{"id":"https://openalex.org/W2071385742","doi":"https://doi.org/10.1007/s11134-008-9103-8","title":"Analysis of the M/G/1 queue with exponentially working vacations\u2014a matrix analytic approach","display_name":"Analysis of the M/G/1 queue with exponentially working vacations\u2014a matrix analytic approach","publication_year":2009,"publication_date":"2009-01-12","ids":{"openalex":"https://openalex.org/W2071385742","doi":"https://doi.org/10.1007/s11134-008-9103-8","mag":"2071385742"},"language":"en","primary_location":{"id":"doi:10.1007/s11134-008-9103-8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11134-008-9103-8","pdf_url":null,"source":{"id":"https://openalex.org/S148503350","display_name":"Queueing Systems","issn_l":"0257-0130","issn":["0257-0130","0340-4384","1572-9443"],"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Queueing Systems","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/A5063383376","display_name":"Jihong Li","orcid":"https://orcid.org/0000-0002-5162-2737"},"institutions":[{"id":"https://openalex.org/I39333907","display_name":"Yanshan University","ror":"https://ror.org/02txfnf15","country_code":"CN","type":"education","lineage":["https://openalex.org/I39333907"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Ji-hong Li","raw_affiliation_strings":["College of Economics and Management, Yanshan University, Qinhuangdao, China","College of Economics and Management, Yanshan University, Qinhuangdao, 066004, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Economics and Management, Yanshan University, Qinhuangdao, China","institution_ids":["https://openalex.org/I39333907"]},{"raw_affiliation_string":"College of Economics and Management, Yanshan University, Qinhuangdao, 066004, China","institution_ids":["https://openalex.org/I39333907"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112716913","display_name":"Naishuo Tian","orcid":null},"institutions":[{"id":"https://openalex.org/I39333907","display_name":"Yanshan University","ror":"https://ror.org/02txfnf15","country_code":"CN","type":"education","lineage":["https://openalex.org/I39333907"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Nai-shuo Tian","raw_affiliation_strings":["College of Science, Yanshan University, Qinhuangdao, China","College of Science, Yanshan University, Qinhuangdao, 066004, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Science, Yanshan University, Qinhuangdao, China","institution_ids":["https://openalex.org/I39333907"]},{"raw_affiliation_string":"College of Science, Yanshan University, Qinhuangdao, 066004, China","institution_ids":["https://openalex.org/I39333907"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055904501","display_name":"Zhe George Zhang","orcid":"https://orcid.org/0000-0001-8058-3522"},"institutions":[{"id":"https://openalex.org/I18014758","display_name":"Simon Fraser University","ror":"https://ror.org/0213rcc28","country_code":"CA","type":"education","lineage":["https://openalex.org/I18014758"]},{"id":"https://openalex.org/I4210133369","display_name":"Decision Sciences (United States)","ror":"https://ror.org/03gcvf773","country_code":"US","type":"company","lineage":["https://openalex.org/I4210133369"]},{"id":"https://openalex.org/I52669646","display_name":"Western Washington University","ror":"https://ror.org/05wn7r715","country_code":"US","type":"education","lineage":["https://openalex.org/I52669646"]}],"countries":["CA","US"],"is_corresponding":true,"raw_author_name":"Zhe George Zhang","raw_affiliation_strings":["Dept. of Decision Sciences, Western Washington University, Bellingham, USA","Faculty of Business Administration, Simon Fraser University, Burnaby, Canada","Dept. of Decision Sciences, Western Washington University, Bellingham, WA, 98225, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dept. of Decision Sciences, Western Washington University, Bellingham, USA","institution_ids":["https://openalex.org/I52669646"]},{"raw_affiliation_string":"Faculty of Business Administration, Simon Fraser University, Burnaby, Canada","institution_ids":["https://openalex.org/I18014758"]},{"raw_affiliation_string":"Dept. of Decision Sciences, Western Washington University, Bellingham, WA, 98225, USA","institution_ids":["https://openalex.org/I4210133369","https://openalex.org/I52669646"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018769601","display_name":"Hsing Luh","orcid":"https://orcid.org/0000-0002-7570-0584"},"institutions":[{"id":"https://openalex.org/I87354575","display_name":"National Chengchi University","ror":"https://ror.org/03rqk8h36","country_code":"TW","type":"education","lineage":["https://openalex.org/I87354575"]}],"countries":["TW"],"is_corresponding":true,"raw_author_name":"Hsing Paul Luh","raw_affiliation_strings":["Department of Mathematical Sciences, National ChengChi University, Taipei, Taiwan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, National ChengChi University, Taipei, Taiwan","institution_ids":["https://openalex.org/I87354575"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5018769601","https://openalex.org/A5055904501","https://openalex.org/A5063383376","https://openalex.org/A5112716913"],"corresponding_institution_ids":["https://openalex.org/I18014758","https://openalex.org/I39333907","https://openalex.org/I4210133369","https://openalex.org/I52669646","https://openalex.org/I87354575"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":null,"fwci":6.2475,"has_fulltext":false,"cited_by_count":64,"citation_normalized_percentile":{"value":0.95922548,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"61","issue":"2-3","first_page":"139","last_page":"166"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10974","display_name":"Advanced Queuing Theory Analysis","score":0.9998999834060669,"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":0.9998999834060669,"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/T11720","display_name":"Probability and Risk Models","score":0.9447000026702881,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10698","display_name":"Transportation Planning and Optimization","score":0.9280999898910522,"subfield":{"id":"https://openalex.org/subfields/3313","display_name":"Transportation"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.6978784203529358},{"id":"https://openalex.org/keywords/stationary-distribution","display_name":"Stationary distribution","score":0.6227362751960754},{"id":"https://openalex.org/keywords/burkes-theorem","display_name":"Burke's