{"id":"https://openalex.org/W2120344322","doi":"https://doi.org/10.1109/cca.2009.5280949","title":"On dynamic optimal toll design problem with traffic-flow dependent tolls and drivers' joint route and departure time choices","display_name":"On dynamic optimal toll design problem with traffic-flow dependent tolls and drivers' joint route and departure time choices","publication_year":2009,"publication_date":"2009-07-01","ids":{"openalex":"https://openalex.org/W2120344322","doi":"https://doi.org/10.1109/cca.2009.5280949","mag":"2120344322"},"language":"en","primary_location":{"id":"doi:10.1109/cca.2009.5280949","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cca.2009.5280949","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 IEEE Control Applications, (CCA) & Intelligent Control, (ISIC)","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/A5037705191","display_name":"Kate\u0159ina Sta\u0148kov\u00e1","orcid":"https://orcid.org/0000-0002-4519-0325"},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]},{"id":"https://openalex.org/I4210124956","display_name":"GIPSA-Lab","ror":"https://ror.org/02wrme198","country_code":"FR","type":"facility","lineage":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I4210124956","https://openalex.org/I899635006","https://openalex.org/I899635006"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Katerina Stankova","raw_affiliation_strings":["NeCS (INRIA Grenoble Rh\u00f4ne-Alpes / Gipsa-lab), France"],"affiliations":[{"raw_affiliation_string":"NeCS (INRIA Grenoble Rh\u00f4ne-Alpes / Gipsa-lab), France","institution_ids":["https://openalex.org/I1326498283","https://openalex.org/I4210124956"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5037705191"],"corresponding_institution_ids":["https://openalex.org/I1326498283","https://openalex.org/I4210124956"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.263898,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"831","last_page":"836"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10698","display_name":"Transportation Planning and Optimization","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T10698","display_name":"Transportation Planning and Optimization","score":1.0,"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/T11942","display_name":"Transportation and Mobility Innovations","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2203","display_name":"Automotive 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/T10524","display_name":"Traffic control and management","score":0.9959999918937683,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/toll","display_name":"Toll","score":0.8733175992965698},{"id":"https://openalex.org/keywords/stackelberg-competition","display_name":"Stackelberg competition","score":0.8583971261978149},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6602840423583984},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4924198389053345},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4854024350643158},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4683854877948761},{"id":"https://openalex.org/keywords/traffic-flow","display_name":"Traffic flow (computer networking)","score":0.46000248193740845},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.44531822204589844},{"id":"https://openalex.org/keywords/flow-network","display_name":"Flow network","score":0.4353655278682709},{"id":"https://openalex.org/keywords/sequential-game","display_name":"Sequential game","score":0.42162367701530457},{"id":"https://openalex.org/keywords/operations-research","display_name":"Operations research","score":0.41734570264816284},{"id":"https://openalex.org/keywords/transport-engineering","display_name":"Transport engineering","score":0.4106701910495758},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.31297236680984497},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.19043010473251343},{"id":"https://openalex.org/keywords/computer-security","display_name":"Computer security","score":0.17292562127113342},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.15906161069869995},{"id":"https://openalex.org/keywords/microeconomics","display_name":"Microeconomics","score":0.15148690342903137},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.12583377957344055}],"concepts":[{"id":"https://openalex.org/C2778025104","wikidata":"https://www.wikidata.org/wiki/Q408004","display_name":"Toll","level":2,"score":0.8733175992965698},{"id":"https://openalex.org/C199510392","wikidata":"https://www.wikidata.org/wiki/Q1184602","display_name":"Stackelberg competition","level":2,"score":0.8583971261978149},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6602840423583984},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4924198389053345},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4854024350643158},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4683854877948761},{"id":"https://openalex.org/C207512268","wikidata":"https://www.wikidata.org/wiki/Q3074551","display_name":"Traffic