{"id":"https://openalex.org/W2130189455","doi":"https://doi.org/10.1109/infcom.1997.631131","title":"Finite and infinite QBD chains: a simple and unifying algorithmic approach","display_name":"Finite and infinite QBD chains: a simple and unifying algorithmic approach","publication_year":2002,"publication_date":"2002-11-23","ids":{"openalex":"https://openalex.org/W2130189455","doi":"https://doi.org/10.1109/infcom.1997.631131","mag":"2130189455"},"language":"en","primary_location":{"id":"doi:10.1109/infcom.1997.631131","doi":"https://doi.org/10.1109/infcom.1997.631131","is_oa":false,"landing_page_url":"https://doi.org/10.1109/infcom.1997.631131","pdf_url":null,"source":{"id":"https://openalex.org/S7407087743","display_name":"IEEE Conference on Computer Communications (INFOCOM)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of INFOCOM '97","raw_type":"proceedings-article"},"volume":null,"type":"conference-paper","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/A5080807022","display_name":"Nail Akar","orcid":"https://orcid.org/0000-0001-8143-1379","observed_orcids":["https://orcid.org/0000-0001-8143-1379"]},"institutions":[{"id":"https://openalex.org/I75421653","display_name":"University of Missouri\u2013Kansas City","ror":"https://ror.org/01w0d5g70","country_code":"US","type":"education","lineage":["https://openalex.org/I75421653"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"N. Akar","raw_affiliation_strings":["Computer Science Telecommunications, University of Missouri, Kansas City, Kansas City, MO, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Science Telecommunications, University of Missouri, Kansas City, Kansas City, MO, USA","institution_ids":["https://openalex.org/I75421653"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008676141","display_name":"Kazem Sohraby","orcid":"https://orcid.org/0000-0003-1523-1445","observed_orcids":["https://orcid.org/0000-0003-1523-1445"]},"institutions":[{"id":"https://openalex.org/I75421653","display_name":"University of Missouri\u2013Kansas City","ror":"https://ror.org/01w0d5g70","country_code":"US","type":"education","lineage":["https://openalex.org/I75421653"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"K. Sohraby","raw_affiliation_strings":["Computer Science Telecommunications, University of Missouri, Kansas City, Kansas City, MO, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Science Telecommunications, University of Missouri, Kansas City, Kansas City, MO, USA","institution_ids":["https://openalex.org/I75421653"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I75421653"],"apc_list":null,"apc_paid":null,"fwci":3.6923,"has_fulltext":false,"cited_by_count":34,"citation_normalized_percentile":{"value":0.92854653,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":88,"max":96},"biblio":{"volume":"3","issue":null,"first_page":"1105","last_page":"1113"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10974","display_name":"Advanced Queuing Theory Analysis","score":0.8306000232696533,"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":0.8306000232696533,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.08470000326633453,"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/T11125","display_name":"Petri Nets in System Modeling","score":0.019200000911951065,"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/quasi-birth-and-death-process","display_name":"quasi-birth-and-death processes","score":0.9620000123977661},{"id":"https://openalex.org/keywords/stationary-distribution","display_name":"stationary distribution","score":0.9279999732971191},{"id":"https://openalex.org/keywords/matrix-geometric-method","display_name":"matrix-geometric method","score":0.7039999961853027},{"id":"https://openalex.org/keywords/invariant-subspace-method","display_name":"invariant subspace method","score":0.9399999976158142},{"id":"https://openalex.org/keywords/nonlinear-matrix-equations","display_name":"nonlinear matrix equations","score":0.7149999737739563},{"id":"https://openalex.org/keywords/quadratic-convergence","display_name":"quadratic