{"id":"https://openalex.org/W2992173884","doi":"https://doi.org/10.1137/19m1258980","title":"Time-Continuous Instantaneous and Past Memory Routing on Traffic Networks: A Mathematical Analysis on the Basis of the Link-Delay Model","display_name":"Time-Continuous Instantaneous and Past Memory Routing on Traffic Networks: A Mathematical Analysis on the Basis of the Link-Delay Model","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2992173884","doi":"https://doi.org/10.1137/19m1258980","mag":"2992173884"},"language":"en","primary_location":{"id":"doi:10.1137/19m1258980","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1258980","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Dynamical Systems","raw_type":"journal-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/A5021116704","display_name":"Alexandre M. Bayen","orcid":"https://orcid.org/0000-0002-6697-222X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Alexandre Bayen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007232092","display_name":"Alexander Keimer","orcid":"https://orcid.org/0000-0003-3825-5853"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alexander Keimer","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-3825-5853","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025130598","display_name":"Emily Porter","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Emily Porter","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5067702863","display_name":"Michele Spinola","orcid":"https://orcid.org/0000-0003-3418-3872"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Michele Spinola","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5021116704"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0865,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.8429918,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"18","issue":"4","first_page":"2143","last_page":"2180"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10698","display_name":"Transportation Planning and Optimization","score":0.9998000264167786,"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":0.9998000264167786,"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/T10524","display_name":"Traffic control and management","score":0.9987999796867371,"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":0.9921000003814697,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/routing","display_name":"Routing (electronic design automation)","score":0.6946314573287964},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.644819438457489},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.5863540172576904},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5478042960166931},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.5237360000610352},{"id":"https://openalex.org/keywords/traffic-flow","display_name":"Traffic flow (computer networking)","score":0.5146392583847046},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.5087235569953918},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.500887393951416},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.480984091758728},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.4767904281616211},{"id":"https://openalex.org/keywords/link","display_name":"Link (geometry)","score":0.4490728974342346},{"id":"https://openalex.org/keywords/flow-network","display_name":"Flow network","score":0.4350410997867584},{"id":"https://openalex.org/keywords/static-routing","display_name":"Static routing","score":0.42223986983299255},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4064546823501587},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3677856922149658},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.31301581859588623},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.26378753781318665},{"id":"https://openalex.org/keywords/routing-protocol","display_name":"Routing protocol","score":0.2433413565158844},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.15440797805786133},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.0959022045135498}],"concepts":[{"id":"https://openalex.org/C74172769","wikidata":"https://www.wikidata.org/wiki/Q1446839","display_name":"Routing (electronic design automation)","level":2,"score":0.6946314573287964},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.644819438457489},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.5863540172576904},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5478042960166931},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.5237360000610352},{"id":"https://openalex.org/C207512268","wikidata":"https://www.wikidata.org/wiki/Q3074551","display_name":"Traffic flow (computer networking)","level":2,"score":0.5146392583847046},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.5087235569953918},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.500887393951416},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.480984091758728},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.4767904281616211},{"id":"https://openalex.org/C2778753846","wikidata":"https://www.wikidata.org/wiki/Q6554239","display_name":"Link (geometry)","level":2,"score":0.4490728974342346},{"id":"https://openalex.org/C114809511","wikidata":"https://www.wikidata.org/wiki/Q1412924","display_name":"Flow network","level":2,"score":0.4350410997867584},{"id":"https://openalex.org/C204948658","wikidata":"https://www.wikidata.org/wiki/Q1119410","display_name":"Static routing","level":4,"score":0.42223986983299255},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4064546823501587},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3677856922149658},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.31301581859588623},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.26378753781318665},{"id":"https://openalex.org/C104954878","wikidata":"https://www.wikidata.org/wiki/Q1648707","display_name":"Routing protocol","level":3,"score":0.2433413565158844},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.15440797805786133},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0959022045135498},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/19m1258980","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1258980","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Dynamical Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G468816831","display_name":null,"funder_award_id":"LE 595/30-1","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W1503349161","https://openalex.org/W1964188844","https://openalex.org/W1965154871","https://openalex.org/W1968740528","https://openalex.org/W1984256031","https://openalex.org/W1992811562","https://openalex.org/W1993802335","https://openalex.org/W2010043493","https://openalex.org/W2017011630","https://openalex.org/W2017899877","https://openalex.org/W2019482021","https://openalex.org/W2022552551","https://openalex.org/W2030745832","https://openalex.org/W2032900376","https://openalex.org/W2036171539","https://openalex.org/W2046579795","https://openalex.org/W2063806083","https://openalex.org/W2066696715","https://openalex.org/W2067124826","https://openalex.org/W2069329869","https://openalex.org/W2080967529","https://openalex.org/W2091037490","https://openalex.org/W2095478217","https://openalex.org/W2114485638","https://openalex.org/W2138137605","https://openalex.org/W2142765609","https://openalex.org/W2142803150","https://openalex.org/W2162264963","https://openalex.org/W2168446094","https://openalex.org/W2177295793","https://openalex.org/W2400172913","https://openalex.org/W2405396227","https://openalex.org/W2794954543","https://openalex.org/W2903839754"],"related_works":["https://openalex.org/W2808944898","https://openalex.org/W4254119641","https://openalex.org/W3196207352","https://openalex.org/W2951724202","https://openalex.org/W3084261076","https://openalex.org/W1996614773","https://openalex.org/W4387820098","https://openalex.org/W2576399385","https://openalex.org/W2963408011","https://openalex.org/W4236324517"],"abstract_inverted_index":{"This":[0,133],"article":[1],"presents":[2],"an":[3],"extensive":[4],"theoretical":[5],"framework":[6,29,134],"to":[7,15,31,40,104,138],"mathematically":[8],"defined":[9],"and":[10,34,69,107,125],"information-based":[11],"routing":[12,48,75,121],"operators,":[13,122],"applied":[14],"the":[16,24,27,38,41,44,52,78,95,123,130],"continuous-time":[17],"dynamic":[18],"traffic":[19,71,141],"assignment":[20],"problem.":[21],"Because":[22],"of":[23,26,37,46,61,64,86,94,120,127],"difficulty":[25],"mathematical":[28],"required":[30],"provide":[32],"existence":[33,124],"uniqueness":[35,126],"proofs":[36],"solution":[39],"problem":[42],"in":[43],"presence":[45],"a":[47,57,62,83,110,116],"operator":[49],"at":[50],"nodes,":[51],"approach":[53],"is":[54],"instantiated":[55],"with":[56],"link":[58],"model,":[59],"consisting":[60],"system":[63],"ordinary":[65],"delay":[66],"differential":[67,147],"equations":[68],"modeling":[70],"flow":[72,80,142],"macroscopically.":[73],"The":[74],"operators":[76],"distributing":[77],"incoming":[79],"can":[81,90,135],"encompass":[82],"wide":[84],"range":[85],"information":[87],"patterns,":[88],"which":[89],"include":[91],"past":[92,100],"knowledge":[93],"network":[96],"state":[97],"(statistical,":[98],"or":[99],"deterministic":[101],"information)":[102],"up":[103],"real":[105],"time":[106],"thus":[108],"satisfying":[109],"nonanticipative":[111],"character.":[112],"We":[113],"show,":[114],"for":[115],"rather":[117],"broad":[118],"class":[119],"solutions":[128],"on":[129],"full":[131],"network.":[132],"be":[136],"extended":[137],"more":[139],"advanced":[140],"models":[143],"such":[144],"as":[145],"partial":[146],"equation":[148],"models.":[149]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}