{"id":"https://openalex.org/W1987359692","doi":"https://doi.org/10.1155/2011/216790","title":"Two Coupled Queues with Vastly Different Arrival Rates: Critical Loading Case","display_name":"Two Coupled Queues with Vastly Different Arrival Rates: Critical Loading Case","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W1987359692","doi":"https://doi.org/10.1155/2011/216790","mag":"1987359692"},"language":"en","primary_location":{"id":"doi:10.1155/2011/216790","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2011/216790","pdf_url":"https://downloads.hindawi.com/journals/aor/2011/216790.pdf","source":{"id":"https://openalex.org/S33782831","display_name":"Advances in Operations Research","issn_l":"1687-9147","issn":["1687-9147","1687-9155"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Operations Research","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://downloads.hindawi.com/journals/aor/2011/216790.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038794095","display_name":"Charles Knessl","orcid":"https://orcid.org/0000-0001-8106-8880"},"institutions":[{"id":"https://openalex.org/I39422238","display_name":"University of Illinois Chicago","ror":"https://ror.org/02mpq6x41","country_code":"US","type":"education","lineage":["https://openalex.org/I39422238"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Charles Knessl","raw_affiliation_strings":["Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, 851 South Morgan Street Chicago, IL 60607-7045, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, 851 South Morgan Street Chicago, IL 60607-7045, USA","institution_ids":["https://openalex.org/I39422238"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111887607","display_name":"John A. Morrison","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"John A. Morrison","raw_affiliation_strings":["Consultant Bell Laboratories, Alcatel-Lucent, 600 Mountain Avenue, Murray Hill, NJ 07974, USA"],"affiliations":[{"raw_affiliation_string":"Consultant Bell Laboratories, Alcatel-Lucent, 600 Mountain Avenue, Murray Hill, NJ 07974, USA","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5038794095"],"corresponding_institution_ids":["https://openalex.org/I39422238"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.533,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.72207571,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"2011","issue":null,"first_page":"1","last_page":"26"},"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/T10138","display_name":"Network Traffic and Congestion Control","score":0.9988999962806702,"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"}},{"id":"https://openalex.org/T10575","display_name":"Wireless Communication Networks Research","score":0.9987999796867371,"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/algorithm","display_name":"Algorithm","score":0.7390379905700684},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5493117570877075},{"id":"https://openalex.org/keywords/queue","display_name":"Queue","score":0.5375160574913025},{"id":"https://openalex.org/keywords/database","display_name":"Database","score":0.4375024139881134},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.05319488048553467}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.7390379905700684},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5493117570877075},{"id":"https://openalex.org/C160403385","wikidata":"https://www.wikidata.org/wiki/Q220543","display_name":"Queue","level":2,"score":0.5375160574913025},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.4375024139881134},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.05319488048553467}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2011/216790","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2011/216790","pdf_url":"https://downloads.hindawi.com/journals/aor/2011/216790.pdf","source":{"id":"https://openalex.org/S33782831","display_name":"Advances in Operations Research","issn_l":"1687-9147","issn":["1687-9147","1687-9155"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Operations Research","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:jnlaor:216790","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/AOR/2011/216790.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"},{"id":"pmh:oai:doaj.org/article:07ea9117d4314df9b0281ee270259654","is_oa":true,"landing_page_url":"https://doaj.org/article/07ea9117d4314df9b0281ee270259654","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Advances in Operations Research, Vol 2011 (2011)","raw_type":"article"},{"id":"pmh:oai:figshare.com:article/10772669","is_oa":true,"landing_page_url":"https://figshare.com/articles/journal_contribution/Two_Coupled_Queues_with_Vastly_Different_Arrival_Rates_Critical_Loading_Case/10772669","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.1155/2011/216790","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2011/216790","pdf_url":"https://downloads.hindawi.com/journals/aor/2011/216790.pdf","source":{"id":"https://openalex.org/S33782831","display_name":"Advances in Operations Research","issn_l":"1687-9147","issn":["1687-9147","1687-9155"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Operations Research","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1898521820","display_name":null,"funder_award_id":"DMS 05-03745","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1987359692.pdf","grobid_xml":"https://content.openalex.org/works/W1987359692.