{"id":"https://openalex.org/W2049787545","doi":"https://doi.org/10.1080/01969720590897198","title":"MAX-PLUS ALGEBRA MODELING FOR A PUBLIC TRANSPORT SYSTEM","display_name":"MAX-PLUS ALGEBRA MODELING FOR A PUBLIC TRANSPORT SYSTEM","publication_year":2005,"publication_date":"2005-01-18","ids":{"openalex":"https://openalex.org/W2049787545","doi":"https://doi.org/10.1080/01969720590897198","mag":"2049787545"},"language":"en","primary_location":{"id":"doi:10.1080/01969720590897198","is_oa":false,"landing_page_url":"https://doi.org/10.1080/01969720590897198","pdf_url":null,"source":{"id":"https://openalex.org/S117436046","display_name":"Cybernetics & Systems","issn_l":"0196-9722","issn":["0196-9722","1087-6553"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Cybernetics and 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/A5070461488","display_name":"Ahmed Nait\u2010Sidi\u2010Moh","orcid":"https://orcid.org/0000-0002-2297-8603"},"institutions":[{"id":"https://openalex.org/I37553959","display_name":"Universit\u00e9 de technologie de belfort-montb\u00e9liard","ror":"https://ror.org/05bn3m307","country_code":"FR","type":"education","lineage":["https://openalex.org/I37553959"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"A. NAIT-SIDI-MOH","raw_affiliation_strings":["Laboratoire Syst\u00e8mes et Transports , University of Technology of Belfort\u2013Montbe\u00b4liard , Belfort cedex, France"],"affiliations":[{"raw_affiliation_string":"Laboratoire Syst\u00e8mes et Transports , University of Technology of Belfort\u2013Montbe\u00b4liard , Belfort cedex, France","institution_ids":["https://openalex.org/I37553959"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017401001","display_name":"Mari\u00e9-Ange Manier","orcid":"https://orcid.org/0000-0002-7958-5210"},"institutions":[{"id":"https://openalex.org/I37553959","display_name":"Universit\u00e9 de technologie de belfort-montb\u00e9liard","ror":"https://ror.org/05bn3m307","country_code":"FR","type":"education","lineage":["https://openalex.org/I37553959"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"M. -A. MANIER","raw_affiliation_strings":["Laboratoire Syst\u00e8mes et Transports , University of Technology of Belfort\u2013Montbe\u00b4liard , Belfort cedex, France"],"affiliations":[{"raw_affiliation_string":"Laboratoire Syst\u00e8mes et Transports , University of Technology of Belfort\u2013Montbe\u00b4liard , Belfort cedex, France","institution_ids":["https://openalex.org/I37553959"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090946345","display_name":"Abdellah El Moudni","orcid":"https://orcid.org/0000-0002-4516-7168"},"institutions":[{"id":"https://openalex.org/I37553959","display_name":"Universit\u00e9 de technologie de belfort-montb\u00e9liard","ror":"https://ror.org/05bn3m307","country_code":"FR","type":"education","lineage":["https://openalex.org/I37553959"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"A. El Moudni","raw_affiliation_strings":["Laboratoire Syst\u00e8mes et Transports , University of Technology of Belfort\u2013Montbe\u00b4liard , Belfort cedex, France"],"affiliations":[{"raw_affiliation_string":"Laboratoire Syst\u00e8mes et Transports , University of Technology of Belfort\u2013Montbe\u00b4liard , Belfort cedex, France","institution_ids":["https://openalex.org/I37553959"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022459090","display_name":"Herv\u00e9 Manier","orcid":"https://orcid.org/0000-0001-8246-2572"},"institutions":[{"id":"https://openalex.org/I37553959","display_name":"Universit\u00e9 de technologie de belfort-montb\u00e9liard","ror":"https://ror.org/05bn3m307","country_code":"FR","type":"education","lineage":["https://openalex.org/I37553959"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"H. MANIER","raw_affiliation_strings":["Laboratoire Syst\u00e8mes et Transports , University of Technology of Belfort\u2013Montbe\u00b4liard , Belfort cedex, France"],"affiliations":[{"raw_affiliation_string":"Laboratoire Syst\u00e8mes et Transports , University of Technology of Belfort\u2013Montbe\u00b4liard , Belfort cedex, France","institution_ids":["https://openalex.org/I37553959"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5070461488"],"corresponding_institution_ids":["https://openalex.org/I37553959"],"apc_list":null,"apc_paid":null,"fwci":1.7568,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.83881975,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"36","issue":"2","first_page":"165","last_page":"180"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11125","display_name":"Petri Nets in System Modeling","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11125","display_name":"Petri Nets in System Modeling","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10703","display_name":"Business Process Modeling and Analysis","score":0.9943000078201294,"subfield":{"id":"https://openalex.org/subfields/1404","display_name":"Management Information Systems"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11195","display_name":"Simulation Techniques and Applications","score":0.9905999898910522,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/petri-net","display_name":"Petri net","score":0.9147437810897827},{"id":"https://openalex.org/keywords/algebraic-structure","display_name":"Algebraic