{"id":"https://openalex.org/W2597270801","doi":"https://doi.org/10.1007/s11134-017-9528-z","title":"Queue-length balance equations in multiclass multiserver queues and their generalizations","display_name":"Queue-length balance equations in multiclass multiserver queues and their generalizations","publication_year":2017,"publication_date":"2017-05-22","ids":{"openalex":"https://openalex.org/W2597270801","doi":"https://doi.org/10.1007/s11134-017-9528-z","mag":"2597270801"},"language":"en","primary_location":{"id":"doi:10.1007/s11134-017-9528-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11134-017-9528-z","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs11134-017-9528-z.pdf","source":{"id":"https://openalex.org/S148503350","display_name":"Queueing Systems","issn_l":"0257-0130","issn":["0257-0130","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007%2Fs11134-017-9528-z.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5055752788","display_name":"Marko Boon","orcid":"https://orcid.org/0000-0001-8804-8743"},"institutions":[{"id":"https://openalex.org/I83019370","display_name":"Eindhoven University of Technology","ror":"https://ror.org/02c2kyt77","country_code":"NL","type":"education","lineage":["https://openalex.org/I83019370"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Marko A. A. Boon","raw_affiliation_strings":["Department of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, The Netherlands"],"raw_orcid":"https://orcid.org/0000-0001-8804-8743","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, The Netherlands","institution_ids":["https://openalex.org/I83019370"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012915432","display_name":"Onno Boxma","orcid":"https://orcid.org/0000-0003-4317-5380"},"institutions":[{"id":"https://openalex.org/I83019370","display_name":"Eindhoven University of Technology","ror":"https://ror.org/02c2kyt77","country_code":"NL","type":"education","lineage":["https://openalex.org/I83019370"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Onno J. Boxma","raw_affiliation_strings":["Department of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, The Netherlands","institution_ids":["https://openalex.org/I83019370"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085238719","display_name":"Offer Kella","orcid":"https://orcid.org/0000-0002-6433-5470"},"institutions":[{"id":"https://openalex.org/I197251160","display_name":"Hebrew University of Jerusalem","ror":"https://ror.org/03qxff017","country_code":"IL","type":"education","lineage":["https://openalex.org/I197251160"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Offer Kella","raw_affiliation_strings":["Department of Statistics, The Hebrew University of Jerusalem, 9190501, Jerusalem, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics, The Hebrew University of Jerusalem, 9190501, Jerusalem, Israel","institution_ids":["https://openalex.org/I197251160"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071505768","display_name":"Masakiyo Miyazawa","orcid":"https://orcid.org/0000-0003-0214-7535"},"institutions":[{"id":"https://openalex.org/I161296585","display_name":"Tokyo University of Science","ror":"https://ror.org/05sj3n476","country_code":"JP","type":"education","lineage":["https://openalex.org/I161296585"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Masakiyo Miyazawa","raw_affiliation_strings":["Department of Information Sciences, Tokyo University of Science, Noda, Chiba, 278 8510, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Information Sciences, Tokyo University of Science, Noda, Chiba, 278 8510, Japan","institution_ids":["https://openalex.org/I161296585"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5055752788"],"corresponding_institution_ids":["https://openalex.org/I83019370"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":1.1696,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.81880676,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"86","issue":"3-4","first_page":"277","last_page":"299"},"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/T11195","display_name":"Simulation Techniques and Applications","score":0.9257000088691711,"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/T14470","display_name":"Advanced Data Processing Techniques","score":0.9161999821662903,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/queue","display_name":"Queue","score":0.7782015800476074},{"id":"https://openalex.org/keywords/balance","display_name":"Balance (ability)","score":0.5284380912780762},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5076121091842651},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4320872724056244},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.35647380352020264},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3215436339378357},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.1515716314315796},{"id":"https://openalex.org/keywords/psychology","display_name":"Psychology","score":0.05378830432891846}],"concepts":[{"id":"https://openalex.org/C160403385","wikidata":"https://www.wikidata.org/wiki/Q220543","display_name":"Queue","level":2,"score":0.7782015800476074},{"id":"https://openalex.org/C168031717","wikidata":"https://www.wikidata.org/wiki/Q1530280","display_name":"Balance (ability)","level":2,"score":0.5284380912780762},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5076121091842651},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4320872724056244},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35647380352020264},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3215436339378357},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.1515716314315796},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.05378830432891846},{"id":"https://openalex.org/C169760540","wikidata":"https://www.wikidata.org/wiki/Q207011","display_name":"Neuroscience","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/s11134-017-9528-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11134-017-9528-z","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs11134-017-9528-z.pdf","source":{"id":"https://openalex.org/S148503350","display_name":"Queueing