{"id":"https://openalex.org/W2113049533","doi":"https://doi.org/10.1109/itw.2006.1633781","title":"Equilibrium of Heterogeneous Congestion Control Protocols","display_name":"Equilibrium of Heterogeneous Congestion Control Protocols","publication_year":2006,"publication_date":"2006-05-25","ids":{"openalex":"https://openalex.org/W2113049533","doi":"https://doi.org/10.1109/itw.2006.1633781","mag":"2113049533"},"language":"en","primary_location":{"id":"doi:10.1109/itw.2006.1633781","is_oa":false,"landing_page_url":"https://doi.org/10.1109/itw.2006.1633781","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2006 IEEE Information Theory Workshop","raw_type":"proceedings-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/A5103277656","display_name":"Ao Tang","orcid":"https://orcid.org/0000-0001-6296-644X"},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Ao Tang","raw_affiliation_strings":["California Institute of Technology, Pasadena, CA, USA","Division of Engineering and Applied Science California Institute of Technology  Pasadena CA 91125 USA"],"affiliations":[{"raw_affiliation_string":"California Institute of Technology, Pasadena, CA, USA","institution_ids":["https://openalex.org/I122411786"]},{"raw_affiliation_string":"Division of Engineering and Applied Science California Institute of Technology  Pasadena CA 91125 USA","institution_ids":["https://openalex.org/I122411786"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100632949","display_name":"Jiantao Wang","orcid":"https://orcid.org/0009-0009-9571-7082"},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jiantao Wang","raw_affiliation_strings":["California Institute of Technology, Pasadena, CA, USA","[Div. of Eng. & Appl. Sci., California Inst. of Technol., Pasadena, CA]"],"affiliations":[{"raw_affiliation_string":"California Institute of Technology, Pasadena, CA, USA","institution_ids":["https://openalex.org/I122411786"]},{"raw_affiliation_string":"[Div. of Eng. & Appl. Sci., California Inst. of Technol., Pasadena, CA]","institution_ids":["https://openalex.org/I122411786"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069455858","display_name":"Steven H. Low","orcid":"https://orcid.org/0000-0001-6476-3048"},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"S. Low","raw_affiliation_strings":["California Institute of Technology, Pasadena, CA, USA","[Div. of Eng. & Appl. Sci., California Inst. of Technol., Pasadena, CA]"],"affiliations":[{"raw_affiliation_string":"California Institute of Technology, Pasadena, CA, USA","institution_ids":["https://openalex.org/I122411786"]},{"raw_affiliation_string":"[Div. of Eng. & Appl. Sci., California Inst. of Technol., Pasadena, CA]","institution_ids":["https://openalex.org/I122411786"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110782105","display_name":"Mung Chiang","orcid":"https://orcid.org/0000-0002-8920-651X"},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mung Chiang","raw_affiliation_strings":["TDepartment of Electrical Engineering, Princeton University, Princeton, NJ, USA","[Department of Electrical Engineering, Princeton University, Princeton, NJ 08544 USA.]"],"affiliations":[{"raw_affiliation_string":"TDepartment of Electrical Engineering, Princeton University, Princeton, NJ, USA","institution_ids":["https://openalex.org/I20089843"]},{"raw_affiliation_string":"[Department of Electrical Engineering, Princeton University, Princeton, NJ 08544 USA.]","institution_ids":["https://openalex.org/I20089843"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5103277656"],"corresponding_institution_ids":["https://openalex.org/I122411786"],"apc_list":null,"apc_paid":null,"fwci":2.1125,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.88623131,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"57","last_page":"61"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10138","display_name":"Network Traffic and Congestion Control","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10138","display_name":"Network Traffic and Congestion Control","score":0.9998999834060669,"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/T11409","display_name":"Advanced Wireless Network Optimization","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11158","display_name":"Wireless Networks and Protocols","score":0.9952999949455261,"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/uniqueness","display_name":"Uniqueness","score":0.7527880668640137},{"id":"https://openalex.org/keywords/network-congestion","display_name":"Network congestion","score":0.7062824368476868},{"id":"https://openalex.org/keywords/utility-maximization-problem","display_name":"Utility maximization problem","score":0.6890286207199097},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6210892200469971},{"id":"https://openalex.org/keywords/protocol","display_name":"Protocol (science)","score":0.6003054976463318},{"id":"https://openalex.org/keywords/utility-maximization","display_name":"Utility