{"id":"https://openalex.org/W2084471687","doi":"https://doi.org/10.1016/0166-5316(91)90016-v","title":"Markovian Petri Net protocols with product form solution","display_name":"Markovian Petri Net protocols with product form solution","publication_year":1991,"publication_date":"1991-01-01","ids":{"openalex":"https://openalex.org/W2084471687","doi":"https://doi.org/10.1016/0166-5316(91)90016-v","mag":"2084471687"},"language":"en","primary_location":{"id":"doi:10.1016/0166-5316(91)90016-v","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0166-5316(91)90016-v","pdf_url":null,"source":{"id":"https://openalex.org/S45003570","display_name":"Performance Evaluation","issn_l":"0166-5316","issn":["0166-5316","1872-745X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Performance Evaluation","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/A5040758341","display_name":"Aurel A. Lazar","orcid":"https://orcid.org/0000-0003-4261-8709"},"institutions":[{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Aurel A. Lazar","raw_affiliation_strings":["Department of Electrical Engineering and Center for Telecommunications Research, Columbia University, New York, NY 10027-6699, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Center for Telecommunications Research, Columbia University, New York, NY 10027-6699, USA","institution_ids":["https://openalex.org/I78577930"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066801270","display_name":"Thomas G. Robertazzi","orcid":"https://orcid.org/0000-0002-2382-1843"},"institutions":[{"id":"https://openalex.org/I59553526","display_name":"Stony Brook University","ror":"https://ror.org/05qghxh33","country_code":"US","type":"education","lineage":["https://openalex.org/I59553526"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Thomas G. Robertazzi","raw_affiliation_strings":["Department of Electrical Engineering, SUNY at Stony Brook, Stony Brook, NY 11794-2350, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, SUNY at Stony Brook, Stony Brook, NY 11794-2350, USA","institution_ids":["https://openalex.org/I59553526"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2900,"currency":"USD","value_usd":2900},"apc_paid":null,"fwci":7.1846,"has_fulltext":false,"cited_by_count":82,"citation_normalized_percentile":{"value":0.98025566,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"12","issue":"1","first_page":"67","last_page":"77"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11125","display_name":"Petri Nets in System Modeling","score":0.9997000098228455,"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":0.9997000098228455,"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/T10974","display_name":"Advanced Queuing Theory Analysis","score":0.9972000122070312,"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/T10772","display_name":"Distributed systems and fault tolerance","score":0.9955999851226807,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/petri-net","display_name":"Petri net","score":0.8140528202056885},{"id":"https://openalex.org/keywords/stochastic-petri-net","display_name":"Stochastic Petri net","score":0.7014970183372498},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.6859298944473267},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.6232485771179199},{"id":"https://openalex.org/keywords/state-space","display_name":"State space","score":0.61191725730896},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6048537492752075},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.5262707471847534},{"id":"https://openalex.org/keywords/net","display_name":"Net (polyhedron)","score":0.5080587863922119},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.4886980354785919},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.473898321390152},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.45902472734451294},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4190230667591095},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.38419845700263977},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3694079518318176},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3463042378425598},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3449212312698364},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.23614996671676636},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09440681338310242},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.08633825182914734}],"concepts":[{"id":"https://openalex.org/C38677869","wikidata":"https://www.wikidata.org/wiki/Q724168","display_name":"Petri net","level":2,"score":0.8140528202056885},{"id":"https://openalex.org/C197551870","wikidata":"https://www.wikidata.org/wiki/Q7617809","display_name":"Stochastic Petri net","level":3,"score":0.7014970183372498},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.6859298944473267},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6232485771179199},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.61191725730896},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6048537492752075},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.5262707471847534},{"id":"https://openalex.org/C14166107","wikidata":"https://www.wikidata.org/wiki/Q253829","display_name":"Net (polyhedron)","level":2,"score":0.5080587863922119},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.4886980354785919},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.473898321390152},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.45902472734451294},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4190230667591095},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.38419845700263977},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3694079518318176},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3463042378425598},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3449212312698364},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.23614996671676636},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09440681338310242},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.08633825182914734},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","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},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/0166-5316(91)90016-v","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0166-5316(91)90016-v","pdf_url":null,"source":{"id":"https://openalex.org/S45003570","display_name":"Performance Evaluation","issn_l":"0166-5316","issn":["0166-5316","1872-745X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Performance Evaluation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":46,"referenced_works":["https://openalex.org/W34758359","https://openalex.org/W49428202","https://openalex.org/W95750126","https://openalex.org/W105568494","https://openalex.org/W116258108","https://openalex.org/W239283595","https://openalex.org/W276650109","https://openalex.org/W1510710339","https://openalex.org/W1520460310","https://openalex.org/W1525194379","https://openalex.org/W1536557058","https://openalex.org/W1542322140","https://openalex.org/W1561267729","https://openalex.org/W1561669240","https://openalex.org/W1789713128","https://openalex.org/W1942480536","https://openalex.org/W1967008488","https://openalex.org/W1994188141","https://openalex.org/W2025493578","https://openalex.org/W2032669921","https://openalex.org/W2041603746","https://openalex.org/W2053491613","https://openalex.org/W2060840612","https://openalex.org/W2077095314","https://openalex.org/W2079636926","https://openalex.org/W2094055697","https://openalex.org/W2101370431","https://openalex.org/W2125739093","https://openalex.org/W2138723607","https://openalex.org/W2279838076","https://openalex.org/W2286705380","https://openalex.org/W4255957816","https://openalex.org/W6600127457","https://openalex.org/W6601993522","https://openalex.org/W6603903687","https://openalex.org/W6604295103","https://openalex.org/W6604754559","https://openalex.org/W6610148414","https://openalex.org/W6630409218","https://openalex.org/W6632590563","https://openalex.org/W6633516562","https://openalex.org/W6633768105","https://openalex.org/W6656579842","https://openalex.org/W6670141535","https://openalex.org/W6671753042","https://openalex.org/W6680829097"],"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/W2148229336","https://openalex.org/W1980200158","https://openalex.org/W1513546254","https://openalex.org/W2091203523","https://openalex.org/W2062463517"],"abstract_inverted_index":null,"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":5}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
