{"id":"https://openalex.org/W1995139215","doi":"https://doi.org/10.1134/s0005117913100032","title":"On the rate of convergence to the stationary distribution in the single-server queuing systems","display_name":"On the rate of convergence to the stationary distribution in the single-server queuing systems","publication_year":2013,"publication_date":"2013-10-01","ids":{"openalex":"https://openalex.org/W1995139215","doi":"https://doi.org/10.1134/s0005117913100032","mag":"1995139215"},"language":"en","primary_location":{"id":"doi:10.1134/s0005117913100032","is_oa":false,"landing_page_url":"https://doi.org/10.1134/s0005117913100032","pdf_url":null,"source":{"id":"https://openalex.org/S134188425","display_name":"Automation and Remote Control","issn_l":"0005-1179","issn":["0005-1179","1608-3032"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Automation and Remote Control","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/A5070425488","display_name":"A. Yu. Veretennikov","orcid":"https://orcid.org/0000-0001-8478-0515"},"institutions":[{"id":"https://openalex.org/I4210107660","display_name":"Institute for Information Transmission Problems","ror":"https://ror.org/013w2d378","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210097085","https://openalex.org/I4210107660"]},{"id":"https://openalex.org/I130828816","display_name":"University of Leeds","ror":"https://ror.org/024mrxd33","country_code":"GB","type":"education","lineage":["https://openalex.org/I130828816"]}],"countries":["GB","RU"],"is_corresponding":true,"raw_author_name":"A. Yu. Veretennikov","raw_affiliation_strings":["Institute for Information Transmission Problems (Kharkevich Institute), Russian Academy of Sciences, Moscow, Russia","School of Mathematics, University of Leeds, Leeds, UK"],"affiliations":[{"raw_affiliation_string":"Institute for Information Transmission Problems (Kharkevich Institute), Russian Academy of Sciences, Moscow, Russia","institution_ids":["https://openalex.org/I4210107660"]},{"raw_affiliation_string":"School of Mathematics, University of Leeds, Leeds, UK","institution_ids":["https://openalex.org/I130828816"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5070425488"],"corresponding_institution_ids":["https://openalex.org/I130828816","https://openalex.org/I4210107660"],"apc_list":null,"apc_paid":null,"fwci":1.579,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.84661007,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"74","issue":"10","first_page":"1620","last_page":"1629"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10974","display_name":"Advanced Queuing Theory Analysis","score":0.9912999868392944,"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":0.9912999868392944,"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":0.9485999941825867,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9020000100135803,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/convergence","display_name":"Convergence (economics)","score":0.7261118292808533},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.6776925325393677},{"id":"https://openalex.org/keywords/queueing-theory","display_name":"Queueing theory","score":0.666041910648346},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.563540518283844},{"id":"https://openalex.org/keywords/stationary-distribution","display_name":"Stationary distribution","score":0.5478519797325134},{"id":"https://openalex.org/keywords/queueing-system","display_name":"Queueing system","score":0.5123006105422974},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5063601732254028},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4408223330974579},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.42024683952331543},{"id":"https://openalex.org/keywords/queue-management-system","display_name":"Queue management system","score":0.4195905923843384},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.37387943267822266},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3295210599899292},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.19480574131011963},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08108639717102051},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.0586601197719574},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.04710301756858826}],"concepts":[{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.7261118292808533},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.6776925325393677},{"id":"https://openalex.org/C22684755","wikidata":"https://www.wikidata.org/wiki/Q847526","display_name":"Queueing theory","level":2,"score":0.666041910648346},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.563540518283844},{"id":"https://openalex.org/C98951983","wikidata":"https://www.wikidata.org/wiki/Q7604341","display_name":"Stationary distribution","level":3,"score":0.5478519797325134},{"id":"https://openalex.org/C2986422491","wikidata":"https://www.wikidata.org/wiki/Q847526","display_name":"Queueing system","level":3,"score":0.5123006105422974},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5063601732254028},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4408223330974579},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.42024683952331543},{"id":"https://openalex.org/C128220111","wikidata":"https://www.wikidata.org/wiki/Q4531011","display_name":"Queue management system","level":3,"score":0.4195905923843384},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37387943267822266},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3295210599899292},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.19480574131011963},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08108639717102051},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0586601197719574},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.04710301756858826},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1134/s0005117913100032","is_oa":false,"landing_page_url":"https://doi.org/10.1134/s0005117913100032","pdf_url":null,"source":{"id":"https://openalex.org/S134188425","display_name":"Automation and Remote Control","issn_l":"0005-1179","issn":["0005-1179","1608-3032"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Automation and Remote Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.6600000262260437,"display_name":"Reduced inequalities"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320328568","display_name":"Hausdorff Center for Mathematics","ror":null},{"id":"https://openalex.org/F4320337180","display_name":"Hausdorff Research Institute for Mathematics","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W91439453","https://openalex.org/W1521662808","https://openalex.org/W1540515733","https://openalex.org/W1991350432","https://openalex.org/W2005844982","https://openalex.org/W2041072514","https://openalex.org/W2067769121","https://openalex.org/W2069858642","https://openalex.org/W2126794261","https://openalex.org/W2313576000","https://openalex.org/W2322669384","https://openalex.org/W2325372724","https://openalex.org/W4213329537","https://openalex.org/W4230556510"],"related_works":["https://openalex.org/W2368961776","https://openalex.org/W1535772705","https://openalex.org/W2361230975","https://openalex.org/W2184312385","https://openalex.org/W2622283040","https://openalex.org/W1983551639","https://openalex.org/W147520506","https://openalex.org/W4388174918","https://openalex.org/W2077478381","https://openalex.org/W2387026039"],"abstract_inverted_index":{"For":[0],"a":[1],"version":[2],"of":[3,21,38,41],"the":[4,16,19,24,35,39,46],"single-server":[5],"infinite-buffer":[6],"queuing":[7],"system":[8],"which":[9],"is":[10],"much":[11],"more":[12],"general":[13],"than":[14],"M/G/1,":[15],"results":[17],"on":[18],"rate":[20,40],"convergence":[22,42],"to":[23],"stationary":[25],"mode":[26],"were":[27,43],"reviewed":[28],"in":[29],"brief.":[30],"New":[31],"sufficient":[32],"conditions":[33],"guaranteeing":[34],"polynomial":[36],"estimate":[37],"established":[44],"using":[45],"\u201cMarkovization\u201d":[47],"method.":[48]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}