{"id":"https://openalex.org/W3195684283","doi":"https://doi.org/10.1080/23799927.2021.1969432","title":"On the law of iterated logarithm for extreme queue length in an open queueing network","display_name":"On the law of iterated logarithm for extreme queue length in an open queueing network","publication_year":2021,"publication_date":"2021-07-03","ids":{"openalex":"https://openalex.org/W3195684283","doi":"https://doi.org/10.1080/23799927.2021.1969432","mag":"3195684283"},"language":"en","primary_location":{"id":"doi:10.1080/23799927.2021.1969432","is_oa":false,"landing_page_url":"https://doi.org/10.1080/23799927.2021.1969432","pdf_url":null,"source":{"id":"https://openalex.org/S4210234901","display_name":"International Journal of Computer Mathematics Computer Systems Theory","issn_l":"2379-9927","issn":["2379-9927","2379-9935"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics: Computer Systems Theory","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/A5082480764","display_name":"Saulius Minkevi\u010dius","orcid":"https://orcid.org/0000-0002-5727-7217"},"institutions":[{"id":"https://openalex.org/I173212132","display_name":"Vilnius University","ror":"https://ror.org/03nadee84","country_code":"LT","type":"education","lineage":["https://openalex.org/I173212132"]}],"countries":["LT"],"is_corresponding":true,"raw_author_name":"S. Minkevi\u010dius","raw_affiliation_strings":["Vilnius University, Institute of Data Science and Digital Technologies, Akademijos St. 4, Vilnius, Lithuania"],"affiliations":[{"raw_affiliation_string":"Vilnius University, Institute of Data Science and Digital Technologies, Akademijos St. 4, Vilnius, Lithuania","institution_ids":["https://openalex.org/I173212132"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5077937900","display_name":"Leonidas Sakalauskas","orcid":"https://orcid.org/0000-0002-7874-7986"},"institutions":[{"id":"https://openalex.org/I173212132","display_name":"Vilnius University","ror":"https://ror.org/03nadee84","country_code":"LT","type":"education","lineage":["https://openalex.org/I173212132"]}],"countries":["LT"],"is_corresponding":false,"raw_author_name":"L. L. Sakalauskas","raw_affiliation_strings":["Vilnius University, Institute of Data Science and Digital Technologies, Akademijos St. 4, Vilnius, Lithuania"],"affiliations":[{"raw_affiliation_string":"Vilnius University, Institute of Data Science and Digital Technologies, Akademijos St. 4, Vilnius, Lithuania","institution_ids":["https://openalex.org/I173212132"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5082480764"],"corresponding_institution_ids":["https://openalex.org/I173212132"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.16798681,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"6","issue":"3","first_page":"220","last_page":"235"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10974","display_name":"Advanced Queuing Theory Analysis","score":0.9998999834060669,"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":0.9998999834060669,"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/T11720","display_name":"Probability and Risk Models","score":0.9952999949455261,"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/T11716","display_name":"Random Matrices and Applications","score":0.9922999739646912,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/law-of-the-iterated-logarithm","display_name":"Law of the iterated logarithm","score":0.7958608269691467},{"id":"https://openalex.org/keywords/queueing-theory","display_name":"Queueing theory","score":0.6847177743911743},{"id":"https://openalex.org/keywords/iterated-logarithm","display_name":"Iterated logarithm","score":0.6845049858093262},{"id":"https://openalex.org/keywords/layered-queueing-network","display_name":"Layered queueing network","score":0.6649961471557617},{"id":"https://openalex.org/keywords/g-network","display_name":"G-network","score":0.6529650688171387},{"id":"https://openalex.org/keywords/bulk-queue","display_name":"Bulk queue","score":0.5974032878875732},{"id":"https://openalex.org/keywords/heavy-traffic-approximation","display_name":"Heavy traffic approximation","score":0.5292113423347473},{"id":"https://openalex.org/keywords/mean-value-analysis","display_name":"Mean value analysis","score":0.5268068313598633},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5236629843711853},{"id":"https://openalex.org/keywords/traffic-equations","display_name":"Traffic equations","score":0.48902711272239685},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.48600324988365173},{"id":"https://openalex.org/keywords/queue","display_name":"Queue","score":0.4464680850505829},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.4398176074028015},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3224943280220032},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.31207573413848877},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.30193138122558594},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.19544348120689392},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.17570805549621582},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1428850293159485}],"concepts":[{"id":"https://openalex.org/C139907963","wikidata":"https://www.wikidata.org/wiki/Q198740","display_name":"Law of the iterated logarithm","level":3,"score":0.7958608269691467},{"id":"https://openalex.org/C22684755","wikidata":"https://www.wikidata.org/wiki/Q847526","display_name":"Queueing