flow (computer networking)","level":2,"score":0.46000248193740845},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.44531822204589844},{"id":"https://openalex.org/C114809511","wikidata":"https://www.wikidata.org/wiki/Q1412924","display_name":"Flow network","level":2,"score":0.4353655278682709},{"id":"https://openalex.org/C73795354","wikidata":"https://www.wikidata.org/wiki/Q287618","display_name":"Sequential game","level":3,"score":0.42162367701530457},{"id":"https://openalex.org/C42475967","wikidata":"https://www.wikidata.org/wiki/Q194292","display_name":"Operations research","level":1,"score":0.41734570264816284},{"id":"https://openalex.org/C22212356","wikidata":"https://www.wikidata.org/wiki/Q775325","display_name":"Transport engineering","level":1,"score":0.4106701910495758},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.31297236680984497},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.19043010473251343},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.17292562127113342},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.15906161069869995},{"id":"https://openalex.org/C175444787","wikidata":"https://www.wikidata.org/wiki/Q39072","display_name":"Microeconomics","level":1,"score":0.15148690342903137},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.12583377957344055},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cca.2009.5280949","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cca.2009.5280949","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 IEEE Control Applications, (CCA) & Intelligent Control, (ISIC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.699999988079071,"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W196976962","https://openalex.org/W203002175","https://openalex.org/W291003596","https://openalex.org/W334704231","https://openalex.org/W1504355632","https://openalex.org/W1538772053","https://openalex.org/W1586632706","https://openalex.org/W1592141884","https://openalex.org/W1964296933","https://openalex.org/W1975006524","https://openalex.org/W2000935698","https://openalex.org/W2001854461","https://openalex.org/W2002370449","https://openalex.org/W2017926861","https://openalex.org/W2028719465","https://openalex.org/W2031628893","https://openalex.org/W2067933667","https://openalex.org/W2075493961","https://openalex.org/W2149334733","https://openalex.org/W2150553854","https://openalex.org/W2155321250","https://openalex.org/W2158503783","https://openalex.org/W2161751035","https://openalex.org/W2172302361","https://openalex.org/W2502655619","https://openalex.org/W2727450595","https://openalex.org/W3029199577","https://openalex.org/W3124657230","https://openalex.org/W3141895774","https://openalex.org/W4390770129","https://openalex.org/W6682291812","https://openalex.org/W6685213032"],"related_works":["https://openalex.org/W2120184307","https://openalex.org/W1000249520","https://openalex.org/W1976052704","https://openalex.org/W2050614322","https://openalex.org/W2087962169","https://openalex.org/W2005538035","https://openalex.org/W1973001558","https://openalex.org/W3124508506","https://openalex.org/W1787893545","https://openalex.org/W2766186138"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"the":[3,13,19,27,51,99,114,122,132],"dynamic":[4,36,93,123],"optimal":[5],"toll":[6],"design":[7],"problem":[8,100,133],"as":[9,22,30,60],"a":[10,70,92,102,107,118],"game":[11],"of":[12,110,121],"Stackelberg":[14],"type":[15],"is":[16,89],"investigated,":[17],"with":[18],"road":[20,28,33,115],"authority":[21,34,116],"leader":[23],"and":[24,56,75,83,117],"drivers":[25,52],"on":[26,40],"network":[29],"followers.":[31],"The":[32,86],"sets":[35],"traffic-flow":[37],"dependent":[38],"tolls":[39],"some":[41],"links":[42],"in":[43,101],"order":[44],"to":[45,61],"minimize":[46,62],"its":[47],"objective":[48,111],"function,":[49],"while":[50],"choose":[53],"their":[54,63,80],"routes":[55],"departure":[57,84],"times":[58],"so":[59,105],"own":[64],"perceived":[65],"travel":[66,71],"costs,":[67],"which":[68],"include":[69],"time":[72],"component,":[73],"tolls,":[74],"penalties":[76],"for":[77,113],"deviation":[78],"from":[79],"preferred":[81],"arrival":[82],"times.":[85],"drivers'":[87],"behavior":[88],"modeled":[90],"using":[91],"user":[94],"equilibrium":[95],"model.":[96],"We":[97,129],"define":[98],"general":[103],"form":[104],"that":[106],"wide":[108,119],"class":[109,120],"functions":[112],"traffic":[124],"equilibria":[125],"can":[126],"be":[127],"employed.":[128],"also":[130],"discuss":[131],"properties.":[134]},"counts_by_year":[{"year":2015,"cited_by_count":1}],"updated_date":"2026-03-25T13:04:00.132906","created_date":"2025-10-10T00:00:00"}