{"id":"https://openalex.org/W2057386609","doi":"https://doi.org/10.1093/comjnl/bxq067","title":"Multiple Class Symmetric G-networks with Phase Type Service Times","display_name":"Multiple Class Symmetric G-networks with Phase Type Service Times","publication_year":2010,"publication_date":"2010-09-03","ids":{"openalex":"https://openalex.org/W2057386609","doi":"https://doi.org/10.1093/comjnl/bxq067","mag":"2057386609"},"language":"en","primary_location":{"id":"doi:10.1093/comjnl/bxq067","is_oa":false,"landing_page_url":"https://doi.org/10.1093/comjnl/bxq067","pdf_url":null,"source":{"id":"https://openalex.org/S44643521","display_name":"The Computer Journal","issn_l":"0010-4620","issn":["0010-4620","1460-2067"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Computer Journal","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/A5059578543","display_name":"Thu-Ha Dao-Thi","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/I195731000","display_name":"Universit\u00e9 de Versailles Saint-Quentin-en-Yvelines","ror":"https://ror.org/03mkjjy25","country_code":"FR","type":"education","lineage":["https://openalex.org/I195731000","https://openalex.org/I277688954"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"T.-H. Dao-Thi","raw_affiliation_strings":["PRiSM, Universit\u00e9 de Versailles St-Quentin, CNRS, UniverSud Paris, Versailles, France","PRiSM, Universit\u00e9 de Versailles St-Quentin, CNRS, UniverSud Paris, Versailles, France#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"PRiSM, Universit\u00e9 de Versailles St-Quentin, CNRS, UniverSud Paris, Versailles, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I195731000"]},{"raw_affiliation_string":"PRiSM, Universit\u00e9 de Versailles St-Quentin, CNRS, UniverSud Paris, Versailles, France#TAB#","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I195731000"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101854002","display_name":"Jean-Michel Fourneau","orcid":"https://orcid.org/0000-0002-8280-0137"},"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/I195731000","display_name":"Universit\u00e9 de Versailles Saint-Quentin-en-Yvelines","ror":"https://ror.org/03mkjjy25","country_code":"FR","type":"education","lineage":["https://openalex.org/I195731000","https://openalex.org/I277688954"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"J.-M. Fourneau","raw_affiliation_strings":["PRiSM, Universit\u00e9 de Versailles St-Quentin, CNRS, UniverSud Paris, Versailles, France","PRiSM, Universit\u00e9 de Versailles St-Quentin, CNRS, UniverSud Paris, Versailles, France#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"PRiSM, Universit\u00e9 de Versailles St-Quentin, CNRS, UniverSud Paris, Versailles, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I195731000"]},{"raw_affiliation_string":"PRiSM, Universit\u00e9 de Versailles St-Quentin, CNRS, UniverSud Paris, Versailles, France#TAB#","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I195731000"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042251987","display_name":"Minh-Anh Tran","orcid":null},"institutions":[{"id":"https://openalex.org/I197681013","display_name":"Universit\u00e9 Paris-Est Cr\u00e9teil","ror":"https://ror.org/05ggc9x40","country_code":"FR","type":"education","lineage":["https://openalex.org/I197681013"]},{"id":"https://openalex.org/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"M.-A. Tran","raw_affiliation_strings":["Universit\u00e9 de Paris Est Cr\u00e9teil, Cr\u00e9teil Cedex, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 de Paris Est Cr\u00e9teil, Cr\u00e9teil Cedex, France","institution_ids":["https://openalex.org/I197681013","https://openalex.org/I204730241"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5059578543"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I195731000"],"apc_list":{"value":2877,"currency":"GBP","value_usd":3794},"apc_paid":null,"fwci":0.9167,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.79890848,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"54","issue":"2","first_page":"274","last_page":"284"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10974","display_name":"Advanced Queuing Theory Analysis","score":0.9983999729156494,"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"}},"topics":[{"id":"https://openalex.org/T10974","display_name":"Advanced Queuing Theory Analysis","score":0.9983999729156494,"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/T11409","display_name":"Advanced Wireless Network Optimization","score":0.9664000272750854,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10829","display_name":"Interconnection Networks and Systems","score":0.9483000040054321,"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/queue","display_name":"Queue","score":0.6835877895355225},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.6245601177215576},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5884956121444702},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5581538677215576},{"id":"https://openalex.org/keywords/service","display_name":"Service (business)","score":0.5512255430221558},{"id":"https://openalex.org/keywords/queueing-theory","display_name":"Queueing