{"id":"https://openalex.org/W4385358124","doi":"https://doi.org/10.1137/22m1489861","title":"Matrix-Analytic Methods for Solving Poisson\u2019s Equation with Applications to Markov Chains of GI/G/1-Type","display_name":"Matrix-Analytic Methods for Solving Poisson\u2019s Equation with Applications to Markov Chains of GI/G/1-Type","publication_year":2023,"publication_date":"2023-07-27","ids":{"openalex":"https://openalex.org/W4385358124","doi":"https://doi.org/10.1137/22m1489861"},"language":"en","primary_location":{"id":"doi:10.1137/22m1489861","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1489861","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis and Applications","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/A5100619673","display_name":"Jinpeng Liu","orcid":"https://orcid.org/0000-0002-3071-4499"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Jinpeng Liu","raw_affiliation_strings":["School of Mathematics and Statistics, Xidian University, Xi\u2019an, Shanxi, 710071, People\u2019s Republic of China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Xidian University, Xi\u2019an, Shanxi, 710071, People\u2019s Republic of China","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066960059","display_name":"Yuanyuan Liu","orcid":"https://orcid.org/0000-0001-8209-3439"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yuanyuan Liu","raw_affiliation_strings":["Corresponding author. School of Mathematics and Statistics, HNP-LAMA, Central South University, Changsha, Hunan, 410083, People\u2019s Republic of China"],"affiliations":[{"raw_affiliation_string":"Corresponding author. School of Mathematics and Statistics, HNP-LAMA, Central South University, Changsha, Hunan, 410083, People\u2019s Republic of China","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025154473","display_name":"Yiqiang Q. Zhao","orcid":"https://orcid.org/0000-0002-7530-8064"},"institutions":[{"id":"https://openalex.org/I67031392","display_name":"Carleton University","ror":"https://ror.org/02qtvee93","country_code":"CA","type":"education","lineage":["https://openalex.org/I67031392"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Yiqiang Q. Zhao","raw_affiliation_strings":["School of Mathematics and Statistics, Carleton University, 1125 Colonel By Drive, Ottawa, ON K1S 5B6, Canada"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Carleton University, 1125 Colonel By Drive, Ottawa, ON K1S 5B6, Canada","institution_ids":["https://openalex.org/I67031392"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100619673"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.6546,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.74051816,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"44","issue":"3","first_page":"1122","last_page":"1145"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10974","display_name":"Advanced Queuing Theory Analysis","score":0.9995999932289124,"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":0.9995999932289124,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9918000102043152,"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"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9865999817848206,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8538235425949097},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.6983742713928223},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.6253902912139893},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5540541410446167},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.47319409251213074},{"id":"https://openalex.org/keywords/poisson-distribution","display_name":"Poisson distribution","score":0.4533490538597107},{"id":"https://openalex.org/keywords/poissons-equation","display_name":"Poisson's equation","score":0.4106464385986328},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.36883455514907837},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3416256308555603},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.32683876156806946},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2477184534072876},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.16920995712280273}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8538235425949097},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.6983742713928223},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.6253902912139893},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5540541410446167},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.47319409251213074},{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.4533490538597107},{"id":"https://openalex.org/C96716743","wikidata":"https://www.wikidata.org/wiki/Q827688","display_name":"Poisson's equation","level":2,"score":0.4106464385986328},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.36883455514907837},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3416256308555603},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.32683876156806946},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2477184534072876},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.16920995712280273},{"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/22m1489861","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1489861","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis and Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2638812502","display_name":null,"funder_award_id":"11971486","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2735205029","display_name":null,"funder_award_id":"315660","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W168626650","https://openalex.org/W633278723","https://openalex.org/W858406950","https://openalex.org/W1483073639","https://openalex.org/W1966549076","https://openalex.org/W1971130323","https://openalex.org/W1980929384","https://openalex.org/W1997739949","https://openalex.org/W2001639855","https://openalex.org/W2003137566","https://openalex.org/W2009290156","https://openalex.org/W2012128802","https://openalex.org/W2022478817","https://openalex.org/W2028192443","https://openalex.org/W2028798402","https://openalex.org/W2060411106","https://openalex.org/W2062573385","https://openalex.org/W2065631710","https://openalex.org/W2077057639","https://openalex.org/W2077115916","https://openalex.org/W2082040833","https://openalex.org/W2086110465","https://openalex.org/W2098432798","https://openalex.org/W2099172085","https://openalex.org/W2107431923","https://openalex.org/W2154602821","https://openalex.org/W2170280569","https://openalex.org/W2234119470","https://openalex.org/W2337533085","https://openalex.org/W2612574518","https://openalex.org/W2799598053","https://openalex.org/W2883184237","https://openalex.org/W2963875220","https://openalex.org/W2984713686","https://openalex.org/W3082711429","https://openalex.org/W3093564309","https://openalex.org/W3104184956","https://openalex.org/W3122576550","https://openalex.org/W3158007355","https://openalex.org/W3206786992","https://openalex.org/W4232661759","https://openalex.org/W4302617909","https://openalex.org/W4302856910"],"related_works":["https://openalex.org/W4385245542","https://openalex.org/W2899525031","https://openalex.org/W4200027177","https://openalex.org/W4287324214","https://openalex.org/W2053895162","https://openalex.org/W2328024097","https://openalex.org/W2392918568","https://openalex.org/W2997699900","https://openalex.org/W2326123730","https://openalex.org/W2015143384"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"are":[4,41,59],"devoted":[5],"to":[6,43,55],"developing":[7],"matrix-analytic":[8],"methods":[9],"for":[10,14],"solving":[11],"Poisson\u2019s":[12],"equation":[13],"irreducible":[15],"and":[16,29,48],"positive":[17],"recurrent":[18],"discrete-time":[19],"Markov":[20,44,57],"chains.":[21],"Two":[22],"special":[23],"solutions,":[24],"including":[25],"the":[26,30],"deviation":[27],"matrix":[28,34],"expected":[31],"additive-type":[32],"functional":[33],",":[35],"will":[36],"be":[37],"considered.":[38],"The":[39],"results":[40],"applied":[42],"chains":[45,58],"of":[46],"-type":[47],"queues":[49],"with":[50],"negative":[51],"customers.":[52],"Further":[53],"extensions":[54],"continuous-time":[56],"also":[60],"investigated.":[61]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}