Systems","issn_l":"0257-0130","issn":["0257-0130","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Queueing Systems","raw_type":"journal-article"},{"id":"pmh:oai:pure.tue.nl:openaire/571405d4-4b23-4aa2-b5c9-346ee0237336","is_oa":true,"landing_page_url":"https://research.tue.nl/en/publications/571405d4-4b23-4aa2-b5c9-346ee0237336","pdf_url":null,"source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Boon, M A A, Boxma, O J, Kella, O & Miyazawa, M 2017, 'Queue-length balance equations in multiclass multiserver queues and their generalizations', Queueing Systems, vol. 86, no. 3-4, pp. 277-299. https://doi.org/10.1007/s11134-017-9528-z","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:RePEc:spr:queues:v:86:y:2017:i:3:d:10.1007_s11134-017-9528-z","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s11134-017-9528-z","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:pure.tue.nl:publications/571405d4-4b23-4aa2-b5c9-346ee0237336","is_oa":true,"landing_page_url":"http://www.scopus.com/inward/record.url?scp=85021050492&partnerID=8YFLogxK","pdf_url":null,"source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Boon, M A A, Boxma, O J, Kella, O & Miyazawa, M 2017, 'Queue-length balance equations in multiclass multiserver queues and their generalizations', Queueing Systems, vol. 86, no. 3-4, pp. 277-299. https://doi.org/10.1007/s11134-017-9528-z","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:tue:oai:pure.tue.nl:publications/571405d4-4b23-4aa2-b5c9-346ee0237336","is_oa":true,"landing_page_url":"https://research.tue.nl/nl/publications/571405d4-4b23-4aa2-b5c9-346ee0237336","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Queueing Systems, 86(3-4), 277 - 299. Springer","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1007/s11134-017-9528-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11134-017-9528-z","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs11134-017-9528-z.pdf","source":{"id":"https://openalex.org/S148503350","display_name":"Queueing Systems","issn_l":"0257-0130","issn":["0257-0130","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Queueing Systems","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4003970224","display_name":null,"funder_award_id":"16H027860001","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G4998108420","display_name":null,"funder_award_id":". 024.002.003","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G6799278589","display_name":null,"funder_award_id":"1462/13","funder_id":"https://openalex.org/F4320322252","funder_display_name":"Israel Science Foundation"},{"id":"https://openalex.org/G7830895999","display_name":null,"funder_award_id":"024.002.003","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"}],"funders":[{"id":"https://openalex.org/F4320321800","display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","ror":"https://ror.org/04jsz6e67"},{"id":"https://openalex.org/F4320322252","display_name":"Israel Science Foundation","ror":"https://ror.org/04sazxf24"},{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2597270801.pdf","grobid_xml":"https://content.openalex.org/works/W2597270801.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W75950780","https://openalex.org/W1479759336","https://openalex.org/W1512308554","https://openalex.org/W1516690362","https://openalex.org/W1538390365","https://openalex.org/W1576140702","https://openalex.org/W1973451033","https://openalex.org/W1981702612","https://openalex.org/W1987807478","https://openalex.org/W2004130186","https://openalex.org/W2037250187","https://openalex.org/W2039613719","https://openalex.org/W2063849764","https://openalex.org/W2066489929","https://openalex.org/W2082587160","https://openalex.org/W2084609230","https://openalex.org/W2119693072","https://openalex.org/W2136888963","https://openalex.org/W2146045634","https://openalex.org/W2257781102","https://openalex.org/W2797915579","https://openalex.org/W2921590837","https://openalex.org/W3102982718"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W2042127053"],"abstract_inverted_index":{"A":[0],"classical":[1],"result":[2,42],"for":[3,40,75,79,106,154,162,174],"the":[4,13,18,27,30,134,171],"steady-state":[5],"queue-length":[6,77],"distribution":[7,16,28],"of":[8,17,29,84,136,150],"single-class":[9],"queueing":[10,164],"systems":[11,156,165],"is":[12,46,66],"following:":[14],"The":[15,38],"queue":[19,31],"length":[20,32],"just":[21,33],"before":[22],"an":[23],"arrival":[24,109],"epoch":[25],"equals":[26],"after":[34],"a":[35,80,95,175],"departure":[36],"epoch.":[37],"constraint":[39],"this":[41],"to":[43,68],"be":[44],"valid":[45],"that":[47,64],"arrivals,":[48],"and":[49,103,111,122,125,157],"also":[50,169],"service":[51,126],"completions,":[52],"with":[53,142,166],"probability":[54],"one":[55],"occur":[56],"individually,":[57],"i.e.,":[58],"not":[59,129],"in":[60,140],"batches.":[61],"We":[62,88,132,168],"show":[63],"it":[65],"easy":[67],"write":[69],"down":[70],"somewhat":[71],"similar":[72],"balance":[73,92,138],"equations":[74,93],"multidimensional":[76],"processes":[78],"quite":[81],"general":[82,96],"network":[83],"multiclass":[85],"multiserver":[86],"queues.":[87],"formally":[89],"derive":[90],"those":[91],"under":[94],"framework.":[97,177],"They":[98],"are":[99,104,120],"called":[100],"distributional":[101,172],"relationships":[102,173],"obtained":[105],"any":[107],"external":[108,123],"process":[110],"state-dependent":[112],"routing":[113],"as":[114,116],"long":[115],"certain":[117],"stationarity":[118],"conditions":[119],"satisfied":[121],"arrivals":[124],"completions":[127],"do":[128],"simultaneously":[130],"occur.":[131],"demonstrate":[133],"use":[135],"these":[137],"equations,":[139],"combination":[141],"PASTA,":[143],"by":[144],"(1)":[145],"providing":[146],"very":[147],"simple":[148],"derivations":[149],"some":[151,163],"known":[152],"results":[153,161],"polling":[155],"(2)":[158],"obtaining":[159],"new":[160],"priorities.":[167],"extend":[170],"nonstationary":[176]},"counts_by_year":[{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
