{"id":"https://openalex.org/W2038023154","doi":"https://doi.org/10.1214/12-aap888","title":"Decay of tails at equilibrium for FIFO join the shortest queue networks","display_name":"Decay of tails at equilibrium for FIFO join the shortest queue networks","publication_year":2013,"publication_date":"2013-08-28","ids":{"openalex":"https://openalex.org/W2038023154","doi":"https://doi.org/10.1214/12-aap888","mag":"2038023154"},"language":"en","primary_location":{"id":"doi:10.1214/12-aap888","doi":"https://doi.org/10.1214/12-aap888","is_oa":true,"landing_page_url":"https://doi.org/10.1214/12-aap888","pdf_url":"https://projecteuclid.org/journals/annals-of-applied-probability/volume-23/issue-5/Decay-of-tails-at-equilibrium-for-FIFO-join-the-shortest/10.1214/12-AAP888.pdf","source":{"id":"https://openalex.org/S9093621","display_name":"The Annals of Applied Probability","issn_l":"1050-5164","issn":["1050-5164","2168-8737"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-a","anvur-class-a","anvur-scientific","cwts-core","dongbi-b","doyens","jufo-3","norway-2","poland-140","russia-white-list-1"],"host_organization":"https://openalex.org/P4310319881","host_organization_name":"Institute of Mathematical Statistics","host_organization_lineage":["https://openalex.org/P4310319881"],"host_organization_lineage_names":["Institute of Mathematical Statistics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Annals of Applied Probability","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://projecteuclid.org/journals/annals-of-applied-probability/volume-23/issue-5/Decay-of-tails-at-equilibrium-for-FIFO-join-the-shortest/10.1214/12-AAP888.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Maury Bramson","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Maury Bramson","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102981342","display_name":"Yi Lu","orcid":"https://orcid.org/0000-0002-6768-7893","observed_orcids":["https://orcid.org/0000-0002-6768-7893"]},"institutions":[{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]},{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yi Lu","raw_affiliation_strings":["PRABHAKAR STANFORD UNIVERSITY DAVID PACKARD BUILDING , ROOM 269 STANFORD , CALIFORNIA 94305 USA","University of Minnesota , University of Illinois and Stanford University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"PRABHAKAR STANFORD UNIVERSITY DAVID PACKARD BUILDING , ROOM 269 STANFORD , CALIFORNIA 94305 USA","institution_ids":["https://openalex.org/I97018004"]},{"raw_affiliation_string":"University of Minnesota , University of Illinois and Stanford University","institution_ids":["https://openalex.org/I130238516","https://openalex.org/I97018004"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018734150","display_name":"Balaji Prabhakar B","orcid":"https://orcid.org/0009-0006-3106-8720","observed_orcids":["https://orcid.org/0009-0006-3106-8720"]},"institutions":[{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]},{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]},{"id":"https://openalex.org/I2801919071","display_name":"University of Illinois System","ror":"https://ror.org/05e94g991","country_code":"US","type":"education","lineage":["https://openalex.org/I2801919071"]},{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Balaji Prabhakar","raw_affiliation_strings":["UNIVERSITY OF ILLINOIS COORDINATED SCIENCE LAB 1308 W. MAIN STREET URBANA , ILLINOIS 61801 USA","University of Minnesota , University of Illinois and Stanford University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"UNIVERSITY OF ILLINOIS COORDINATED SCIENCE LAB 1308 W. MAIN STREET URBANA , ILLINOIS 61801 USA","institution_ids":["https://openalex.org/I157725225","https://openalex.org/I2801919071"]},{"raw_affiliation_string":"University of Minnesota , University of Illinois and Stanford University","institution_ids":["https://openalex.org/I130238516","https://openalex.org/I97018004"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.3761,"has_fulltext":true,"cited_by_count":32,"citation_normalized_percentile":{"value":0.95001207,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"23","issue":"5","first_page":"1841","last_page":"1878"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10974","display_name":"Advanced Queuing Theory Analysis","score":0.9970999956130981,"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":0.9970999956130981,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.00039999998989515007,"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"}},{"id":"https://openalex.org/T10138","display_name":"Network Traffic and Congestion Control","score":9.999999747378752e-05,"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/join-the-shortest-queue","display_name":"join-the-shortest-queue","score":0.8889999985694885},{"id":"https://openalex.org/keywords/heavy-tailed-distributions","display_name":"heavy-tailed distributions","score":0.515999972820282},{"id":"https://openalex.org/keywords/large-system-limit","display_name":"large system limit","score":0.33500000834465027},{"id":"https://openalex.org/keywords/poisson-arrivals","display_name":"Poisson