maximization","score":0.5579431653022766},{"id":"https://openalex.org/keywords/maximization","display_name":"Maximization","score":0.5336604118347168},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.49194666743278503},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.48902973532676697},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.3975571393966675},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.24648728966712952},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.24101999402046204}],"concepts":[{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.7527880668640137},{"id":"https://openalex.org/C195563490","wikidata":"https://www.wikidata.org/wiki/Q180368","display_name":"Network congestion","level":3,"score":0.7062824368476868},{"id":"https://openalex.org/C2779044140","wikidata":"https://www.wikidata.org/wiki/Q3274096","display_name":"Utility maximization problem","level":3,"score":0.6890286207199097},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6210892200469971},{"id":"https://openalex.org/C2780385302","wikidata":"https://www.wikidata.org/wiki/Q367158","display_name":"Protocol (science)","level":3,"score":0.6003054976463318},{"id":"https://openalex.org/C2985793214","wikidata":"https://www.wikidata.org/wiki/Q3274096","display_name":"Utility maximization","level":2,"score":0.5579431653022766},{"id":"https://openalex.org/C2776330181","wikidata":"https://www.wikidata.org/wiki/Q18358244","display_name":"Maximization","level":2,"score":0.5336604118347168},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.49194666743278503},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.48902973532676697},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.3975571393966675},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.24648728966712952},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.24101999402046204},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C204787440","wikidata":"https://www.wikidata.org/wiki/Q188504","display_name":"Alternative medicine","level":2,"score":0.0},{"id":"https://openalex.org/C142724271","wikidata":"https://www.wikidata.org/wiki/Q7208","display_name":"Pathology","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C158379750","wikidata":"https://www.wikidata.org/wiki/Q214111","display_name":"Network packet","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/itw.2006.1633781","is_oa":false,"landing_page_url":"https://doi.org/10.1109/itw.2006.1633781","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2006 IEEE Information Theory Workshop","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W60924091","https://openalex.org/W97159709","https://openalex.org/W1487444668","https://openalex.org/W1531897854","https://openalex.org/W1578630563","https://openalex.org/W1597220786","https://openalex.org/W1978613623","https://openalex.org/W1991274232","https://openalex.org/W2002469635","https://openalex.org/W2037710455","https://openalex.org/W2041064634","https://openalex.org/W2041238958","https://openalex.org/W2058502981","https://openalex.org/W2059654406","https://openalex.org/W2071314114","https://openalex.org/W2078595922","https://openalex.org/W2103481633","https://openalex.org/W2109100253","https://openalex.org/W2112651106","https://openalex.org/W2118600142","https://openalex.org/W2123740318","https://openalex.org/W2126956578","https://openalex.org/W2147524058","https://openalex.org/W2150339484","https://openalex.org/W2152178735","https://openalex.org/W2159715570","https://openalex.org/W2174430759","https://openalex.org/W2324882973","https://openalex.org/W3123834724","https://openalex.org/W3123988786","https://openalex.org/W3152369594","https://openalex.org/W4240896209","https://openalex.org/W4301621763","https://openalex.org/W6602455940"],"related_works":["https://openalex.org/W2951390543","https://openalex.org/W3121912968","https://openalex.org/W2949260239","https://openalex.org/W2949594337","https://openalex.org/W3123067344","https://openalex.org/W2953072363","https://openalex.org/W3125423763","https://openalex.org/W30823005","https://openalex.org/W4299412355","https://openalex.org/W2267645079"],"abstract_inverted_index":{"When":[0],"heterogeneous":[1],"congestion":[2],"control":[3],"protocols":[4],"that":[5,74,80],"react":[6],"to":[7,26,84],"different":[8],"pricing":[9],"signals":[10],"share":[11],"the":[12,15,27,34,49,76,89],"same":[13],"network,":[14],"resulting":[16],"equilibrium":[17,37],"may":[18],"no":[19],"longer":[20],"be":[21,63],"interpreted":[22],"as":[23],"a":[24],"solution":[25],"standard":[28],"utility":[29],"maximization":[30],"problem.":[31],"We":[32],"prove":[33],"existence":[35],"of":[36],"in":[38,58],"general":[39],"multi-protocol":[40],"networks":[41],"under":[42],"mild":[43],"assumptions.":[44],"For":[45],"almost":[46],"all":[47,62],"networks,":[48],"equilibria":[50],"are":[51,91],"locally":[52,64],"unique,":[53],"and":[54,56],"finite":[55],"odd":[57],"number.":[59],"They":[60],"cannot":[61],"stable":[65],"unless":[66],"it":[67],"is":[68,96],"globally":[69],"unique.":[70],"Finally,":[71],"we":[72],"show":[73],"if":[75],"price":[77],"mapping":[78],"functions":[79],"map":[81],"link":[82],"prices":[83,86],"effective":[85],"observed":[87],"by":[88],"sources":[90],"similar,":[92],"then":[93],"global":[94],"uniqueness":[95],"guaranteed.":[97]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
