{"id":"https://openalex.org/W3092885859","doi":"https://doi.org/10.3390/math8101803","title":"Approximations in Performance Analysis of a Controllable Queueing System with Heterogeneous Servers","display_name":"Approximations in Performance Analysis of a Controllable Queueing System with Heterogeneous Servers","publication_year":2020,"publication_date":"2020-10-16","ids":{"openalex":"https://openalex.org/W3092885859","doi":"https://doi.org/10.3390/math8101803","mag":"3092885859"},"language":"en","primary_location":{"id":"doi:10.3390/math8101803","doi":"https://doi.org/10.3390/math8101803","is_oa":true,"landing_page_url":"https://doi.org/10.3390/math8101803","pdf_url":"https://www.mdpi.com/2227-7390/8/10/1803/pdf?version=1602842096","source":{"id":"https://openalex.org/S4210192031","display_name":"Mathematics","issn_l":"2227-7390","issn":["2227-7390"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2227-7390/8/10/1803/pdf?version=1602842096","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5084201217","display_name":"Dmitry Efrosinin","orcid":"https://orcid.org/0000-0002-0902-6640","observed_orcids":["https://orcid.org/0000-0002-0902-6640"]},"institutions":[{"id":"https://openalex.org/I121883995","display_name":"Johannes Kepler University of Linz","ror":"https://ror.org/052r2xn60","country_code":"AT","type":"education","lineage":["https://openalex.org/I121883995"]},{"id":"https://openalex.org/I126527374","display_name":"Peoples' Friendship University of Russia","ror":"https://ror.org/02dn9h927","country_code":"RU","type":"education","lineage":["https://openalex.org/I126527374"]}],"countries":["AT","RU"],"is_corresponding":false,"raw_author_name":"Dmitry Efrosinin","raw_affiliation_strings":["Department of Information Technologies, Faculty of Mathematics and Natural Sciences, Peoples\u2019 Friendship University of Russia (RUDN University), 117198 Moscow, Russia","Insitute for Stochastics, Johannes Kepler University, 4040 Linz, Austria"],"raw_orcid":"https://orcid.org/0000-0002-0902-6640","affiliations":[{"raw_affiliation_string":"Department of Information Technologies, Faculty of Mathematics and Natural Sciences, Peoples\u2019 Friendship University of Russia (RUDN University), 117198 Moscow, Russia","institution_ids":["https://openalex.org/I126527374"]},{"raw_affiliation_string":"Insitute for Stochastics, Johannes Kepler University, 4040 Linz, Austria","institution_ids":["https://openalex.org/I121883995"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102879479","display_name":"Natalia V. Stepanova","orcid":"https://orcid.org/0000-0001-5920-1358","observed_orcids":["https://orcid.org/0000-0001-5920-1358"]},"institutions":[{"id":"https://openalex.org/I4210157430","display_name":"V. A. Trapeznikov Institute of Control Sciences","ror":"https://ror.org/05f3yt521","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210157430","https://openalex.org/I4210164537"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Natalia Stepanova","raw_affiliation_strings":["Laboratory N17, Trapeznikov Institute of Control Sciences of RAS, 117997 Moscow, Russia"],"raw_orcid":"https://orcid.org/0000-0001-5920-1358","affiliations":[{"raw_affiliation_string":"Laboratory N17, Trapeznikov Institute of Control Sciences of RAS, 117997 Moscow, Russia","institution_ids":["https://openalex.org/I4210157430"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057460510","display_name":"J\u00e1nos Sztrik","orcid":"https://orcid.org/0000-0002-5303-818X","observed_orcids":["https://orcid.org/0000-0002-5303-818X"]},"institutions":[{"id":"https://openalex.org/I132735039","display_name":"University of Debrecen","ror":"https://ror.org/02xf66n48","country_code":"HU","type":"education","lineage":["https://openalex.org/I132735039"]}],"countries":["HU"],"is_corresponding":true,"raw_author_name":"Janos Sztrik","raw_affiliation_strings":["Department of Informatics and Networks, Faculty of Informatics, University of Debrecen, 4032 Debrecen, Hungary"],"raw_orcid":"https://orcid.org/0000-0002-5303-818X","affiliations":[{"raw_affiliation_string":"Department of Informatics and Networks, Faculty of Informatics, University of Debrecen, 4032 Debrecen, Hungary","institution_ids":["https://openalex.org/I132735039"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022765907","display_name":"Andreas Plank","orcid":"https://orcid.org/0000-0002-2653-0689","observed_orcids":["https://orcid.org/0000-0002-2653-0689"]},"institutions":[{"id":"https://openalex.org/I121883995","display_name":"Johannes Kepler University of Linz","ror":"https://ror.org/052r2xn60","country_code":"AT","type":"education","lineage":["https://openalex.org/I121883995"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Andreas Plank","raw_affiliation_strings":["Insitute for Stochastics, Johannes Kepler University, 4040 Linz, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Insitute for Stochastics, Johannes Kepler University, 4040 