arrivals","score":0.5059999823570251},{"id":"https://openalex.org/keywords/decreasing-hazard-rate","display_name":"decreasing hazard rate","score":0.4399999976158142}],"concepts":[{"id":"https://openalex.org/C2777145635","wikidata":"https://www.wikidata.org/wiki/Q515636","display_name":"FIFO (computing and electronics)","level":2,"score":0.7402999997138977},{"id":"https://openalex.org/C160403385","wikidata":"https://www.wikidata.org/wiki/Q220543","display_name":"Queue","level":2,"score":0.6103000044822693},{"id":"https://openalex.org/C124444977","wikidata":"https://www.wikidata.org/wiki/Q4025962","display_name":"Fork\u2013join queue","level":4,"score":0.5699999928474426},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5038999915122986},{"id":"https://openalex.org/C2780378061","wikidata":"https://www.wikidata.org/wiki/Q25351891","display_name":"Service (business)","level":2,"score":0.4851999878883362},{"id":"https://openalex.org/C55350006","wikidata":"https://www.wikidata.org/wiki/Q237193","display_name":"Exponential distribution","level":2,"score":0.4571000039577484},{"id":"https://openalex.org/C130979935","wikidata":"https://www.wikidata.org/wiki/Q568954","display_name":"Ansatz","level":2,"score":0.4453999996185303},{"id":"https://openalex.org/C87950461","wikidata":"https://www.wikidata.org/wiki/Q4996486","display_name":"Bulk queue","level":3,"score":0.43070000410079956},{"id":"https://openalex.org/C2776124973","wikidata":"https://www.wikidata.org/wiki/Q3183033","display_name":"Join (topology)","level":2,"score":0.4296000003814697},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.3840000033378601},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.3808000087738037},{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.37049999833106995},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.3635999858379364},{"id":"https://openalex.org/C201511382","wikidata":"https://www.wikidata.org/wiki/Q16801758","display_name":"Multilevel queue","level":4,"score":0.3497999906539917},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3287999927997589},{"id":"https://openalex.org/C2779084733","wikidata":"https://www.wikidata.org/wiki/Q17097343","display_name":"Processor sharing","level":3,"score":0.31940001249313354},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3142000138759613},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3010999858379364},{"id":"https://openalex.org/C774472","wikidata":"https://www.wikidata.org/wiki/Q6760393","display_name":"Margin (machine learning)","level":2,"score":0.299699991941452},{"id":"https://openalex.org/C22684755","wikidata":"https://www.wikidata.org/wiki/Q847526","display_name":"Queueing theory","level":2,"score":0.2962000072002411},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.2953000068664551},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.275299996137619},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.25429999828338623}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1214/12-aap888","doi":"https://doi.org/10.1214/12-aap888","is_oa":true,"landing_page_url":"https://doi.org/10.1214/12-aap888","pdf_url":"https://projecteuclid.org/journals/annals-of-applied-probability/volume-23/issue-5/Decay-of-tails-at-equilibrium-for-FIFO-join-the-shortest/10.1214/12-AAP888.pdf","source":{"id":"https://openalex.org/S9093621","display_name":"The Annals of Applied Probability","issn_l":"1050-5164","issn":["1050-5164","2168-8737"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-a","anvur-class-a","anvur-scientific","cwts-core","dongbi-b","doyens","jufo-3","norway-2","poland-140","russia-white-list-1"],"host_organization":"https://openalex.org/P4310319881","host_organization_name":"Institute of Mathematical Statistics","host_organization_lineage":["https://openalex.org/P4310319881"],"host_organization_lineage_names":["Institute of Mathematical Statistics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Annals of Applied Probability","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1106.4582","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1106.4582","pdf_url":"https://arxiv.org/pdf/1106.4582","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"pmh:oai:CULeuclid:euclid.aoap/1377696300","doi":null,"is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.aoap/1377696300","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"doi:10.48550/arxiv.1106.4582","doi":"https://doi.org/10.48550/arxiv.1106.4582","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1106.4582","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.1214/12-aap888","doi":"https://doi.org/10.1214/12-aap888","is_oa":true,"landing_page_url":"https://doi.org/10.1214/12-aap888","pdf_url":"https://projecteuclid.org/journals/annals-of-applied-probability/volume-23/issue-5/Decay-of-tails-at-equilibrium-for-FIFO-join-the-shortest/10.1214/12-AAP888.pdf","source":{"id":"https://openalex.org/S9093621","display_name":"The Annals of Applied