{"id":"https://openalex.org/W2309849535","doi":"https://doi.org/10.1109/tsmca.2009.2019867","title":"A Dioid Model for Invariant Resource Sharing Problems","display_name":"A Dioid Model for Invariant Resource Sharing Problems","publication_year":2009,"publication_date":"2009-05-27","ids":{"openalex":"https://openalex.org/W2309849535","doi":"https://doi.org/10.1109/tsmca.2009.2019867","mag":"2309849535"},"language":"en","primary_location":{"id":"doi:10.1109/tsmca.2009.2019867","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsmca.2009.2019867","pdf_url":null,"source":{"id":"https://openalex.org/S4210201610","display_name":"IEEE Transactions on Systems Man and Cybernetics - Part A Systems and Humans","issn_l":"1083-4427","issn":["1083-4427","1558-2426"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans","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/A5076292567","display_name":"Aur\u00e9lien Corr\u00e9\u00efa","orcid":null},"institutions":[{"id":"https://openalex.org/I4210142752","display_name":"Hitachi (France)","ror":"https://ror.org/04yk3c231","country_code":"FR","type":"company","lineage":["https://openalex.org/I4210142752","https://openalex.org/I65143321"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"A. Correia","raw_affiliation_strings":["Hitachi Europe SAS, Velizy, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Hitachi Europe SAS, Velizy, France","institution_ids":["https://openalex.org/I4210142752"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087519995","display_name":"Abdeljalil Abbas\u2010Turki","orcid":"https://orcid.org/0000-0002-4443-0542"},"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. Abbas-Turki","raw_affiliation_strings":["Universit\u00e9 de Technologie de Belfort Montbeliard, Belfort, France","Universit\u00e9 de Technologie de Belfort Montb\u00e9liard, Belfort Cedex, France#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 de Technologie de Belfort Montbeliard, Belfort, France","institution_ids":["https://openalex.org/I37553959"]},{"raw_affiliation_string":"Universit\u00e9 de Technologie de Belfort Montb\u00e9liard, Belfort Cedex, France#TAB#","institution_ids":["https://openalex.org/I37553959"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045659519","display_name":"Rachid Bouyekhf","orcid":null},"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":"R. Bouyekhf","raw_affiliation_strings":["Universit\u00e9 de Technologie de Belfort Montbeliard, Belfort, France","Universit\u00e9 de Technologie de Belfort Montb\u00e9liard, Belfort Cedex, France#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 de Technologie de Belfort Montbeliard, Belfort, France","institution_ids":["https://openalex.org/I37553959"]},{"raw_affiliation_string":"Universit\u00e9 de Technologie de Belfort Montb\u00e9liard, Belfort Cedex, France#TAB#","institution_ids":["https://openalex.org/I37553959"]}]},{"author_position":"last","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":["Universit\u00e9 de Technologie de Belfort Montbeliard, Belfort, France","Universit\u00e9 de Technologie de Belfort Montb\u00e9liard, Belfort Cedex, France#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 de Technologie de Belfort Montbeliard, Belfort, France","institution_ids":["https://openalex.org/I37553959"]},{"raw_affiliation_string":"Universit\u00e9 de Technologie de Belfort Montb\u00e9liard, Belfort Cedex, France#TAB#","institution_ids":["https://openalex.org/I37553959"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.7774,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.90812371,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"39","issue":"4","first_page":"770","last_page":"781"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11125","display_name":"Petri Nets in System Modeling","score":0.9998999834060669,"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":0.9998999834060669,"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/T10142","display_name":"Formal Methods in Verification","score":0.9983000159263611,"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/T10933","display_name":"Real-Time Systems Scheduling","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.8056538105010986},{"id":"https://openalex.org/keywords/shared-resource","display_name":"Shared resource","score":0.6253359913825989},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.6012298464775085},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5608643889427185},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5581672787666321},{"id":"https://openalex.org/keywords/resource","display_name":"Resource (disambiguation)","score":0.5148802995681763},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5047742128372192},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.49563276767730713},{"id":"https://openalex.org/keywords/event","display_name":"Event (particle