{"id":"https://openalex.org/W2000228116","doi":"https://doi.org/10.1287/10-ssy009","title":"An ODE for an Overloaded X Model Involving a Stochastic Averaging Principle","display_name":"An ODE for an Overloaded X Model Involving a Stochastic Averaging Principle","publication_year":2011,"publication_date":"2011-06-01","ids":{"openalex":"https://openalex.org/W2000228116","doi":"https://doi.org/10.1287/10-ssy009","mag":"2000228116"},"language":"en","primary_location":{"id":"doi:10.1287/10-ssy009","doi":"https://doi.org/10.1287/10-ssy009","is_oa":true,"landing_page_url":"https://doi.org/10.1287/10-ssy009","pdf_url":null,"source":{"id":"https://openalex.org/S4210232382","display_name":"Stochastic Systems","issn_l":"1946-5238","issn":["1946-5238"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","jufo-1","norway-1","poland-20","russia-white-list-1"],"host_organization":"https://openalex.org/P4310315699","host_organization_name":"Institute for Operations Research and the Management Sciences","host_organization_lineage":["https://openalex.org/P4310315699"],"host_organization_lineage_names":["Institute for Operations Research and the Management Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Stochastic Systems","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.1287/10-ssy009","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5069853831","display_name":"Ohad Perry","orcid":"https://orcid.org/0000-0002-4584-3015","observed_orcids":["https://orcid.org/0000-0002-4584-3015"]},"institutions":[{"id":"https://openalex.org/I1341640284","display_name":"Centrum Wiskunde & Informatica","ror":"https://ror.org/00x7ekv49","country_code":"NL","type":"facility","lineage":["https://openalex.org/I1341640284","https://openalex.org/I2800991832","https://openalex.org/I4405262988"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Ohad Perry","raw_affiliation_strings":["CWI, Science Park 123, 1098 XG Amsterdam, The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CWI, Science Park 123, 1098 XG Amsterdam, The Netherlands","institution_ids":["https://openalex.org/I1341640284"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083215472","display_name":"Ward Whitt","orcid":"https://orcid.org/0000-0003-4298-9964","observed_orcids":["https://orcid.org/0000-0003-4298-9964"]},"institutions":[{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ward Whitt","raw_affiliation_strings":["Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027-6699"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027-6699","institution_ids":["https://openalex.org/I78577930"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":7.1121,"has_fulltext":false,"cited_by_count":29,"citation_normalized_percentile":{"value":0.95981435,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":88,"max":97},"biblio":{"volume":"1","issue":"1","first_page":"59","last_page":"108"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10974","display_name":"Advanced Queuing Theory Analysis","score":0.9990000128746033,"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":0.9990000128746033,"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":9.999999747378752e-05,"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/T11720","display_name":"Probability and Risk Models","score":9.999999747378752e-05,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/x-model","display_name":"X model","score":0.8220000267028809},{"id":"https://openalex.org/keywords/ordinary-differential-equations","display_name":"ordinary differential equations","score":0.5809999704360962}],"concepts":[{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.9086461663246155},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.6405758857727051},{"id":"https://openalex.org/C160403385","wikidata":"https://www.wikidata.org/wiki/Q220543","display_name":"Queue","level":2,"score":0.6275012493133545},{"id":"https://openalex.org/C22684755","wikidata":"https://www.wikidata.org/wiki/Q847526","display_name":"Queueing theory","level":2,"score":0.598263144493103},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5498894453048706},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.4329929053783417},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4185103178024292},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3770520091056824},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.35684362053871155},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3512619733810425},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.28076791763305664},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.2075575590133667},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15225034952163696},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.13502433896064758},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1287/10-ssy009","doi":"https://doi.org/10.1287/10-ssy009","is_oa":true,"landing_page_url":"https://doi.org/10.1287/10-ssy009","pdf_url":null,"source":{"id":"https://openalex.org/S4210232382","display_name":"Stochastic Systems","issn_l":"1946-5238","issn":["1946-5238"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","jufo-1","norway-1","poland-20","russia-white-list-1"],"host_organization":"https://openalex.org/P4310315699","host_organization_name":"Institute for Operations Research and the Management Sciences","host_organization_lineage":["https://openalex.org/P4310315699"],"host_organization_lineage_names":["Institute for Operations Research and the Management Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Stochastic