theory","score":0.5419901013374329},{"id":"https://openalex.org/keywords/signal","display_name":"SIGNAL (programming language)","score":0.5203789472579956},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.5078437924385071},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4849884510040283},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.3862162232398987},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.34002596139907837},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1330890655517578},{"id":"https://openalex.org/keywords/business","display_name":"Business","score":0.11755034327507019},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10080474615097046},{"id":"https://openalex.org/keywords/marketing","display_name":"Marketing","score":0.06439819931983948}],"concepts":[{"id":"https://openalex.org/C160403385","wikidata":"https://www.wikidata.org/wiki/Q220543","display_name":"Queue","level":2,"score":0.6835877895355225},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.6245601177215576},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5884956121444702},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5581538677215576},{"id":"https://openalex.org/C2780378061","wikidata":"https://www.wikidata.org/wiki/Q25351891","display_name":"Service (business)","level":2,"score":0.5512255430221558},{"id":"https://openalex.org/C22684755","wikidata":"https://www.wikidata.org/wiki/Q847526","display_name":"Queueing theory","level":2,"score":0.5419901013374329},{"id":"https://openalex.org/C2779843651","wikidata":"https://www.wikidata.org/wiki/Q7390335","display_name":"SIGNAL (programming language)","level":2,"score":0.5203789472579956},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.5078437924385071},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4849884510040283},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.3862162232398987},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.34002596139907837},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1330890655517578},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"score":0.11755034327507019},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10080474615097046},{"id":"https://openalex.org/C162853370","wikidata":"https://www.wikidata.org/wiki/Q39809","display_name":"Marketing","level":1,"score":0.06439819931983948},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1093/comjnl/bxq067","is_oa":false,"landing_page_url":"https://doi.org/10.1093/comjnl/bxq067","pdf_url":null,"source":{"id":"https://openalex.org/S44643521","display_name":"The Computer Journal","issn_l":"0010-4620","issn":["0010-4620","1460-2067"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Computer Journal","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Industry, innovation and infrastructure","id":"https://metadata.un.org/sdg/9","score":0.47999998927116394}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3162204513","https://openalex.org/W2371138613","https://openalex.org/W2048963458","https://openalex.org/W43109613","https://openalex.org/W2359952343","https://openalex.org/W2080152487","https://openalex.org/W2239445980","https://openalex.org/W3083152911","https://openalex.org/W2120455979","https://openalex.org/W3022347918"],"abstract_inverted_index":{"We":[0,104,149],"consider":[1],"a":[2,80,94,107,113,116,138,147,157,162],"queueing":[3,26],"network":[4,158],"of":[5,68,97,110,122,135,159],"symmetric":[6],"G-queues":[7],"with":[8,28,42,55,100],"customers":[9],"and":[10,30,57,144],"signals.":[11],"Since":[12],"the":[13,19,85,120,123,152],"seminal":[14],"papers":[15,76],"by":[16],"Gelenbe":[17],"in":[18,125],"early":[20],"1990s":[21],"(Gelenbe,":[22],"E.":[23,39,52],"(1991)":[24],"Product-form":[25],"networks":[27,67],"negative":[29],"positive":[31],"customers.":[32],"J.":[33,46],"Appl.":[34,47],"Probab.,":[35,48],"28,":[36],"656\u2013663;":[37],"Gelenbe,":[38,51],"(1993);":[40],"G-networks":[41],"instantaneous":[43],"customer":[44,124,139],"movement.":[45],"30,":[49],"742\u2013748;":[50],"(1993)":[53],"G-Networks":[54],"signals":[56],"batch":[58],"removal.":[59],"Probab.":[60],"Eng.":[61],"Inform.":[62],"Sci.,":[63],"7,":[64],"335\u2013342),":[65],"generalized":[66],"queues":[69,160],"have":[70],"received":[71],"considerable":[72],"attention.":[73],"But":[74],"most":[75],"assume":[77,106],"to":[78,141],"obtain":[79],"product":[81,163],"form":[82,164],"such":[83,156],"that":[84,151],"service":[86,102,126],"times":[87],"follow":[88],"exponential":[89],"distributions.":[90],"Here,":[91],"we":[92],"propose":[93],"new":[95,108],"generalization":[96],"this":[98],"model":[99],"phase-type":[101],"times.":[103],"also":[105],"type":[109],"signal.":[111,148],"When":[112],"signal":[114],"enters":[115],"queue,":[117],"it":[118],"changes":[119],"phase":[121],"if":[127],"there":[128],"is":[129],"any.":[130],"As":[131],"usual,":[132],"after":[133],"completion":[134],"its":[136],"service,":[137],"moves":[140],"another":[142],"queue":[143],"may":[145],"become":[146],"prove":[150],"steady-state":[153],"distribution":[154],"for":[155],"has":[161],"solution.":[165]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}