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W590465523","https://openalex.org/W1518011073","https://openalex.org/W1556192255","https://openalex.org/W1561734496","https://openalex.org/W1580092694","https://openalex.org/W2008154388","https://openalex.org/W2018165881","https://openalex.org/W2021088586","https://openalex.org/W2022941684","https://openalex.org/W2032312967","https://openalex.org/W2037250187","https://openalex.org/W2048952601","https://openalex.org/W2054620716","https://openalex.org/W2057825077","https://openalex.org/W2058274202","https://openalex.org/W2061904818","https://openalex.org/W2073121338","https://openalex.org/W2092305220","https://openalex.org/W2126260018","https://openalex.org/W2140096940","https://openalex.org/W2151463257","https://openalex.org/W2157005274","https://openalex.org/W2176566884","https://openalex.org/W2587121237","https://openalex.org/W4233124504","https://openalex.org/W4238270389"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2390279801","https://openalex.org/W4391913857","https://openalex.org/W2358668433","https://openalex.org/W4396701345","https://openalex.org/W2376932109"],"abstract_inverted_index":{"We":[0,75,139],"consider":[1],"two":[2,165],"coupled":[3],"queues":[4],"with":[5],"a":[6,16,141],"generalized":[7],"processor":[8,36],"sharing":[9,37],"service":[10,29],"discipline.":[11],"The":[12,35,53],"second":[13,60,130,176],"queue":[14,61,80,88,102,119,131,177,189],"has":[15],"much":[17],"smaller":[18],"Poisson":[19],"arrival":[20,73,97],"rate":[21,98],"than":[22],"the":[23,27,45,59,65,69,72,78,86,95,100,112,117,129,152,159,164,175],"first":[24,46,118],"queue,":[25,47],"while":[26,126],"customer":[28],"times":[30],"are":[31],"of":[32,41,55,64,71,114,123,136,158,161],"comparable":[33],"magnitude.":[34],"server":[38],"devotes":[39],"most":[40],"its":[42],"resources":[43,56],"to":[44,58,99,180,187],"except":[48],"when":[49],"it":[50],"is":[51,62,81,89],"empty.":[52],"fraction":[54],"devoted":[57],"small,":[63],"same":[66],"order":[67],"as":[68],"ratio":[70],"rates.":[74],"assume":[76],"that":[77,85,127,170,191],"primary":[79],"heavily":[82,182],"loaded":[83],"and":[84,148],"secondary":[87,101],"critically":[90],"loaded.":[91],"If":[92],"we":[93],"let":[94],"small":[96],"be<mml:math":[103],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>O</mml:mi><mml:mo>(</mml:mo><mml:mi>\u03b5</mml:mi><mml:mo>)</mml:mo></mml:math>,":[104],"where<mml:math":[105],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mn>0</mml:mn><mml:mo>\u2264</mml:mo><mml:mi>\u03b5</mml:mi><mml:mo>\u226a</mml:mo><mml:mn>1</mml:mn></mml:math>,":[106],"then":[107],"in":[108,116,128,163,171],"this":[109,146],"asymptotic":[110],"limit":[111],"number":[113],"customers":[115,162],"will":[120,132],"be":[121,133,181],"large,":[122],"order<mml:math":[124,137],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>O</mml:mi><mml:mo>(</mml:mo><mml:msup><mml:mrow><mml:mi>\u03b5</mml:mi></mml:mrow><mml:mrow><mml:mo>-</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:math>,":[125],"somewhat":[134],"smaller,":[135],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>O</mml:mi><mml:mo>(</mml:mo><mml:msup><mml:mrow><mml:mi>\u03b5</mml:mi></mml:mrow><mml:mrow><mml:mo>-</mml:mo><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:math>.":[138],"obtain":[140],"two-dimensional":[142],"diffusion":[143],"approximation":[144],"for":[145,151],"model":[147],"explicitly":[149],"solve":[150],"joint":[153],"steady":[154],"state":[155],"probability":[156],"distribution":[157],"numbers":[160],"queues.":[166],"This":[167],"work":[168],"complements":[169],"(Morrison,":[172],"2010),":[173],"which":[174],"was":[178],"assumed":[179],"or":[183],"lightly":[184],"loaded,":[185],"leading":[186],"mean":[188],"lengths":[190],"were<mml:math":[192],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>O</mml:mi><mml:mo>(</mml:mo><mml:msup><mml:mrow><mml:mi>\u03b5</mml:mi></mml:mrow><mml:mrow><mml:mo>-</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:math>or<mml:math":[193],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>O</mml:mi><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:math>,":[194],"respectively.":[195]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}