convergence","score":0.6460000276565552}],"concepts":[{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.757718026638031},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6603060960769653},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4200612008571625},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.409170538187027},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.34485185146331787},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2685600519180298},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/infcom.1997.631131","doi":"https://doi.org/10.1109/infcom.1997.631131","is_oa":false,"landing_page_url":"https://doi.org/10.1109/infcom.1997.631131","pdf_url":null,"source":{"id":"https://openalex.org/S7407087743","display_name":"IEEE Conference on Computer Communications (INFOCOM)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of INFOCOM '97","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.44.5079","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.44.5079","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cstp.umkc.edu/org/tn/telpack/publications/infocom_97.ps.gz","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.45.4328","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.45.4328","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://ftp.cstp.umkc.edu/telpack/publications/infocom_97.ps","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1510002263","https://openalex.org/W1560592371","https://openalex.org/W1906034359","https://openalex.org/W1968661925","https://openalex.org/W1990765246","https://openalex.org/W1995258411","https://openalex.org/W2015001720","https://openalex.org/W2070689535","https://openalex.org/W2077760421","https://openalex.org/W2092378115","https://openalex.org/W2121854030","https://openalex.org/W2123413355","https://openalex.org/W2164138681","https://openalex.org/W2610166414"],"related_works":["https://openalex.org/W1966239579","https://openalex.org/W7154984339","https://openalex.org/W7095176987","https://openalex.org/W2008971889","https://openalex.org/W2381432618","https://openalex.org/W26471643","https://openalex.org/W2027086139","https://openalex.org/W1549825974","https://openalex.org/W2006367632","https://openalex.org/W2121854030"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"present":[4],"a":[5,71,143],"novel":[6],"algorithmic":[7],"approach,":[8],"the":[9,17,22,39,54,115,121,139,159,181,184,189,195,198,206,218],"hybrid":[10],"matrix":[11,73,99,122,145,220],"geometric/invariant":[12],"subspace":[13],"method,":[14],"for":[15,57,230],"finding":[16,138],"stationary":[18],"probability":[19],"distribution":[20],"of":[21,32,135,142,157,183,186,209],"finite":[23],"quasi-birth-death":[24],"(QBD)":[25],"process":[26],"which":[27,178],"arises":[28],"in":[29,45,70,205],"performance":[30],"analysis":[31],"computer":[33],"and":[34,51,90,101,105,127,165,204],"communication":[35],"systems.":[36],"Assuming":[37],"that":[38,120,180],"QBD":[40,232],"state":[41],"space":[42],"is":[43,66,169,192,201,214],"defined":[44],"two":[46,97],"dimensions":[47],"with":[48,150],"m":[49],"phases":[50],"K+1":[52],"levels,":[53],"solution":[55,222],"vector":[56],"level":[58],"k,":[59],"/spl":[60,76,102,106,162,166,223],"pi//sub":[61,77,224,226],"k/,":[62],"0/spl":[63],"les/k/spl":[64],"les/K":[65],"shown":[67,170,215],"to":[68,96,111,171,216],"be":[69,112,132,172],"modified":[72],"geometric":[74,123,221],"form":[75],"k/=/spl":[78,225],"upsi//sub":[79,83,103,107,163,167],"1/R/sub":[80],"1//sup":[81,228],"k/+/spl":[82],"2/R/sub":[84],"2//sup":[85],"K-k/":[86],"where":[87],"R/sub":[88,91,125,128],"1/":[89,104,126,164],"2/":[92,108,129,168,176],"are":[93,109],"certain":[94],"solutions":[95],"nonlinear":[98],"equations":[100],"vectors":[110,161],"determined":[113],"using":[114],"boundary":[116],"conditions.":[117],"We":[118],"show":[119],"factors":[124],"can":[130],"simultaneously":[131],"obtained":[133],"independently":[134],"K":[136],"via":[137],"sign":[140],"function":[141],"real":[144],"by":[146],"an":[147],"iterative":[148],"algorithm":[149,191],"quadratic":[151],"convergence":[152],"rates.":[153],"The":[154],"time":[155],"complexity":[156],"obtaining":[158],"coefficient":[160],"O(m/sup":[173],"3/":[174],"log/sub":[175],"K)":[177],"indicates":[179],"contribution":[182],"number":[185],"levels":[187],"on":[188],"overall":[190],"minimal.":[193],"Besides":[194],"numerical":[196],"efficiency,":[197],"proposed":[199],"method":[200],"numerically":[202],"stable":[203],"limiting":[207],"case":[208],"K/spl":[210],"rarr//spl":[211],"infin/,":[212],"it":[213],"yield":[217],"well-known":[219],"0/R/sub":[227],"k/":[229],"infinite":[231],"chain.":[233]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2016-06-24T00:00:00"}