Systems","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.453.7387","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.453.7387","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://users.iems.northwestern.edu/~perry/PerryWhitt_SSY.pdf","raw_type":"text"},{"id":"pmh:cwi:oai:cwi.nl:19438","doi":null,"is_oa":false,"landing_page_url":"https://ir.cwi.nl/pub/19438","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Stochastic Systems, 1, 59 - 108","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:cwi.nl:19438","doi":null,"is_oa":false,"landing_page_url":"https://ir.cwi.nl/pub/19438","pdf_url":null,"source":{"id":"https://openalex.org/S7407055335","display_name":"Centrum Wiskunde & Informatica (CWI), the national research institute for mathematics and computer science in the Netherlands","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Stochastic Systems vol. 1, pp. 59-108","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:doaj.org/article:32c622e1c76348acacd75c7fc27ec72e","doi":null,"is_oa":false,"landing_page_url":"https://doaj.org/article/32c622e1c76348acacd75c7fc27ec72e","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Stochastic Systems, Vol 1, Iss 1, Pp 59-108 (2011)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1287/10-ssy009","doi":"https://doi.org/10.1287/10-ssy009","is_oa":true,"landing_page_url":"https://doi.org/10.1287/10-ssy009","pdf_url":null,"source":{"id":"https://openalex.org/S4210232382","display_name":"Stochastic Systems","issn_l":"1946-5238","issn":["1946-5238"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","jufo-1","norway-1","poland-20","russia-white-list-1"],"host_organization":"https://openalex.org/P4310315699","host_organization_name":"Institute for Operations Research and the Management Sciences","host_organization_lineage":["https://openalex.org/P4310315699"],"host_organization_lineage_names":["Institute for Operations Research and the Management Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Stochastic Systems","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W240029891","https://openalex.org/W1521738998","https://openalex.org/W1559882669","https://openalex.org/W1629501955","https://openalex.org/W1967274424","https://openalex.org/W1971619516","https://openalex.org/W2037137759","https://openalex.org/W2054587269","https://openalex.org/W2058244810","https://openalex.org/W2062573385","https://openalex.org/W2067265108","https://openalex.org/W2069926892","https://openalex.org/W2103353463","https://openalex.org/W2118679801","https://openalex.org/W2121605635","https://openalex.org/W2126794261","https://openalex.org/W2135726648","https://openalex.org/W2138685211","https://openalex.org/W2148727583","https://openalex.org/W2799598053","https://openalex.org/W3101606912","https://openalex.org/W3160954918","https://openalex.org/W4213329537","https://openalex.org/W4230289530","https://openalex.org/W4242750545","https://openalex.org/W4252302949","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W7098536337","https://openalex.org/W7100681392","https://openalex.org/W2952578988","https://openalex.org/W1559882669","https://openalex.org/W7100199786","https://openalex.org/W2037284244","https://openalex.org/W2054770070","https://openalex.org/W2171582516","https://openalex.org/W2148727583","https://openalex.org/W7100490821"],"abstract_inverted_index":{"We":[0],"study":[1],"an":[2,67,115],"ordinary":[3],"differential":[4],"equation":[5],"(ODE)":[6],"arising":[7],"as":[8,33,54],"the":[9,34,38,43,93,134,146,152,154,170],"many-server":[10],"heavy-traffic":[11,174],"fluid":[12],"limit":[13],"of":[14,17,66,167],"a":[15,51,55,78,97,122,129,140,149,173],"sequence":[16],"overloaded":[18],"Markovian":[19],"queueing":[20,135],"models":[21],"with":[22,87],"two":[23,27,94],"customer":[24],"classes":[25],"and":[26],"service":[28,59],"pools.":[29],"The":[30,109,117],"system,":[31],"known":[32],"X":[35],"model":[36],"in":[37,50,64,128,145],"call-center":[39],"literature,":[40],"operates":[41,127],"under":[42],"fixed-queue-ratio-with-thresholds":[44],"(FQR-T)":[45],"control,":[46],"which":[47,126],"we":[48],"proposed":[49],"recent":[52],"paper":[53],"way":[56],"for":[57,151],"one":[58],"system":[60,112],"to":[61],"help":[62],"another":[63],"face":[65],"unanticipated":[68],"overload.":[69,116],"Each":[70],"pool":[71],"serves":[72],"only":[73],"its":[74,160],"own":[75],"class":[76],"until":[77],"threshold":[79],"is":[80,85,106,119,157],"exceeded;":[81],"then":[82,91],"one-way":[83],"sharing":[84],"activated":[86],"all":[88],"customer-server":[89],"assignments":[90],"driving":[92,155],"queues":[95],"toward":[96],"fixed":[98,104],"ratio.":[99],"For":[100],"large":[101],"systems,":[102],"that":[103],"ratio":[105],"achieved":[107],"approximately.":[108],"ODE":[110,171],"describes":[111],"performance":[113],"during":[114],"control":[118],"driven":[120],"by":[121,159],"queue-difference":[123],"stochastic":[124],"process,":[125],"faster":[130],"time":[131],"scale":[132],"than":[133],"processes":[136],"themselves,":[137],"thus":[138],"achieving":[139],"time-dependent":[141],"steady":[142],"state":[143],"instantaneously":[144],"limit.":[147],"As":[148],"result,":[150],"ODE,":[153],"process":[156],"replaced":[158],"long-run":[161],"average":[162],"behavior":[163],"at":[164],"each":[165],"instant":[166],"time;":[168],"i.e.,":[169],"involves":[172],"averaging":[175],"principle":[176],"(AP).":[177]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":3}],"updated_date":"2026-10-30T12:39:25.321706","created_date":"2016-06-24T00:00:00"}