theorem","score":0.61902916431427},{"id":"https://openalex.org/keywords/bulk-queue","display_name":"Bulk queue","score":0.5783621072769165},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5412333607673645},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5316988229751587},{"id":"https://openalex.org/keywords/fork\u2013join-queue","display_name":"Fork\u2013join queue","score":0.49779224395751953},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.45936957001686096},{"id":"https://openalex.org/keywords/queue","display_name":"Queue","score":0.45667383074760437},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.4384554922580719},{"id":"https://openalex.org/keywords/stochastic-matrix","display_name":"Stochastic matrix","score":0.43247905373573303},{"id":"https://openalex.org/keywords/queueing-theory","display_name":"Queueing theory","score":0.4197996258735657},{"id":"https://openalex.org/keywords/continuous-time-markov-chain","display_name":"Continuous-time Markov chain","score":0.4174043536186218},{"id":"https://openalex.org/keywords/exponential-distribution","display_name":"Exponential distribution","score":0.4162098169326782},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4158722162246704},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38929641246795654},{"id":"https://openalex.org/keywords/balance-equation","display_name":"Balance equation","score":0.3522827625274658},{"id":"https://openalex.org/keywords/markov-model","display_name":"Markov model","score":0.2346647083759308},{"id":"https://openalex.org/keywords/queue-management-system","display_name":"Queue management system","score":0.16989368200302124},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.13762354850769043}],"concepts":[{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.6978784203529358},{"id":"https://openalex.org/C98951983","wikidata":"https://www.wikidata.org/wiki/Q7604341","display_name":"Stationary distribution","level":3,"score":0.6227362751960754},{"id":"https://openalex.org/C66295387","wikidata":"https://www.wikidata.org/wiki/Q4998912","display_name":"Burke's theorem","level":5,"score":0.61902916431427},{"id":"https://openalex.org/C87950461","wikidata":"https://www.wikidata.org/wiki/Q4996486","display_name":"Bulk queue","level":3,"score":0.5783621072769165},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5412333607673645},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5316988229751587},{"id":"https://openalex.org/C124444977","wikidata":"https://www.wikidata.org/wiki/Q4025962","display_name":"Fork\u2013join queue","level":4,"score":0.49779224395751953},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.45936957001686096},{"id":"https://openalex.org/C160403385","wikidata":"https://www.wikidata.org/wiki/Q220543","display_name":"Queue","level":2,"score":0.45667383074760437},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.4384554922580719},{"id":"https://openalex.org/C49555168","wikidata":"https://www.wikidata.org/wiki/Q176583","display_name":"Stochastic matrix","level":3,"score":0.43247905373573303},{"id":"https://openalex.org/C22684755","wikidata":"https://www.wikidata.org/wiki/Q847526","display_name":"Queueing theory","level":2,"score":0.4197996258735657},{"id":"https://openalex.org/C147080032","wikidata":"https://www.wikidata.org/wiki/Q176720","display_name":"Continuous-time Markov chain","level":5,"score":0.4174043536186218},{"id":"https://openalex.org/C55350006","wikidata":"https://www.wikidata.org/wiki/Q237193","display_name":"Exponential distribution","level":2,"score":0.4162098169326782},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4158722162246704},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38929641246795654},{"id":"https://openalex.org/C158917313","wikidata":"https://www.wikidata.org/wiki/Q4849964","display_name":"Balance equation","level":4,"score":0.3522827625274658},{"id":"https://openalex.org/C163836022","wikidata":"https://www.wikidata.org/wiki/Q6771326","display_name":"Markov model","level":3,"score":0.2346647083759308},{"id":"https://openalex.org/C128220111","wikidata":"https://www.wikidata.org/wiki/Q4531011","display_name":"Queue management system","level":3,"score":0.16989368200302124},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.13762354850769043},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","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},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11134-008-9103-8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11134-008-9103-8","pdf_url":null,"source":{"id":"https://openalex.org/S148503350","display_name":"Queueing Systems","issn_l":"0257-0130","issn":["0257-0130","0340-4384","1572-9443"],"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Queueing Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.6100000143051147,"id":"https://metadata.un.org/sdg/8","display_name":"Decent work and economic growth"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320324869","display_name":"Yanshan University","ror":"https://ror.org/02txfnf15"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W67811138","https://openalex.org/W108513215","https://openalex.org/W118388751","https://openalex.org/W577991167","https://openalex.org/W1967401610","https://openalex.org/W1968661925","https://openalex.org/W1998843914","https://openalex.org/W2005098937","https://openalex.org/W2011245215","https://openalex.org/W2013047337","https://openalex.org/W2016348677","https://openalex.org/W2020786814","https://openalex.org/W2055593329","https://openalex.org/W2090255546","https://openalex.org/W2093817726","https://openalex.org/W2102918867","https://openalex.org/W2152530926","https://openalex.org/W2610166414","https://openalex.org/W2798387839","https://openalex.org/W2799598053","https://openalex.org/W2921590837","https://openalex.org/W3027878608","https://openalex.org/W3153489343","https://openalex.org/W4285719527","https://openalex.org/W4292926198","https://openalex.org/W6603287499","https://openalex.org/W6673482784"],"related_works":["https://openalex.org/W1505066891","https://openalex.org/W1973811578","https://openalex.org/W2159840783","https://openalex.org/W2089046940","https://openalex.org/W1992938514","https://openalex.org/W2000789082","https://openalex.org/W2809475525","https://openalex.org/W2171788592","https://openalex.org/W1501151544","https://openalex.org/W1032487330"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":6},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":9},{"year":2012,"cited_by_count":3}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}