{"id":"https://openalex.org/W1589945377","doi":"https://doi.org/10.1007/3-540-63139-9_36","title":"Efficient handling of Phase-type distributions in generalized stochastic Petri nets","display_name":"Efficient handling of Phase-type distributions in generalized stochastic Petri nets","publication_year":1997,"publication_date":"1997-01-01","ids":{"openalex":"https://openalex.org/W1589945377","doi":"https://doi.org/10.1007/3-540-63139-9_36","mag":"1589945377"},"language":"en","primary_location":{"id":"doi:10.1007/3-540-63139-9_36","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-63139-9_36","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://basepub.dauphine.fr/handle/123456789/5616","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5006881035","display_name":"Serge Haddad","orcid":"https://orcid.org/0000-0002-1759-1201"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I56435720","display_name":"Universit\u00e9 Paris Dauphine-PSL","ror":"https://ror.org/052bz7812","country_code":"FR","type":"education","lineage":["https://openalex.org/I2746051580","https://openalex.org/I56435720"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Serge Haddad","raw_affiliation_strings":["LAMSADE-URA CNRS 825, Universit\u00e9 Paris Dauphine, Paris, France","Universite paris dauphine"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LAMSADE-URA CNRS 825, Universit\u00e9 Paris Dauphine, Paris, France","institution_ids":["https://openalex.org/I56435720","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"Universite paris dauphine","institution_ids":["https://openalex.org/I56435720"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061570881","display_name":"Patrice Moreaux","orcid":null},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I56435720","display_name":"Universit\u00e9 Paris Dauphine-PSL","ror":"https://ror.org/052bz7812","country_code":"FR","type":"education","lineage":["https://openalex.org/I2746051580","https://openalex.org/I56435720"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Patrice Moreaux","raw_affiliation_strings":["LAMSADE-URA CNRS 825, Universit\u00e9 Paris Dauphine, Paris, France","Universite paris dauphine"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LAMSADE-URA CNRS 825, Universit\u00e9 Paris Dauphine, Paris, France","institution_ids":["https://openalex.org/I56435720","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"Universite paris dauphine","institution_ids":["https://openalex.org/I56435720"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111495052","display_name":"Giovanni Chiola","orcid":null},"institutions":[{"id":"https://openalex.org/I83816512","display_name":"University of Genoa","ror":"https://ror.org/0107c5v14","country_code":"IT","type":"education","lineage":["https://openalex.org/I83816512"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Giovanni Chiola","raw_affiliation_strings":["DISI, Universit\u00e0 di Genova, Genova, Italy","Universit\u00e0 di Genova"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"DISI, Universit\u00e0 di Genova, Genova, Italy","institution_ids":["https://openalex.org/I83816512"]},{"raw_affiliation_string":"Universit\u00e0 di Genova","institution_ids":["https://openalex.org/I83816512"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":1.0349,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.76374903,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"175","last_page":"194"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11125","display_name":"Petri Nets in System Modeling","score":1.0,"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":1.0,"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":0.9987999796867371,"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":0.9940000176429749,"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/stochastic-petri-net","display_name":"Stochastic Petri net","score":0.7632511854171753},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.6433824300765991},{"id":"https://openalex.org/keywords/petri-net","display_name":"Petri net","score":0.5996994376182556},{"id":"https://openalex.org/keywords/generator","display_name":"Generator (circuit theory)","score":0.5704056620597839},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5136103630065918},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5064893960952759},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.5002717971801758},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49286460876464844},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.4733445942401886},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.47128525376319885},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45652642846107483},{"id":"https://openalex.org/keywords/state-space","display_name":"State space","score":0.4518142342567444},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4349965751171112},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.4228353500366211},{"id":"https://openalex.org/keywords/expression","display_name":"Expression (computer