theory","level":2,"score":0.6847177743911743},{"id":"https://openalex.org/C130594498","wikidata":"https://www.wikidata.org/wiki/Q2028293","display_name":"Iterated logarithm","level":3,"score":0.6845049858093262},{"id":"https://openalex.org/C33891772","wikidata":"https://www.wikidata.org/wiki/Q6505536","display_name":"Layered queueing network","level":3,"score":0.6649961471557617},{"id":"https://openalex.org/C122039914","wikidata":"https://www.wikidata.org/wiki/Q5511950","display_name":"G-network","level":4,"score":0.6529650688171387},{"id":"https://openalex.org/C87950461","wikidata":"https://www.wikidata.org/wiki/Q4996486","display_name":"Bulk queue","level":3,"score":0.5974032878875732},{"id":"https://openalex.org/C193290586","wikidata":"https://www.wikidata.org/wiki/Q17022030","display_name":"Heavy traffic approximation","level":2,"score":0.5292113423347473},{"id":"https://openalex.org/C129978463","wikidata":"https://www.wikidata.org/wiki/Q6803663","display_name":"Mean value analysis","level":4,"score":0.5268068313598633},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5236629843711853},{"id":"https://openalex.org/C113804518","wikidata":"https://www.wikidata.org/wiki/Q17097358","display_name":"Traffic equations","level":4,"score":0.48902711272239685},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.48600324988365173},{"id":"https://openalex.org/C160403385","wikidata":"https://www.wikidata.org/wiki/Q220543","display_name":"Queue","level":2,"score":0.4464680850505829},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.4398176074028015},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3224943280220032},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.31207573413848877},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.30193138122558594},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.19544348120689392},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.17570805549621582},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1428850293159485}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/23799927.2021.1969432","is_oa":false,"landing_page_url":"https://doi.org/10.1080/23799927.2021.1969432","pdf_url":null,"source":{"id":"https://openalex.org/S4210234901","display_name":"International Journal of Computer Mathematics Computer Systems Theory","issn_l":"2379-9927","issn":["2379-9927","2379-9935"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics: Computer Systems Theory","raw_type":"journal-article"},{"id":"pmh:oai:vdu.lt:20.500.12259/265412","is_oa":false,"landing_page_url":"https://hdl.handle.net/20.500.12259/265412","pdf_url":null,"source":{"id":"https://openalex.org/S7407055361","display_name":"Vytautas Magnus University","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"research article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.4399999976158142,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W62053411","https://openalex.org/W93532501","https://openalex.org/W1964975282","https://openalex.org/W1965146059","https://openalex.org/W1965833900","https://openalex.org/W1994769971","https://openalex.org/W2011819105","https://openalex.org/W2013077658","https://openalex.org/W2013077976","https://openalex.org/W2026989004","https://openalex.org/W2041058815","https://openalex.org/W2055491565","https://openalex.org/W2076406848","https://openalex.org/W2082851249","https://openalex.org/W2083969236","https://openalex.org/W2132887128","https://openalex.org/W2145420589","https://openalex.org/W2151518886","https://openalex.org/W2157714062","https://openalex.org/W2161269853","https://openalex.org/W2164862117","https://openalex.org/W2168246988","https://openalex.org/W2191768192","https://openalex.org/W2412144447","https://openalex.org/W2793085414","https://openalex.org/W2802694236","https://openalex.org/W2802739963","https://openalex.org/W2964263781","https://openalex.org/W3125723919","https://openalex.org/W4232334520","https://openalex.org/W4237138370","https://openalex.org/W4244239304","https://openalex.org/W4299533062"],"related_works":["https://openalex.org/W2014955369","https://openalex.org/W2042042241","https://openalex.org/W2943669389","https://openalex.org/W2758458231","https://openalex.org/W2011819105","https://openalex.org/W2073987053","https://openalex.org/W2600727783","https://openalex.org/W3195684283","https://openalex.org/W2937300145","https://openalex.org/W2366846308"],"abstract_inverted_index":{"The":[0],"purpose":[1],"of":[2,8,18,27,31,45,49,55,61,71,89],"this":[3],"research":[4],"in":[5,33,86,97],"the":[6,9,16,19,24,28,42,46,51,56,77],"field":[7],"open":[10,35,94],"queueing":[11,36,57,95],"network":[12,96],"is":[13,39],"to":[14],"prove":[15],"Law":[17],"Iterated":[20],"Logarithm":[21],"(LIL)":[22],"for":[23,41,67],"extreme":[25,43,68],"value":[26],"queue":[29,47,69],"length":[30,48,70],"customers":[32,50],"an":[34,93],"network.":[37],"LIL":[38],"proved":[40],"values":[44],"important":[52],"probability":[53],"characteristic":[54],"system":[58],"under":[59],"conditions":[60,88],"heavy":[62],"traffic.":[63],"Also,":[64],"we":[65],"present":[66],"jobs":[72],"Probability":[73],"Laws":[74],"((theorems":[75],"on":[76],"LIL,":[78],"Fluid":[79],"Limits":[80],"Theorem":[81],"and":[82,91,100],"Diffusion":[83],"Limit":[84],"Theorem)":[85],"various":[87],"traffic":[90],"simulating":[92],"Appendices":[98],"1":[99],"2.":[101]},"counts_by_year":[],"updated_date":"2026-03-02T08:37:19.008085","created_date":"2025-10-10T00:00:00"}
