{"id":"https://openalex.org/W2122267005","doi":"https://doi.org/10.23919/acc.2004.1384731","title":"On structural properties of Helbing's gas-kinetic traffic flow model","display_name":"On structural properties of Helbing's gas-kinetic traffic flow model","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W2122267005","doi":"https://doi.org/10.23919/acc.2004.1384731","mag":"2122267005"},"language":"en","primary_location":{"id":"doi:10.23919/acc.2004.1384731","is_oa":false,"landing_page_url":"https://doi.org/10.23919/acc.2004.1384731","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2004 American Control Conference","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019114471","display_name":"Ion Necoara","orcid":"https://orcid.org/0000-0003-1102-2654"},"institutions":[{"id":"https://openalex.org/I98358874","display_name":"Delft University of Technology","ror":"https://ror.org/02e2c7k09","country_code":"NL","type":"education","lineage":["https://openalex.org/I98358874"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"I. Necoara","raw_affiliation_strings":["Delft Center for Systems and Control, Delft University of Technology, Delft, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Delft Center for Systems and Control, Delft University of Technology, Delft, The Netherlands","institution_ids":["https://openalex.org/I98358874"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026547410","display_name":"Bart De Schutter","orcid":"https://orcid.org/0000-0001-9867-6196"},"institutions":[{"id":"https://openalex.org/I98358874","display_name":"Delft University of Technology","ror":"https://ror.org/02e2c7k09","country_code":"NL","type":"education","lineage":["https://openalex.org/I98358874"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"B. De Schutter","raw_affiliation_strings":["Delft Center for Systems and Control, Delft University of Technology, Delft, The Netherlands","Technische Universiteit Delft, Delft, Zuid-Holland, NL"],"affiliations":[{"raw_affiliation_string":"Delft Center for Systems and Control, Delft University of Technology, Delft, The Netherlands","institution_ids":["https://openalex.org/I98358874"]},{"raw_affiliation_string":"Technische Universiteit Delft, Delft, Zuid-Holland, NL","institution_ids":["https://openalex.org/I98358874"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089638702","display_name":"Hans Hellendoorn","orcid":"https://orcid.org/0000-0003-1848-5694"},"institutions":[{"id":"https://openalex.org/I98358874","display_name":"Delft University of Technology","ror":"https://ror.org/02e2c7k09","country_code":"NL","type":"education","lineage":["https://openalex.org/I98358874"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"H. Hellendoorn","raw_affiliation_strings":["Delft Center for Syst. & Control, Delft Univ. of Technol., Netherlands"],"affiliations":[{"raw_affiliation_string":"Delft Center for Syst. & Control, Delft Univ. of Technol., Netherlands","institution_ids":["https://openalex.org/I98358874"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5019114471"],"corresponding_institution_ids":["https://openalex.org/I98358874"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.11101405,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"5508","last_page":"5513 vol.6"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10524","display_name":"Traffic control and management","score":0.9997000098228455,"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":0.9997000098228455,"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/T10698","display_name":"Transportation Planning and Optimization","score":0.9851999878883362,"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"}},{"id":"https://openalex.org/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9832000136375427,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/rarefaction","display_name":"Rarefaction (ecology)","score":0.7811601758003235},{"id":"https://openalex.org/keywords/discontinuity","display_name":"Discontinuity (linguistics)","score":0.6966927647590637},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.6533427238464355},{"id":"https://openalex.org/keywords/microscopic-traffic-flow-model","display_name":"Microscopic traffic flow model","score":0.6439203023910522},{"id":"https://openalex.org/keywords/shock-wave","display_name":"Shock wave","score":0.6363959312438965},{"id":"https://openalex.org/keywords/riemann-problem","display_name":"Riemann problem","score":0.6204197406768799},{"id":"https://openalex.org/keywords/traffic-flow","display_name":"Traffic flow (computer networking)","score":0.6197726726531982},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.5737156867980957},{"id":"https://openalex.org/keywords/kinetic-theory","display_name":"Kinetic theory","score":0.56539386510849},{"id":"https://openalex.org/keywords/kinetic-energy","display_name":"Kinetic energy","score":0.5417206883430481},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.5326670408248901},{"id":"https://openalex.org/keywords/shock","display_name":"Shock (circulatory)","score":0.47495126724243164},{"id":"https://openalex.org/keywords/kinematic-wave","display_name":"Kinematic wave","score":0.46320855617523193},{"id":"https://openalex.org/keywords/riemann-hypothesis","display_name":"Riemann hypothesis","score":0.45660972595214844},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.4122105538845062},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3994830846786499},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.3456680476665497},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.29547685384750366},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.27579134702682495},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.25681012868881226},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2391972839832306},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08293461799621582}],"concepts":[{"id":"https://openalex.org/C132705693","wikidata":"https://www.wikidata.org/wiki/Q7294543","display_name":"Rarefaction (ecology)","level":3,"score":0.7811601758003235},{"id":"https://openalex.org/C2777042112","wikidata":"https://www.wikidata.org/wiki/Q5281658","display_name":"Discontinuity (linguistics)","level":2,"score":0.6966927647590637},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.6533427238464355},{"id":"https://openalex.org/C205269179","wikidata":"https://www.wikidata.org/wiki/Q17144160","display_name":"Microscopic traffic flow model","level":3,"score":0.6439203023910522},{"id":"https://openalex.org/C70477161","wikidata":"https://www.wikidata.org/wiki/Q190688","display_name":"Shock wave","level":2,"score":0.6363959312438965},{"id":"https://openalex.org/C40709475","wikidata":"https://www.wikidata.org/wiki/Q2152221","display_name":"Riemann problem","level":3,"score":0.6204197406768799},{"id":"https://openalex.org/C207512268","wikidata":"https://www.wikidata.org/wiki/Q3074551","display_name":"Traffic flow (computer networking)","level":2,"score":0.6197726726531982},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.5737156867980957},{"id":"https://openalex.org/C19979193","wikidata":"https://www.wikidata.org/wiki/Q25100325","display_name":"Kinetic theory","level":2,"score":0.56539386510849},{"id":"https://openalex.org/C135889238","wikidata":"https://www.wikidata.org/wiki/Q46276","display_name":"Kinetic energy","level":2,"score":0.5417206883430481},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5326670408248901},{"id":"https://openalex.org/C2781300812","wikidata":"https://www.wikidata.org/wiki/Q178061","display_name":"Shock (circulatory)","level":2,"score":0.47495126724243164},{"id":"https://openalex.org/C43978264","wikidata":"https://www.wikidata.org/wiki/Q6410695","display_name":"Kinematic wave","level":3,"score":0.46320855617523193},{"id":"https://openalex.org/C199479865","wikidata":"https://www.wikidata.org/wiki/Q205966","display_name":"Riemann hypothesis","level":2,"score":0.45660972595214844},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4122105538845062},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3994830846786499},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.3456680476665497},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.29547685384750366},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.27579134702682495},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.25681012868881226},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2391972839832306},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08293461799621582},{"id":"https://openalex.org/C50477045","wikidata":"https://www.wikidata.org/wiki/Q1444790","display_name":"Surface runoff","level":2,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C126322002","wikidata":"https://www.wikidata.org/wiki/Q11180","display_name":"Internal medicine","level":1,"score":0.0},{"id":"https://openalex.org/C53565203","wikidata":"https://www.wikidata.org/wiki/Q17146659","display_name":"Species richness","level":2,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C176715033","wikidata":"https://www.wikidata.org/wiki/Q2080768","display_name":"Traffic generation model","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.23919/acc.2004.1384731","is_oa":false,"landing_page_url":"https://doi.org/10.23919/acc.2004.1384731","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2004 American Control Conference","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","score":0.8500000238418579,"display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W32452329","https://openalex.org/W63101075","https://openalex.org/W586537409","https://openalex.org/W1583468962","https://openalex.org/W1583892864","https://openalex.org/W1584201434","https://openalex.org/W1601100443","https://openalex.org/W1982463111","https://openalex.org/W1986788497","https://openalex.org/W1987425339","https://openalex.org/W2013271219","https://openalex.org/W2014346895","https://openalex.org/W2025409601","https://openalex.org/W2034976587","https://openalex.org/W2069750330","https://openalex.org/W2074423942","https://openalex.org/W2086453056","https://openalex.org/W2093921901","https://openalex.org/W2094167530","https://openalex.org/W2095797625","https://openalex.org/W2112548197","https://openalex.org/W2122803663","https://openalex.org/W2168901008","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2800583016","https://openalex.org/W1992723975","https://openalex.org/W1979469089","https://openalex.org/W2902100385","https://openalex.org/W2921770740","https://openalex.org/W4315706594","https://openalex.org/W2120510379","https://openalex.org/W3207219416","https://openalex.org/W2147173065","https://openalex.org/W4297360044"],"abstract_inverted_index":{"There":[0],"exist":[1],"several":[2],"types":[3],"of":[4,10,27,40,50,102,118,133],"models":[5],"that":[6,44,115],"describe":[7],"the":[8,33,45,53,62,68,74,85,97,100,103,111,116,127,134],"evolution":[9],"traffic":[11,30,37],"flow":[12,31,38,124,141],"on":[13,23,130],"freeways":[14],"and":[15,61,80,91,123],"urban":[16],"roads.":[17],"In":[18],"this":[19,108,119],"paper,":[20],"we":[21],"focus":[22],"some":[24],"structural":[25],"properties":[26],"one":[28,57,64],"particular":[29],"model:":[32],"macroscopic,":[34],"second-order":[35],"gas-kinetic":[36],"model":[39,46,109],"Helbing.":[41],"We":[42,94],"show":[43],"has":[47],"two":[48],"families":[49],"characteristics":[51],"for":[52,99],"shock":[54],"wave":[55],"solutions:":[56],"characteristic":[58,76,87],"is":[59,65],"slower":[60,75],"other":[63],"faster":[66,86],"than":[67],"average":[69],"vehicle":[70],"speed.":[71],"Corresponding":[72],"to":[73,84,139],"there":[77,88],"are":[78,89],"1-shocks":[79],"1-rarefaction":[81],"waves,":[82],"corresponding":[83],"2-shocks":[90],"2-rarefaction":[92],"waves.":[93],"also":[95],"derive":[96],"formulas":[98],"solution":[101,117],"Riemann":[104],"problem":[105,120],"associated":[106],"with":[107,121],"in":[110,126],"equilibrium":[112],"case,":[113],"proving":[114],"density":[122,143],"non-negative":[125],"initial":[128],"condition":[129],"either":[131],"side":[132],"discontinuity":[135],"cannot":[136],"give":[137],"rise":[138],"negative":[140],"or":[142],"later":[144],"on.":[145]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}