science)","score":0.419017493724823},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.37425094842910767},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.25708675384521484},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2223978340625763},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.16758152842521667},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0968782901763916}],"concepts":[{"id":"https://openalex.org/C197551870","wikidata":"https://www.wikidata.org/wiki/Q7617809","display_name":"Stochastic Petri net","level":3,"score":0.7632511854171753},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.6433824300765991},{"id":"https://openalex.org/C38677869","wikidata":"https://www.wikidata.org/wiki/Q724168","display_name":"Petri net","level":2,"score":0.5996994376182556},{"id":"https://openalex.org/C2780992000","wikidata":"https://www.wikidata.org/wiki/Q17016113","display_name":"Generator (circuit theory)","level":3,"score":0.5704056620597839},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5136103630065918},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5064893960952759},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5002717971801758},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49286460876464844},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.4733445942401886},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.47128525376319885},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45652642846107483},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.4518142342567444},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4349965751171112},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.4228353500366211},{"id":"https://openalex.org/C90559484","wikidata":"https://www.wikidata.org/wiki/Q778379","display_name":"Expression (computer science)","level":2,"score":0.419017493724823},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.37425094842910767},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.25708675384521484},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2223978340625763},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.16758152842521667},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0968782901763916},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/3-540-63139-9_36","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-63139-9_36","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.22.9921","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.22.9921","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.lamsade.dauphine.fr/~haddad/articles/97-APN/97-APN.ps.gz","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.40.425","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.40.425","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.lamsade.dauphine.fr/~moreaux/phgspn/atpn97.ps.gz","raw_type":"text"},{"id":"pmh:oai:basepub.dauphine.fr:123456789/5616","is_oa":true,"landing_page_url":"https://basepub.dauphine.fr/handle/123456789/5616","pdf_url":null,"source":{"id":"https://openalex.org/S4306401007","display_name":"Base Institutionnelle de Recherche de l'universit\u00e9 Paris-Dauphine (BIRD) (University Paris-Dauphine)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I102197404","host_organization_name":"Universit\u00e9 Paris-Sud","host_organization_lineage":["https://openalex.org/I102197404"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Communication / Conf\u00e9rence"}],"best_oa_location":{"id":"pmh:oai:basepub.dauphine.fr:123456789/5616","is_oa":true,"landing_page_url":"https://basepub.dauphine.fr/handle/123456789/5616","pdf_url":null,"source":{"id":"https://openalex.org/S4306401007","display_name":"Base Institutionnelle de Recherche de l'universit\u00e9 Paris-Dauphine (BIRD) (University Paris-Dauphine)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I102197404","host_organization_name":"Universit\u00e9 Paris-Sud","host_organization_lineage":["https://openalex.org/I102197404"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Communication / Conf\u00e9rence"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W6366938","https://openalex.org/W49450320","https://openalex.org/W95750126","https://openalex.org/W1481465901","https://openalex.org/W1502246203","https://openalex.org/W1534876514","https://openalex.org/W1537544083","https://openalex.org/W1537624148","https://openalex.org/W1575092567","https://openalex.org/W2078423317","https://openalex.org/W2079636926","https://openalex.org/W2093419235","https://openalex.org/W2097006422","https://openalex.org/W2098506306","https://openalex.org/W2117886447","https://openalex.org/W2147607210","https://openalex.org/W2150951765","https://openalex.org/W2154602821","https://openalex.org/W2161584651","https://openalex.org/W2293878396","https://openalex.org/W2561908894","https://openalex.org/W3026026050","https://openalex.org/W4210740339","https://openalex.org/W4243290645","https://openalex.org/W6603903687","https://openalex.org/W6991927141"],"related_works":["https://openalex.org/W1543378523","https://openalex.org/W2016850136","https://openalex.org/W1491709828","https://openalex.org/W2916743419","https://openalex.org/W1557425998","https://openalex.org/W2381491984","https://openalex.org/W1590870019","https://openalex.org/W2257573499","https://openalex.org/W2154785561","https://openalex.org/W2062463517"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