Probability","issn_l":"1050-5164","issn":["1050-5164","2168-8737"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-a","anvur-class-a","anvur-scientific","cwts-core","dongbi-b","doyens","jufo-3","norway-2","poland-140","russia-white-list-1"],"host_organization":"https://openalex.org/P4310319881","host_organization_name":"Institute of Mathematical Statistics","host_organization_lineage":["https://openalex.org/P4310319881"],"host_organization_lineage_names":["Institute of Mathematical Statistics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Annals of Applied Probability","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G3613407323","display_name":"Collaborative Research:  Flow level models and the design of flow-aware networks","funder_award_id":"0729537","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4045088442","display_name":"Asymptotics for Queueing Networks, Branching Random Walks, and Interacting Particle Systems","funder_award_id":"1105668","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2038023154.pdf","grobid_xml":"https://content.openalex.org/works/W2038023154.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W51438938","https://openalex.org/W1969667871","https://openalex.org/W2021321016","https://openalex.org/W2023246505","https://openalex.org/W2027273107","https://openalex.org/W2066004598","https://openalex.org/W2070666741","https://openalex.org/W2117702591","https://openalex.org/W2126391667","https://openalex.org/W2906188306","https://openalex.org/W2914659449","https://openalex.org/W3011913216","https://openalex.org/W4247619688","https://openalex.org/W4301809784"],"related_works":["https://openalex.org/W7100875075","https://openalex.org/W2032825369","https://openalex.org/W2027273107","https://openalex.org/W1489479792","https://openalex.org/W7097737196","https://openalex.org/W2168928846","https://openalex.org/W2072315029","https://openalex.org/W2001070016","https://openalex.org/W2240818951","https://openalex.org/W103460599"],"abstract_inverted_index":{"In":[0,214,282],"join":[1],"the":[2,11,39,48,65,86,89,97,107,111,199,205,219,225,231,237,255,261,264,276,286,294,302],"shortest":[3,12],"queue":[4,13,91,112,229,266],"networks,":[5],"incoming":[6],"jobs":[7,45,130],"are":[8],"assigned":[9],"to":[10,51,129],"from":[14],"among":[15],"a":[16,24,36,52,103,210,228,242,246,269,297],"randomly":[17],"chosen":[18],"subset":[19],"of":[20,26,31,88,170,174,224,263,272],"$D$":[21],"queues,":[22],"in":[23,75,96,118,147,165,183,186],"system":[25,49],"$N$":[27],"queues;":[28],"after":[29],"completion":[30],"service":[32,60,66,133,142,200,206,232,238],"at":[33,61,67,227],"its":[34],"queue,":[35],"job":[37],"leaves":[38],"network.":[40],"We":[41,252],"also":[42],"assume":[43],"that":[44,85,163],"arrive":[46],"into":[47],"according":[50],"rate-$\\alpha":[53],"N$":[54],"Poisson":[55],"process,":[56],"$\\alpha<1$,":[57],"with":[58,131,245],"rate-$1$":[59],"each":[62],"queue.":[63],"When":[64,300],"queues":[68,171],"is":[69,102,202,234,288,304],"exponentially":[70,95,305],"distributed,":[71],"it":[72],"was":[73,145,181],"shown":[74],"Vvedenskaya":[76],"et":[77,149,188],"al.":[78,150,189],"[Probl.":[79,119],"Inf.":[80,120],"Transm.":[81,121],"32":[82,122],"(1996)":[83,123],"15\u201329]":[84,124],"tail":[87,262,287,295,303],"equilibrium":[90,226,265],"size":[92,113,267],"decays":[93,114],"doubly":[94,289],"limit":[98],"as":[99,177,222,259],"$N\\rightarrow\\infty$.":[100,178],"This":[101,179],"substantial":[104],"improvement":[105],"over":[106],"case":[108],"$D=1$,":[109],"where":[110,198],"exponentially.":[115],"The":[116,157],"reasoning":[117],"does":[125],"not":[126],"easily":[127],"generalize":[128],"nonexponential":[132],"time":[134,143,207,239],"distributions.":[135],"A":[136],"modularized":[137],"program":[138,158],"for":[139,196,250],"treating":[140],"general":[141],"distributions":[144],"introduced":[146],"Bramson":[148,187],"[In":[151],"Proc.":[152],"ACM":[153],"SIGMETRICS":[154],"(2010)":[155],"275\u2013286].":[156],"relies":[159],"on":[160,275],"an":[161],"ansatz":[162,180,257],"asserts,":[164],"equilibrium,":[166],"any":[167],"fixed":[168],"number":[169],"become":[172],"independent":[173],"one":[175],"another":[176],"demonstrated":[182],"several":[184],"settings":[185],"[Queueing":[190],"Syst.":[191],"71":[192],"(2012)":[193],"247\u2013292],":[194],"including":[195],"networks":[197],"discipline":[201,233],"FIFO":[203,235],"and":[204,236,280],"distribution":[208,240],"has":[209,241,296],"decreasing":[211],"hazard":[212],"rate.":[213],"this":[215],"article,":[216],"we":[217],"investigate":[218],"limiting":[220],"behavior,":[221],"$N\\rightarrow\\infty$,":[223,260],"when":[230],"power":[243,298],"law":[244],"given":[247],"exponent":[248],"$-\\beta$,":[249],"$\\beta>1$.":[251],"show":[253],"under":[254],"above":[256],"that,":[258],"exhibits":[268],"wide":[270],"range":[271],"behavior":[273],"depending":[274],"relationship":[277],"between":[278],"$\\beta$":[279],"$D$.":[281],"particular,":[283],"if":[284,292],"$\\beta>D/(D-1)$,":[285],"exponential":[290],"and,":[291],"$\\beta<D/(D-1)$,":[293],"law.":[299],"$\\beta=D/(D-1)$,":[301],"distributed.":[306]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-10-30T12:39:25.321706","created_date":"2016-06-24T00:00:00"}