Linz, Austria","institution_ids":["https://openalex.org/I121883995"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5057460510"],"corresponding_institution_ids":["https://openalex.org/I132735039"],"apc_list":{"value":1200,"currency":"CHF","value_usd":1267},"apc_paid":{"value":1200,"currency":"CHF","value_usd":1267},"fwci":1.0345,"has_fulltext":true,"cited_by_count":11,"citation_normalized_percentile":{"value":0.78066183,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":96},"biblio":{"volume":"8","issue":"10","first_page":"1803","last_page":"1803"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10974","display_name":"Advanced Queuing Theory Analysis","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T10974","display_name":"Advanced Queuing Theory Analysis","score":1.0,"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/T12288","display_name":"Optimization and Search Problems","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"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/T13553","display_name":"Age of Information Optimization","score":0.0,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/heterogeneous-servers","display_name":"heterogeneous servers","score":0.9369999766349792},{"id":"https://openalex.org/keywords/multi-server-queues","display_name":"multi-server queues","score":0.8560000061988831},{"id":"https://openalex.org/keywords/optimal-control-policy","display_name":"optimal control policy","score":0.6769999861717224},{"id":"https://openalex.org/keywords/markov-decision-process","display_name":"Markov decision process","score":0.6430000066757202},{"id":"https://openalex.org/keywords/policy-iteration","display_name":"policy iteration","score":0.9760000109672546},{"id":"https://openalex.org/keywords/approximation-bounds","display_name":"approximation bounds","score":0.4269999861717224},{"id":"https://openalex.org/keywords/preemption","display_name":"preemption","score":0.7540000081062317},{"id":"https://openalex.org/keywords/sensitivity-analysis","display_name":"sensitivity analysis","score":0.6890000104904175}],"concepts":[{"id":"https://openalex.org/C93996380","wikidata":"https://www.wikidata.org/wiki/Q44127","display_name":"Server","level":2,"score":0.8235470652580261},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7030961513519287},{"id":"https://openalex.org/C22684755","wikidata":"https://www.wikidata.org/wiki/Q847526","display_name":"Queueing theory","level":2,"score":0.6827466487884521},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.6278177499771118},{"id":"https://openalex.org/C160403385","wikidata":"https://www.wikidata.org/wiki/Q220543","display_name":"Queue","level":2,"score":0.6156808137893677},{"id":"https://openalex.org/C206952183","wikidata":"https://www.wikidata.org/wiki/Q1193100","display_name":"Preemption","level":2,"score":0.6039049029350281},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5336279273033142},{"id":"https://openalex.org/C106189395","wikidata":"https://www.wikidata.org/wiki/Q176789","display_name":"Markov decision process","level":3,"score":0.5188449621200562},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.4964361786842346},{"id":"https://openalex.org/C33891772","wikidata":"https://www.wikidata.org/wiki/Q6505536","display_name":"Layered queueing network","level":3,"score":0.47724294662475586},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4718458652496338},{"id":"https://openalex.org/C2780378061","wikidata":"https://www.wikidata.org/wiki/Q25351891","display_name":"Service (business)","level":2,"score":0.41027626395225525},{"id":"https://openalex.org/C79403827","wikidata":"https://www.wikidata.org/wiki/Q3988","display_name":"Real-time computing","level":1,"score":0.4012691378593445},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.3766401410102844},{"id":"https://openalex.org/C120314980","wikidata":"https://www.wikidata.org/wiki/Q180634","display_name":"Distributed computing","level":1,"score":0.32533299922943115},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.20036935806274414},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1058414876461029},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.07593527436256409},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C136264566","wikidata":"https://www.wikidata.org/wiki/Q159810","display_name":"Economy","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/math8101803","doi":"https://doi.org/10.3390/math8101803","is_oa":true,"landing_page_url":"https://doi.org/10.3390/math8101803","pdf_url":"https://www.mdpi.com/2227-7390/8/10/1803/pdf?version=1602842096","source":{"id":"https://openalex.org/S4210192031","display_name":"Mathematics","issn_l":"2227-7390","issn":["2227-7390"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:dea.lib.unideb.hu:2437/297084","doi":null,"is_oa":true,"landing_page_url":"http://hdl.handle.net/2437/297084","pdf_url":"https://dea.lib.unideb.hu/bitstreams/406aa952-3bdc-4780-a639-46682ca37c03/download","source":{"id":"https://openalex.org/S4306402089","display_name":"University of Debrecen Electronic Archive (University of Debrecen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I132735039","host_organization_name":"University of