{"id":"https://openalex.org/W4388457104","doi":"https://doi.org/10.1137/21m1433125","title":"Long-Time Limit of Nonlinearly Coupled Measure-Valued Equations that Model Many-Server Queues with Reneging","display_name":"Long-Time Limit of Nonlinearly Coupled Measure-Valued Equations that Model Many-Server Queues with Reneging","publication_year":2023,"publication_date":"2023-11-07","ids":{"openalex":"https://openalex.org/W4388457104","doi":"https://doi.org/10.1137/21m1433125"},"language":"en","primary_location":{"id":"doi:10.1137/21m1433125","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1433125","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","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/A5053398044","display_name":"Rami Atar","orcid":"https://orcid.org/0000-0001-8341-5049"},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Rami Atar","raw_affiliation_strings":["Viterbi Faculty of Electrical and Computer Engineering, Technion, Haifa, Israel"],"affiliations":[{"raw_affiliation_string":"Viterbi Faculty of Electrical and Computer Engineering, Technion, Haifa, Israel","institution_ids":["https://openalex.org/I174306211"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5113041589","display_name":"Weining Kang","orcid":"https://orcid.org/0009-0009-5047-1832"},"institutions":[{"id":"https://openalex.org/I79272384","display_name":"University of Maryland, Baltimore County","ror":"https://ror.org/02qskvh78","country_code":"US","type":"education","lineage":["https://openalex.org/I79272384"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Weining Kang","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Maryland, Baltimore County, Baltimore, MD 21250 USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Maryland, Baltimore County, Baltimore, MD 21250 USA","institution_ids":["https://openalex.org/I79272384"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018674260","display_name":"Haya Kaspi","orcid":null},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Haya Kaspi","raw_affiliation_strings":["Department of Industrial Engineering and Management, Technion, Haifa, Israel"],"affiliations":[{"raw_affiliation_string":"Department of Industrial Engineering and Management, Technion, Haifa, Israel","institution_ids":["https://openalex.org/I174306211"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072223676","display_name":"Kavita Ramanan","orcid":"https://orcid.org/0000-0003-2114-6677"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kavita Ramanan","raw_affiliation_strings":["Division of Applied Mathematics, Brown University, Providence, RI 02118 USA"],"affiliations":[{"raw_affiliation_string":"Division of Applied Mathematics, Brown University, Providence, RI 02118 USA","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5053398044"],"corresponding_institution_ids":["https://openalex.org/I174306211"],"apc_list":null,"apc_paid":null,"fwci":1.6418,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.86531061,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"55","issue":"6","first_page":"7189","last_page":"7239"},"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":0.9876000285148621,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9725000262260437,"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/mathematics","display_name":"Mathematics","score":0.8007358312606812},{"id":"https://openalex.org/keywords/invariant-measure","display_name":"Invariant measure","score":0.7400339841842651},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5114156603813171},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.49501746892929077},{"id":"https://openalex.org/keywords/dirac-measure","display_name":"Dirac measure","score":0.461130291223526},{"id":"https://openalex.org/keywords/ergodic-theory","display_name":"Ergodic theory","score":0.45075082778930664},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.42653176188468933},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.33285871148109436}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8007358312606812},{"id":"https://openalex.org/C115667082","wikidata":"https://www.wikidata.org/wiki/Q4200518","display_name":"Invariant measure","level":3,"score":0.7400339841842651},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5114156603813171},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.49501746892929077},{"id":"https://openalex.org/C111118313","wikidata":"https://www.wikidata.org/wiki/Q1227387","display_name":"Dirac measure","level":5,"score":0.461130291223526},{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.45075082778930664},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.42653176188468933},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.33285871148109436},{"id":"https://openalex.org/C156785651","wikidata":"https://www.wikidata.org/wiki/Q688945","display_name":"Dirac spinor","level":4,"score":0.0},{"id":"https://openalex.org/C149545384","wikidata":"https://www.wikidata.org/wiki/Q5280160","display_name":"Dirac algebra","level":3,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C82601208","wikidata":"https://www.wikidata.org/wiki/Q272621","display_name":"Dirac