{"id":"https://openalex.org/W2086509969","doi":"https://doi.org/10.1137/s003613990139756x","title":"Two-Time-Scale Markov Chains and Applications to Quasi-Birth-Death Queues","display_name":"Two-Time-Scale Markov Chains and Applications to Quasi-Birth-Death Queues","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W2086509969","doi":"https://doi.org/10.1137/s003613990139756x","mag":"2086509969"},"language":"en","primary_location":{"id":"doi:10.1137/s003613990139756x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s003613990139756x","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Mathematics","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/A5008853967","display_name":"George Yin","orcid":"https://orcid.org/0000-0002-2951-0704"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"G. Yin","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5102976329","display_name":"Hanqin Zhang","orcid":"https://orcid.org/0000-0003-3539-8146"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210093841","display_name":"Institute of Applied Mathematics","ror":"https://ror.org/00h9jx107","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I1313323035","https://openalex.org/I4210093841","https://openalex.org/I4210124601","https://openalex.org/I4210148470"]}],"countries":["CN","RU"],"is_corresponding":false,"raw_author_name":"Hanqin Zhang","raw_affiliation_strings":["Institute of Applied Mathematics, Chinese Academy of Sciences;"],"affiliations":[{"raw_affiliation_string":"Institute of Applied Mathematics, Chinese Academy of Sciences;","institution_ids":["https://openalex.org/I4210093841","https://openalex.org/I19820366"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5008853967"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.9287,"has_fulltext":false,"cited_by_count":29,"citation_normalized_percentile":{"value":0.87522559,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"65","issue":"2","first_page":"567","last_page":"586"},"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":0.9957000017166138,"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/T11716","display_name":"Random Matrices and Applications","score":0.9932000041007996,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.7949070930480957},{"id":"https://openalex.org/keywords/queue","display_name":"Queue","score":0.5468490123748779},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5454888343811035},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.5428109765052795},{"id":"https://openalex.org/keywords/birth\u2013death-process","display_name":"Birth\u2013death process","score":0.5180583000183105},{"id":"https://openalex.org/keywords/scale","display_name":"Scale (ratio)","score":0.5126532912254333},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.4992694854736328},{"id":"https://openalex.org/keywords/generator","display_name":"Generator (circuit theory)","score":0.4956439733505249},{"id":"https://openalex.org/keywords/continuous-time-markov-chain","display_name":"Continuous-time Markov chain","score":0.478990763425827},{"id":"https://openalex.org/keywords/markov-renewal-process","display_name":"Markov renewal process","score":0.4479425251483917},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43127351999282837},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.37763819098472595},{"id":"https://openalex.org/keywords/variable-order-markov-model","display_name":"Variable-order Markov model","score":0.3462202548980713},{"id":"https://openalex.org/keywords/markov-model","display_name":"Markov model","score":0.336297869682312},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3344784080982208},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.10497787594795227},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07426425814628601}],"concepts":[{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.7949070930480957},{"id":"https://openalex.org/C160403385","wikidata":"https://www.wikidata.org/wiki/Q220543","display_name":"Queue","level":2,"score":0.5468490123748779},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5454888343811035},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.5428109765052795},{"id":"https://openalex.org/C65990518","wikidata":"https://www.wikidata.org/wiki/Q1456275","display_name":"Birth\u2013death process","level":3,"score":0.5180583000183105},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.5126532912254333},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.4992694854736328},{"id":"https://openalex.org/C2780992000","wikidata":"https://www.wikidata.org/wiki/Q17016113","display_name":"Generator (circuit theory)","level":3,"score":0.4956439733505249},{"id":"https://openalex.org/C147080032","wikidata":"https://www.wikidata.org/wiki/Q176720","display_name":"Continuous-time Markov chain","level":5,"score":0.478990763425827},{"id":"https://openalex.org/C163540672","wikidata":"https://www.wikidata.org/wiki/Q1115431","display_name":"Markov renewal process","level":5,"score":0.4479425251483917},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43127351999282837},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37763819098472595},{"id":"https://openalex.org/C54907487","wikidata":"https://www.wikidata.org/wiki/Q7915688","display_name":"Variable-order Markov model","level":4,"score":0.3462202548980713},{"id":"https://openalex.org/C163836022","wikidata":"https://www.wikidata.org/wiki/Q6771326","display_name":"Markov model","level":3,"score":0.336297869682312},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3344784080982208},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.10497787594795227},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07426425814628601},{"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/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s003613990139756x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s003613990139756x","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.91.700","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.91.700","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://madis1.iss.ac.cn/madis.files/pub-papers/2005/27.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W583893368","https://openalex.org/W1522714617","https://openalex.org/W1527296550","https://openalex.org/W1968661925","https://openalex.org/W1969848360","https://openalex.org/W1975083310","https://openalex.org/W1998844177","https://openalex.org/W2007560378","https://openalex.org/W2028493795","https://openalex.org/W2032309370","https://openalex.org/W2049422957","https://openalex.org/W2057808525","https://openalex.org/W2067280726","https://openalex.org/W2073287487","https://openalex.org/W2080156047","https://openalex.org/W2085857497","https://openalex.org/W2086715755","https://openalex.org/W2092911205","https://openalex.org/W2121672706","https://openalex.org/W2125227081","https://openalex.org/W2125645157","https://openalex.org/W2137236287","https://openalex.org/W2143706916","https://openalex.org/W2160013177","https://openalex.org/W2166323094","https://openalex.org/W2484199605","https://openalex.org/W2610166414","https://openalex.org/W2799137445","https://openalex.org/W2802739963","https://openalex.org/W4247619688","https://openalex.org/W4252302949","https://openalex.org/W4299533062"],"related_works":["https://openalex.org/W1493775604","https://openalex.org/W2393621008","https://openalex.org/W2118728396","https://openalex.org/W2540690809","https://openalex.org/W4240129243","https://openalex.org/W1974839821","https://openalex.org/W3166133680","https://openalex.org/W2987631717","https://openalex.org/W2749469577","https://openalex.org/W2735859191"],"abstract_inverted_index":{"Aiming":[0],"at":[1],"reduction":[2],"of":[3,20,30,79,87],"complexity,":[4],"this":[5],"work":[6],"is":[7,44,55,69],"concerned":[8],"with":[9,58,85],"two-time-scale":[10],"Markov":[11,32,51],"chains":[12],"and":[13,25],"applications":[14],"to":[15,46,48,60,71,73],"quasi-birth-death":[16,88],"queues.":[17,89],"Asymptotic":[18],"expansions":[19],"probability":[21],"vectors":[22],"are":[23,82],"constructed":[24],"justified.":[26],"Lumping":[27],"all":[28],"states":[29],"the":[31,61,80],"chain":[33,52],"in":[34],"each":[35],"subspace":[36],"into":[37],"a":[38,49,65,74],"single":[39],"state,":[40],"an":[41,56],"aggregated":[42],"process":[43],"shown":[45,70],"converge":[47,72],"continuous-time":[50],"whose":[53],"generator":[54],"average":[57],"respect":[59],"stationary":[62],"measures.":[63],"Then":[64],"suitably":[66],"scaled":[67],"sequence":[68],"switching":[75],"diffusion":[76],"process.":[77],"Extensions":[78],"results":[81],"presented":[83],"together":[84],"examples":[86]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":11}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