Debrecen","host_organization_lineage":["https://openalex.org/I132735039"],"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":null,"raw_type":"foly\u00f3iratcikk"},{"id":"pmh:oai:RePEc:gam:jmathe:v:8:y:2020:i:10:p:1803-:d:429103","doi":null,"is_oa":false,"landing_page_url":"https://www.mdpi.com/2227-7390/8/10/1803/","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,"listed_in":[],"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:dea.lib.unideb.hu:2437/297085","doi":null,"is_oa":true,"landing_page_url":"http://hdl.handle.net/2437/297085","pdf_url":null,"source":{"id":"https://openalex.org/S4306402089","display_name":"University of Debrecen Electronic Archive (University of Debrecen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I132735039","host_organization_name":"University of Debrecen","host_organization_lineage":["https://openalex.org/I132735039"],"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":"","raw_type":null},{"id":"pmh:oai:doaj.org/article:55f89ac39f374cb68405fb6d11ffd072","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/55f89ac39f374cb68405fb6d11ffd072","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics, Vol 8, Iss 10, p 1803 (2020)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/math8101803","doi":"https://doi.org/10.3390/math8101803","is_oa":true,"landing_page_url":"https://doi.org/10.3390/math8101803","pdf_url":"https://www.mdpi.com/2227-7390/8/10/1803/pdf?version=1602842096","source":{"id":"https://openalex.org/S4210192031","display_name":"Mathematics","issn_l":"2227-7390","issn":["2227-7390"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3092885859.pdf","grobid_xml":"https://content.openalex.org/works/W3092885859.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W1541744154","https://openalex.org/W1558804239","https://openalex.org/W1964272258","https://openalex.org/W1973249198","https://openalex.org/W2006358910","https://openalex.org/W2028145673","https://openalex.org/W2052694905","https://openalex.org/W2057872473","https://openalex.org/W2069613863","https://openalex.org/W2075558808","https://openalex.org/W2079783788","https://openalex.org/W2086751597","https://openalex.org/W2088393393","https://openalex.org/W2107267987","https://openalex.org/W2128313599","https://openalex.org/W2143920039","https://openalex.org/W2148273873","https://openalex.org/W2157996788","https://openalex.org/W2164255506","https://openalex.org/W2259379633","https://openalex.org/W2332948009","https://openalex.org/W2334782222","https://openalex.org/W2808652411","https://openalex.org/W2970599601","https://openalex.org/W3005996204","https://openalex.org/W4244122339"],"related_works":["https://openalex.org/W3205067799","https://openalex.org/W2498176466","https://openalex.org/W1973249198","https://openalex.org/W2080475451","https://openalex.org/W2503272205","https://openalex.org/W7100742695","https://openalex.org/W7036158754","https://openalex.org/W3120409924","https://openalex.org/W1985564669","https://openalex.org/W2125171850"],"abstract_inverted_index":{"The":[0,24,51,72],"paper":[1],"studies":[2],"a":[3,36,89,113,122,157],"controllable":[4],"multi-server":[5],"heterogeneous":[6,153],"queueing":[7,154],"system":[8,46,155,168],"where":[9],"servers":[10,33],"operate":[11],"at":[12],"different":[13],"service":[14,20,196],"rates":[15],"without":[16],"preemption,":[17],"i.e.,":[18],"the":[19,29,32,39,45,56,63,77,96,100,126,134,140,161,167,171,175,185,191],"times":[21],"are":[22,59],"uninterrupted.":[23],"optimal":[25,64,73,127,172],"control":[26],"policy":[27,66],"allocates":[28],"customers":[30,43,165],"between":[31],"in":[34,44,166,190],"such":[35],"way":[37],"that":[38],"mean":[40,69,162],"number":[41,115,163],"of":[42,80,84,91,102,116,125,164,184,193],"reaches":[47],"its":[48],"minimal":[49],"value.":[50],"Markov":[52],"decision":[53],"model":[54],"and":[55,67,129,143,195],"policy-iteration":[57],"algorithm":[58],"used":[60,179],"to":[61,159,180,188],"calculate":[62],"allocation":[65],"corresponding":[68],"performance":[70],"characteristics.":[71],"policy,":[74],"when":[75],"neglecting":[76],"weak":[78],"influence":[79],"slow":[81],"servers,":[82,117],"is":[83,178],"threshold":[85,92],"type":[86],"defined":[87],"as":[88],"sequence":[90],"levels":[93],"which":[94],"specifies":[95],"queue":[97],"lengths":[98],"for":[99,110],"usage":[101],"any":[103],"slower":[104],"server.":[105],"To":[106],"avoid":[107],"time-consuming":[108],"calculations":[109],"systems":[111],"with":[112,133,156],"large":[114],"we":[118],"focus":[119],"here":[120],"on":[121,148],"heuristic":[123,186],"evaluation":[124],"thresholds":[128],"compare":[130],"this":[131],"solution":[132,187],"real":[135],"values.":[136],"We":[137],"develop":[138],"also":[139],"simple":[141],"lower":[142],"upper":[144],"bound":[145],"methods":[146],"based":[147],"approximation":[149],"by":[150],"an":[151],"equivalent":[152],"preemption":[158],"measure":[160],"operating":[169],"under":[170],"policy.":[173],"Finally,":[174],"simulation":[176],"technique":[177],"provide":[181],"sensitivity":[182],"analysis":[183],"changes":[189],"form":[192],"inter-arrival":[194],"time":[197],"distributions.":[198]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2020-10-22T00:00:00"}
