018018","is_oa":true,"landing_page_url":"https://doi.org/10.3934/nhm.2018018","pdf_url":"https://www.aimsciences.org/article/exportPdf?id=badc26c7-2aba-4fa7-ac1e-df5dd50f4a42","source":{"id":"https://openalex.org/S21752972","display_name":"Networks and Heterogeneous Media","issn_l":"1556-1801","issn":["1556-1801","1556-181X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks & Heterogeneous Media","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1702.01718","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1702.01718","pdf_url":"https://arxiv.org/pdf/1702.01718","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:2760695377","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1702.01718","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:brage.bibsys.no:11250/2578280","is_oa":true,"landing_page_url":"http://hdl.handle.net/11250/2578280","pdf_url":null,"source":{"id":"https://openalex.org/S4306401716","display_name":"Duo Research Archive (University of Oslo)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I184942183","host_organization_name":"University of Oslo","host_organization_lineage":["https://openalex.org/I184942183"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"409-421","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:doaj.org/article:61e3b484a5614f849d80b2f605eebd97","is_oa":false,"landing_page_url":"https://doaj.org/article/61e3b484a5614f849d80b2f605eebd97","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Networks and Heterogeneous Media, Vol 13, Iss 3, Pp 409-421 (2018)","raw_type":"article"},{"id":"pmh:oai:www.duo.uio.no:10852/71799","is_oa":true,"landing_page_url":"http://urn.nb.no/URN:NBN:no-74930","pdf_url":null,"source":{"id":"https://openalex.org/S4306401717","display_name":"Duo Research Archive (University of Oslo)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I184942183","host_organization_name":"University of Oslo","host_organization_lineage":["https://openalex.org/I184942183"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"1556-1801","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.1702.01718","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1702.01718","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.3934/nhm.2018018","is_oa":true,"landing_page_url":"https://doi.org/10.3934/nhm.2018018","pdf_url":"https://www.aimsciences.org/article/exportPdf?id=badc26c7-2aba-4fa7-ac1e-df5dd50f4a42","source":{"id":"https://openalex.org/S21752972","display_name":"Networks and Heterogeneous Media","issn_l":"1556-1801","issn":["1556-1801","1556-181X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks & Heterogeneous Media","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Life in Land","id":"https://metadata.un.org/sdg/15","score":0.5600000023841858}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2760695377.pdf","grobid_xml":"https://content.openalex.org/works/W2760695377.grobid-xml"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W1531416578","https://openalex.org/W1654435376","https://openalex.org/W2032966561","https://openalex.org/W2046162815","https://openalex.org/W2199554119","https://openalex.org/W2400630831","https://openalex.org/W2949557983","https://openalex.org/W2962778765"],"related_works":["https://openalex.org/W2964148485","https://openalex.org/W1974722153","https://openalex.org/W3027812325","https://openalex.org/W2083649567","https://openalex.org/W3110959819","https://openalex.org/W2022085542","https://openalex.org/W3015077048","https://openalex.org/W2065685870","https://openalex.org/W117905546","https://openalex.org/W1534622988","https://openalex.org/W2798744386","https://openalex.org/W2018887357","https://openalex.org/W2022552551","https://openalex.org/W2133986346","https://openalex.org/W3120907160","https://openalex.org/W1982774291","https://openalex.org/W1672066978","https://openalex.org/W2788109297","https://openalex.org/W2181636444","https://openalex.org/W2462991808"],"abstract_inverted_index":{"We":[0],"show":[1],"how":[2],"to":[3,14,39],"view":[4],"the":[5,17,20,40,58,67,77],"standard":[6],"Follow-the-Leader":[7],"(FtL)":[8],"model":[9,23,42],"as":[10],"a":[11,28,32],"numerical":[12,61],"method":[13],"compute":[15],"numerically":[16],"solution":[18],"of":[19,60,69,73],"Lighthill-Whitham-Richards":[21],"(LWR)":[22],"for":[24,43,63],"traffic":[25,44,47],"flow.":[26],"As":[27],"result":[29],"we":[30],"offer":[31],"simple":[33],"proof":[34,51],"that":[35],"FtL":[36],"models":[37],"converge":[38],"LWR":[41],"flow":[45],"when":[46],"becomes":[48],"dense.":[49],"The":[50],"is":[52],"based":[53],"on":[54],"techniques":[55],"used":[56],"in":[57,76],"analysis":[59],"schemes":[62],"conservation":[64,74],"laws,":[65],"and":[66,79],"equivalence":[68],"weak":[70],"entropy":[71],"solutions":[72],"laws":[75],"Lagrangian":[78],"Eulerian":[80],"formulation.":[81]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}