structure","score":0.6515025496482849},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.626741886138916},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5889528393745422},{"id":"https://openalex.org/keywords/graph-algebra","display_name":"Graph algebra","score":0.5773871541023254},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.574318528175354},{"id":"https://openalex.org/keywords/stochastic-petri-net","display_name":"Stochastic Petri net","score":0.5654107332229614},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5480868220329285},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.476523756980896},{"id":"https://openalex.org/keywords/event","display_name":"Event (particle physics)","score":0.46300461888313293},{"id":"https://openalex.org/keywords/net","display_name":"Net (polyhedron)","score":0.4314326047897339},{"id":"https://openalex.org/keywords/petri-dish","display_name":"Petri dish","score":0.4261839985847473},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.2539202570915222},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.25388002395629883},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.09910634160041809},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.07803595066070557},{"id":"https://openalex.org/keywords/voltage-graph","display_name":"Voltage graph","score":0.05649617314338684}],"concepts":[{"id":"https://openalex.org/C38677869","wikidata":"https://www.wikidata.org/wiki/Q724168","display_name":"Petri net","level":2,"score":0.9147437810897827},{"id":"https://openalex.org/C182419690","wikidata":"https://www.wikidata.org/wiki/Q205464","display_name":"Algebraic structure","level":2,"score":0.6515025496482849},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.626741886138916},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5889528393745422},{"id":"https://openalex.org/C45961005","wikidata":"https://www.wikidata.org/wiki/Q5597072","display_name":"Graph algebra","level":5,"score":0.5773871541023254},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.574318528175354},{"id":"https://openalex.org/C197551870","wikidata":"https://www.wikidata.org/wiki/Q7617809","display_name":"Stochastic Petri net","level":3,"score":0.5654107332229614},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5480868220329285},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.476523756980896},{"id":"https://openalex.org/C2779662365","wikidata":"https://www.wikidata.org/wiki/Q5416694","display_name":"Event (particle physics)","level":2,"score":0.46300461888313293},{"id":"https://openalex.org/C14166107","wikidata":"https://www.wikidata.org/wiki/Q253829","display_name":"Net (polyhedron)","level":2,"score":0.4314326047897339},{"id":"https://openalex.org/C146763376","wikidata":"https://www.wikidata.org/wiki/Q81714","display_name":"Petri dish","level":2,"score":0.4261839985847473},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.2539202570915222},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.25388002395629883},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.09910634160041809},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.07803595066070557},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.05649617314338684},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/01969720590897198","is_oa":false,"landing_page_url":"https://doi.org/10.1080/01969720590897198","pdf_url":null,"source":{"id":"https://openalex.org/S117436046","display_name":"Cybernetics & Systems","issn_l":"0196-9722","issn":["0196-9722","1087-6553"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Cybernetics and Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W114286715","https://openalex.org/W1983700630","https://openalex.org/W1991466857","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W1543378523","https://openalex.org/W1491709828","https://openalex.org/W2916743419","https://openalex.org/W2381491984","https://openalex.org/W2257573499","https://openalex.org/W1980200158","https://openalex.org/W1513546254","https://openalex.org/W2148229336","https://openalex.org/W2091203523","https://openalex.org/W2125164140"],"abstract_inverted_index":{"Abstract":[0],"This":[1],"paper":[2],"discusses":[3],"the":[4,25,41],"use":[5],"of":[6,24,43,73],"Petri":[7,55,75],"net":[8,56,76],"languages,":[9],"particularly,":[10],"its":[11],"subclass":[12],"\u201ctimed":[13],"event":[14],"graph\u201d":[15],"for":[16],"modeling":[17,42],"a":[18,30,45,54],"public":[19],"transport":[20],"network.":[21],"The":[22,71],"behavior":[23,72],"network":[26,46,64],"is":[27,47,81,85],"described":[28],"by":[29],"particular":[31],"algebraic":[32],"structure":[33],"called":[34],"(max,":[35,78],"+)":[36,79],"algebra.":[37],"We":[38,52],"show":[39],"that":[40],"such":[44],"possible":[48],"under":[49],"some":[50,59],"hypotheses.":[51],"propose":[53],"tool":[57],"with":[58],"conflicts":[60],"to":[61,87],"model":[62],"this":[63,74],"without":[65],"taking":[66],"into":[67],"account":[68],"these":[69],"assumptions.":[70],"in":[77],"algebra":[80],"presented.":[82],"An":[83],"example":[84],"given":[86],"illustrate":[88],"our":[89],"results.":[90]},"counts_by_year":[{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}