physics)","score":0.44011390209198},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4194289445877075},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32314497232437134},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2853441834449768},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.24809718132019043},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.0759689211845398}],"concepts":[{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.8056538105010986},{"id":"https://openalex.org/C51332947","wikidata":"https://www.wikidata.org/wiki/Q1172305","display_name":"Shared resource","level":2,"score":0.6253359913825989},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6012298464775085},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5608643889427185},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5581672787666321},{"id":"https://openalex.org/C206345919","wikidata":"https://www.wikidata.org/wiki/Q20380951","display_name":"Resource (disambiguation)","level":2,"score":0.5148802995681763},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5047742128372192},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.49563276767730713},{"id":"https://openalex.org/C2779662365","wikidata":"https://www.wikidata.org/wiki/Q5416694","display_name":"Event (particle physics)","level":2,"score":0.44011390209198},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4194289445877075},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32314497232437134},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2853441834449768},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.24809718132019043},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.0759689211845398},{"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/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tsmca.2009.2019867","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsmca.2009.2019867","pdf_url":null,"source":{"id":"https://openalex.org/S4210201610","display_name":"IEEE Transactions on Systems Man and Cybernetics - Part A Systems and Humans","issn_l":"1083-4427","issn":["1083-4427","1558-2426"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Decent work and economic growth","score":0.4699999988079071,"id":"https://metadata.un.org/sdg/8"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W658511890","https://openalex.org/W1488422606","https://openalex.org/W1513496693","https://openalex.org/W1533742649","https://openalex.org/W1553057651","https://openalex.org/W1929012437","https://openalex.org/W1962985716","https://openalex.org/W1969974611","https://openalex.org/W1979885075","https://openalex.org/W1991466857","https://openalex.org/W1996109622","https://openalex.org/W1996305369","https://openalex.org/W2024085737","https://openalex.org/W2151008975","https://openalex.org/W2154634540","https://openalex.org/W2613020344","https://openalex.org/W3044911583","https://openalex.org/W3137220996","https://openalex.org/W4241496298","https://openalex.org/W4250661196"],"related_works":["https://openalex.org/W2504004674","https://openalex.org/W1595229445","https://openalex.org/W2498744856","https://openalex.org/W4390482104","https://openalex.org/W322408318","https://openalex.org/W149041114","https://openalex.org/W2963177394","https://openalex.org/W1965815883","https://openalex.org/W763418848","https://openalex.org/W2024638892"],"abstract_inverted_index":{"<para":[0],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[1],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[2],"This":[3,98],"paper":[4,99],"proposes":[5],"a":[6,27,64],"model":[7,84],"for":[8,19],"invariant":[9],"resource":[10,49,79],"sharing":[11,50],"problems":[12],"in":[13,51],"dioid":[14],"algebra.":[15],"A":[16],"strong":[17],"motivation":[18],"investigating":[20],"the":[21,24,57,78,90,94],"issue":[22],"is":[23],"absence":[25],"of":[26,93,104,113],"general":[28],"systematic":[29],"technique":[30],"which":[31,74],"can":[32,60],"be":[33,61],"used":[34],"to":[35,47,88],"tackle":[36],"these":[37],"problems.":[38],"<formula":[39,69],"formulatype=\"inline\"><tex":[40,70],"Notation=\"TeX\">$(\\min,":[41,71],"+)$</tex></formula>":[42],"constraints":[43],"have":[44],"been":[45,86],"developed":[46],"handle":[48],"Discrete-Event":[52],"Dynamic":[53],"Systems.":[54],"In":[55],"particular,":[56],"part":[58],"that":[59,106],"modeled":[62,108],"by":[63,77,111],"Timed":[65],"Event":[66],"Graph":[67],"induce":[68],"+)$</tex></formula>-linear":[72],"equations":[73],"are":[75,107],"constrained":[76],"availability.":[80],"The":[81],"proposed":[82],"algebraic":[83],"has":[85],"proved":[87],"describe":[89],"actual":[91],"behavior":[92],"systems":[95,105],"dealt":[96],"with.":[97],"will":[100],"show":[101],"two":[102],"examples":[103],"and":[109],"controlled":[110],"means":[112],"this":[114],"approach.":[115],"</para>":[116]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2020,"cited_by_count":4},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