equation","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/21m1433125","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1433125","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1624626908","display_name":null,"funder_award_id":"N0014-21-1-2887","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G4267587929","display_name":null,"funder_award_id":"1035/20","funder_id":"https://openalex.org/F4320322252","funder_display_name":"Israel Science Foundation"},{"id":"https://openalex.org/G8254636693","display_name":null,"funder_award_id":"W911NF2010133","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"}],"funders":[{"id":"https://openalex.org/F4320322252","display_name":"Israel Science Foundation","ror":"https://ror.org/04sazxf24"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"},{"id":"https://openalex.org/F4320338281","display_name":"Army Research Office","ror":"https://ror.org/05epdh915"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W64816550","https://openalex.org/W196325668","https://openalex.org/W1511806896","https://openalex.org/W1528744274","https://openalex.org/W1965732238","https://openalex.org/W1971170413","https://openalex.org/W1980410876","https://openalex.org/W1987592119","https://openalex.org/W1995245183","https://openalex.org/W2000383392","https://openalex.org/W2042980410","https://openalex.org/W2047891589","https://openalex.org/W2087958752","https://openalex.org/W2088912230","https://openalex.org/W2107055524","https://openalex.org/W2107546595","https://openalex.org/W2120133964","https://openalex.org/W2125337870","https://openalex.org/W2140283201","https://openalex.org/W2146892592","https://openalex.org/W2168246988","https://openalex.org/W2502318419","https://openalex.org/W2515875444","https://openalex.org/W2547205106","https://openalex.org/W2601653921","https://openalex.org/W2963143024","https://openalex.org/W2963237502","https://openalex.org/W2971493348","https://openalex.org/W2977319513","https://openalex.org/W2980142919","https://openalex.org/W2999610888","https://openalex.org/W3027610659","https://openalex.org/W3035296581","https://openalex.org/W3099991955","https://openalex.org/W3106241424","https://openalex.org/W3126255430","https://openalex.org/W4252302949","https://openalex.org/W4253991977","https://openalex.org/W4302366875","https://openalex.org/W4302856910"],"related_works":["https://openalex.org/W2134654202","https://openalex.org/W2057711290","https://openalex.org/W4298162610","https://openalex.org/W3048177030","https://openalex.org/W2950551861","https://openalex.org/W2026069322","https://openalex.org/W4300889323","https://openalex.org/W2070293309","https://openalex.org/W2963808895","https://openalex.org/W1971327519"],"abstract_inverted_index":{"The":[0,180],"large-time":[1,178,256],"behavior":[2],"of":[3,8,33,57,110,122,132,189,213,218,265],"a":[4,18,54,93,211,219,252,263,270],"nonlinearly":[5],"coupled":[6,266],"pair":[7],"measure-valued":[9,267],"transport":[10],"equations":[11,26,91,268],"with":[12,36,60,66,227],"discontinuous":[13],"boundary":[14],"conditions,":[15],"parameterized":[16],"by":[17],"positive":[19],"real-valued":[20],"parameter":[21],",":[22,154],"is":[23,74,85,105,143,156,209,223,236],"considered.":[24],"These":[25],"describe":[27],"the":[28,89,98,106,111,119,128,133,139,147,159,162,177,186,192,199,205,214,232,243],"hydrodynamic":[29],"or":[30,77],"fluid":[31,90,112,135,163],"limit":[32],"many-server":[34],"queues":[35],"reneging":[37,58],"(with":[38],"traffic":[39],"intensity":[40],"),":[41],"which":[42],"model":[43],"phenomena":[44],"in":[45,176,216,225],"diverse":[46],"disciplines,":[47],"including":[48],"biology":[49],"and":[50,63,69,82,202,241],"operations":[51],"research.":[52],"For":[53],"broad":[55],"class":[56],"distributions":[59,65,121],"finite":[61,67],"mean,":[62],"service":[64,149,193],"mean":[68,140,148],"hazard":[70,206,233],"rate":[71,142,207,234],"function":[72,208,235],"that":[73,87,118,151,158],"either":[75],"nonincreasing":[76],"bounded":[78,237],"away":[79,238],"from":[80,166,239],"zero":[81,240],"infinity,":[83,242],"it":[84,155],"shown":[86,157],"if":[88],"have":[92],"unique":[94,107,129,173],"invariant":[95,103,108,130,174],"state,":[96],"then":[97],"Dirac":[99],"measure":[100],"at":[101],"this":[102,116,172],"state":[104,131,175],"distribution":[109],"equations.":[113,136],"In":[114],"particular,":[115],"implies":[117],"stationary":[120],"scaled":[123],"-server":[124],"systems":[125],"converge":[126],"to":[127,146,161,171],"corresponding":[134],"Moreover,":[137],"when":[138,153],"arrival":[141],"not":[144],"equal":[145],"rate,":[150],"is,":[152],"solution":[160],"equation":[164,222],"starting":[165],"any":[167],"initial":[168],"condition":[169],"converges":[170],"limit.":[179],"proof":[181,244],"techniques":[182],"are":[183,259],"different":[184],"under":[185,198],"two":[187,200],"sets":[188],"assumptions":[190],"on":[191],"distribution,":[194],"as":[195,197,251],"well":[196],"regimes":[201],".":[203],"When":[204,231],"nonincreasing,":[210],"reformulation":[212],"dynamics":[215],"terms":[217],"certain":[220],"renewal":[221],"used,":[224],"conjunction":[226],"recursive":[228],"asymptotic":[229],"estimates.":[230],"uses":[245],"an":[246],"extended":[247],"relative":[248],"entropy":[249],"functional":[250],"Lyapunov":[253],"function.":[254],"Analogous":[255],"convergence":[257],"results":[258],"also":[260],"established":[261],"for":[262],"system":[264],"modeling":[269],"multiclass":[271],"queue.":[272]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}