{"id":"https://openalex.org/W2139499282","doi":"https://doi.org/10.1109/tac.2010.2041998","title":"Convergence Rates of Distributed Average Consensus With Stochastic Link Failures","display_name":"Convergence Rates of Distributed Average Consensus With Stochastic Link Failures","publication_year":2010,"publication_date":"2010-02-11","ids":{"openalex":"https://openalex.org/W2139499282","doi":"https://doi.org/10.1109/tac.2010.2041998","mag":"2139499282"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2010.2041998","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2010.2041998","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","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/A5081738999","display_name":"Stacy Patterson","orcid":"https://orcid.org/0000-0001-7711-6018"},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"S. Patterson","raw_affiliation_strings":["Department of Mechanical Engineering, University of California, Santa Barbara, CA, USA","Dept. of Mech. Eng., Univ. of California, Santa Barbara, CA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, University of California, Santa Barbara, CA, USA","institution_ids":["https://openalex.org/I154570441"]},{"raw_affiliation_string":"Dept. of Mech. Eng., Univ. of California, Santa Barbara, CA, USA","institution_ids":["https://openalex.org/I154570441"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071239059","display_name":"Bassam Bamieh","orcid":"https://orcid.org/0000-0001-9237-4613"},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"B. Bamieh","raw_affiliation_strings":["Department of Mechanical Engineering, University of California, Santa Barbara, CA, USA","Dept. of Mech. Eng., Univ. of California, Santa Barbara, CA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, University of California, Santa Barbara, CA, USA","institution_ids":["https://openalex.org/I154570441"]},{"raw_affiliation_string":"Dept. of Mech. Eng., Univ. of California, Santa Barbara, CA, USA","institution_ids":["https://openalex.org/I154570441"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039292004","display_name":"Amr El Abbadi","orcid":"https://orcid.org/0000-0003-4692-3268"},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"A. El Abbadi","raw_affiliation_strings":["Department of Computer Science, University of California, Santa Barbara, CA, USA","[Dept. of Computer Science, University of California, Santa Barbara, CA, USA]"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of California, Santa Barbara, CA, USA","institution_ids":["https://openalex.org/I154570441"]},{"raw_affiliation_string":"[Dept. of Computer Science, University of California, Santa Barbara, CA, USA]","institution_ids":["https://openalex.org/I154570441"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5081738999"],"corresponding_institution_ids":["https://openalex.org/I154570441"],"apc_list":null,"apc_paid":null,"fwci":18.1622,"has_fulltext":false,"cited_by_count":153,"citation_normalized_percentile":{"value":0.99484316,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":93,"max":100},"biblio":{"volume":"55","issue":"4","first_page":"880","last_page":"892"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10249","display_name":"Distributed Control Multi-Agent Systems","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/T10249","display_name":"Distributed Control Multi-Agent Systems","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/T10064","display_name":"Complex Network Analysis Techniques","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11896","display_name":"Opportunistic and Delay-Tolerant Networks","score":0.9969000220298767,"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/convergence","display_name":"Convergence (economics)","score":0.6687496900558472},{"id":"https://openalex.org/keywords/recursion","display_name":"Recursion (computer science)","score":0.6580849885940552},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.6231300830841064},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.48649924993515015},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4666725695133209},{"id":"https://openalex.org/keywords/variance","display_name":"Variance (accounting)","score":0.44974520802497864},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4356522560119629},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4325827658176422},{"id":"https://openalex.org/keywords/convergence-of-random-variables","display_name":"Convergence of random variables","score":0.4292074143886566},{"id":"https://openalex.org/keywords/stochastic-process","display_name":"Stochastic process","score":0.41400736570358276},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.37411874532699585},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3581875264644623},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.34644952416419983},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2520816922187805}],"concepts":[{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6687496900558472},{"id":"https://openalex.org/C168773036","wikidata":"https://www.wikidata.org/wiki/Q264164","display_name":"Recursion (computer science)","level":2,"score":0.6580849885940552},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.6231300830841064},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.48649924993515015},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4666725695133209},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.44974520802497864},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4356522560119629},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4325827658176422},{"id":"https://openalex.org/C95763700","wikidata":"https://www.wikidata.org/wiki/Q578985","display_name":"Convergence of random variables","level":3,"score":0.4292074143886566},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.41400736570358276},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.37411874532699585},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3581875264644623},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.34644952416419983},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2520816922187805},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C121955636","wikidata":"https://www.wikidata.org/wiki/Q4116214","display_name":"Accounting","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2010.2041998","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2010.2041998","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W1547358136","https://openalex.org/W1558467505","https://openalex.org/W1563885070","https://openalex.org/W1603765807","https://openalex.org/W1964647857","https://openalex.org/W2067153340","https://openalex.org/W2074796812","https://openalex.org/W2080631799","https://openalex.org/W2089598668","https://openalex.org/W2092835885","https://openalex.org/W2098863504","https://openalex.org/W2106221286","https://openalex.org/W2107396783","https://openalex.org/W2110100895","https://openalex.org/W2114403255","https://openalex.org/W2115428923","https://openalex.org/W2115747965","https://openalex.org/W2117905067","https://openalex.org/W2122093006","https://openalex.org/W2124451866","https://openalex.org/W2125668987","https://openalex.org/W2136657801","https://openalex.org/W2151685478","https://openalex.org/W2159499856","https://openalex.org/W2165744313","https://openalex.org/W2166417226","https://openalex.org/W2168354577","https://openalex.org/W2172813797","https://openalex.org/W2504031346","https://openalex.org/W2536420883","https://openalex.org/W2541488199","https://openalex.org/W3143219376","https://openalex.org/W3146923599","https://openalex.org/W3210839039","https://openalex.org/W4244375620","https://openalex.org/W4247555059","https://openalex.org/W4285719527","https://openalex.org/W6793127252"],"related_works":["https://openalex.org/W650906410","https://openalex.org/W2414029657","https://openalex.org/W2917004389","https://openalex.org/W138209035","https://openalex.org/W3085309344","https://openalex.org/W150281603","https://openalex.org/W2183541783","https://openalex.org/W1969020126","https://openalex.org/W2040180057","https://openalex.org/W1555149096"],"abstract_inverted_index":{"<para":[0],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[1],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[2],"We":[3,37,58,84,102],"consider":[4],"a":[5,11,47,130],"distributed":[6],"average":[7,76],"consensus":[8],"algorithm":[9],"over":[10],"network":[12,115,127],"in":[13,28,77,91,113],"which":[14,54],"communication":[15],"links":[16],"fail":[17],"with":[18,50,79],"independent":[19],"probability.":[20,135],"In":[21],"such":[22],"stochastic":[23],"networks,":[24],"convergence":[25,89],"is":[26],"defined":[27],"terms":[29],"of":[30,33,72,95,125,132],"the":[31,41,68,73,88,92,109,123],"variance":[32],"deviation":[34,74],"from":[35,75],"average.":[36],"first":[38],"show":[39],"how":[40],"problem":[42],"can":[43],"be":[44],"recast":[45],"as":[46,129],"linear":[48],"system":[49],"multiplicative":[51],"random":[52],"inputs":[53],"model":[55,116],"link":[56,133],"failures.":[57],"then":[59],"use":[60,118],"our":[61],"formulation":[62],"to":[63,121],"derive":[64],"recursion":[65],"equations":[66],"for":[67,87,107],"second":[69,110],"order":[70,111],"statistics":[71,112],"networks":[78],"and":[80,99,117],"without":[81],"additive":[82],"noise.":[83],"give":[85],"expressions":[86],"behavior":[90,124],"asymptotic":[93],"limits":[94],"small":[96],"failure":[97,134],"probability":[98],"large":[100],"networks.":[101],"also":[103],"present":[104],"simulation-free":[105],"methods":[106,120],"computing":[108],"each":[114],"these":[119],"study":[122],"various":[126],"examples":[128],"function":[131],"</para>":[136]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":12},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":14},{"year":2017,"cited_by_count":10},{"year":2016,"cited_by_count":10},{"year":2015,"cited_by_count":11},{"year":2014,"cited_by_count":16},{"year":2013,"cited_by_count":18},{"year":2012,"cited_by_count":15}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}