{"id":"https://openalex.org/W1518839214","doi":"https://doi.org/10.1007/3-540-68061-6_20","title":"Structured Characterization of the Markov Chain of Phase-Type SPN","display_name":"Structured Characterization of the Markov Chain of Phase-Type SPN","publication_year":1998,"publication_date":"1998-01-01","ids":{"openalex":"https://openalex.org/W1518839214","doi":"https://doi.org/10.1007/3-540-68061-6_20","mag":"1518839214"},"language":"en","primary_location":{"id":"doi:10.1007/3-540-68061-6_20","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-68061-6_20","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/123456789/5688","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5084007973","display_name":"Susanna Donatelli","orcid":"https://orcid.org/0000-0002-0911-8457"},"institutions":[{"id":"https://openalex.org/I55143463","display_name":"University of Turin","ror":"https://ror.org/048tbm396","country_code":"IT","type":"education","lineage":["https://openalex.org/I55143463"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Susanna Donatelli","raw_affiliation_strings":["Dipartimento di Informatica, Universit\u00e0 di Torino, Torino","Universit\u00e0 di Torino"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Informatica, Universit\u00e0 di Torino, Torino","institution_ids":["https://openalex.org/I55143463"]},{"raw_affiliation_string":"Universit\u00e0 di Torino","institution_ids":["https://openalex.org/I55143463"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006881035","display_name":"Serge Haddad","orcid":"https://orcid.org/0000-0002-1759-1201"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Serge Haddad","raw_affiliation_strings":["LAMSADE, France","LAMSADE"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LAMSADE, France","institution_ids":[]},{"raw_affiliation_string":"LAMSADE","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061570881","display_name":"Patrice Moreaux","orcid":null},"institutions":[{"id":"https://openalex.org/I4400008916","display_name":"REGARDS Recherches en \u00c9conomie Gestion AgroRessources Durabilit\u00e9 Sant\u00e9","ror":"https://ror.org/03nr3p279","country_code":"FR","type":"facility","lineage":["https://openalex.org/I4400008916","https://openalex.org/I96226040"]},{"id":"https://openalex.org/I96226040","display_name":"Universit\u00e9 de Reims Champagne-Ardenne","ror":"https://ror.org/03hypw319","country_code":"FR","type":"education","lineage":["https://openalex.org/I96226040"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Patrice Moreaux","raw_affiliation_strings":["LAMSADE, France","Universit\u00e9 de Reims Champagne-Ardenne, Reims","Universit\u00e9 de Reims Champagne-Ardenne","LAMSADE"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LAMSADE, France","institution_ids":[]},{"raw_affiliation_string":"Universit\u00e9 de Reims Champagne-Ardenne, Reims","institution_ids":["https://openalex.org/I96226040"]},{"raw_affiliation_string":"Universit\u00e9 de Reims Champagne-Ardenne","institution_ids":["https://openalex.org/I96226040","https://openalex.org/I4400008916"]},{"raw_affiliation_string":"LAMSADE","institution_ids":[]}]}],"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":1.0152,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.73183521,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"243","last_page":"254"},"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":0.9973000288009644,"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":0.9940999746322632,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/stochastic-petri-net","display_name":"Stochastic Petri net","score":0.7376542091369629},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.7262502312660217},{"id":"https://openalex.org/keywords/generator","display_name":"Generator (circuit theory)","score":0.6208364963531494},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5735904574394226},{"id":"https://openalex.org/keywords/state-space","display_name":"State space","score":0.5467438101768494},{"id":"https://openalex.org/keywords/infinitesimal","display_name":"Infinitesimal","score":0.5395926237106323},{"id":"https://openalex.org/keywords/characterization","display_name":"Characterization (materials science)","score":0.5022802352905273},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.4926798939704895},{"id":"https://openalex.org/keywords/petri-net","display_name":"Petri net","score":0.486774206161499},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.4791816473007202},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.45265620946884155},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.43485569953918457},{"id":"https://openalex.org/keywords/generator-matrix","display_name":"Generator matrix","score":0.4252910017967224},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.35334038734436035},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3452046513557434},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2820472717285156},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.10553005337715149},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09342020750045776}],"concepts":[{"id":"https://openalex.org/C197551870","wikidata":"https://www.wikidata.org/wiki/Q7617809","display_name":"Stochastic Petri net","level":3,"score":0.7376542091369629},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.7262502312660217},{"id":"https://openalex.org/C2780992000","wikidata":"https://www.wikidata.org/wiki/Q17016113","display_name":"Generator (circuit theory)","level":3,"score":0.6208364963531494},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5735904574394226},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.5467438101768494},{"id":"https://openalex.org/C91229774","wikidata":"https://www.wikidata.org/wiki/Q193885","display_name":"Infinitesimal","level":2,"score":0.5395926237106323},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.5022802352905273},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.4926798939704895},{"id":"https://openalex.org/C38677869","wikidata":"https://www.wikidata.org/wiki/Q724168","display_name":"Petri net","level":2,"score":0.486774206161499},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4791816473007202},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.45265620946884155},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.43485569953918457},{"id":"https://openalex.org/C1842014","wikidata":"https://www.wikidata.org/wiki/Q1502046","display_name":"Generator matrix","level":3,"score":0.4252910017967224},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.35334038734436035},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3452046513557434},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2820472717285156},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.10553005337715149},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09342020750045776},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"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/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.0},{"id":"https://openalex.org/C171250308","wikidata":"https://www.wikidata.org/wiki/Q11468","display_name":"Nanotechnology","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/3-540-68061-6_20","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-68061-6_20","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:basepub.dauphine.fr:123456789/5688","is_oa":true,"landing_page_url":"https://basepub.dauphine.fr/handle/123456789/5688","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:123456789/5688","is_oa":true,"landing_page_url":"https://basepub.dauphine.fr/handle/123456789/5688","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1481465901","https://openalex.org/W1518839214","https://openalex.org/W1534876514","https://openalex.org/W1537544083","https://openalex.org/W1537624148","https://openalex.org/W1575092567","https://openalex.org/W1589945377","https://openalex.org/W1607116124","https://openalex.org/W1987249037","https://openalex.org/W2097006422","https://openalex.org/W2118129665","https://openalex.org/W2126835091","https://openalex.org/W2150951765","https://openalex.org/W2154049364","https://openalex.org/W2154602821","https://openalex.org/W2161584651","https://openalex.org/W2163831082","https://openalex.org/W2561908894","https://openalex.org/W2916064013","https://openalex.org/W4232058373","https://openalex.org/W4243290645"],"related_works":["https://openalex.org/W1543378523","https://openalex.org/W2081678986","https://openalex.org/W1491709828","https://openalex.org/W2916743419","https://openalex.org/W2381491984","https://openalex.org/W2257573499","https://openalex.org/W2148229336","https://openalex.org/W1980200158","https://openalex.org/W1513546254","https://openalex.org/W2062463517"],"abstract_inverted_index":null,"counts_by_year":[{"year":2017,"cited_by_count":3},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}