{"id":"https://openalex.org/W2167541004","doi":"https://doi.org/10.1109/glocom.2009.5425885","title":"Phase Transition Width of Connectivity of Wireless Multi-Hop Networks in Shadowing Environment","display_name":"Phase Transition Width of Connectivity of Wireless Multi-Hop Networks in Shadowing Environment","publication_year":2009,"publication_date":"2009-11-01","ids":{"openalex":"https://openalex.org/W2167541004","doi":"https://doi.org/10.1109/glocom.2009.5425885","mag":"2167541004"},"language":"en","primary_location":{"id":"doi:10.1109/glocom.2009.5425885","is_oa":false,"landing_page_url":"https://doi.org/10.1109/glocom.2009.5425885","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"GLOBECOM 2009 - 2009 IEEE Global Telecommunications Conference","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/A5001758927","display_name":"Xiaoyuan Ta","orcid":null},"institutions":[{"id":"https://openalex.org/I42894916","display_name":"Data61","ror":"https://ror.org/03q397159","country_code":"AU","type":"other","lineage":["https://openalex.org/I1292875679","https://openalex.org/I2801453606","https://openalex.org/I42894916","https://openalex.org/I4387156119"]},{"id":"https://openalex.org/I129604602","display_name":"University of Sydney","ror":"https://ror.org/0384j8v12","country_code":"AU","type":"education","lineage":["https://openalex.org/I129604602"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Xiaoyuan Ta","raw_affiliation_strings":["NICTA, Sydney, Australia","School of Electrical and Information Engineering, University of Sydney, Australia"],"affiliations":[{"raw_affiliation_string":"NICTA, Sydney, Australia","institution_ids":["https://openalex.org/I42894916"]},{"raw_affiliation_string":"School of Electrical and Information Engineering, University of Sydney, Australia","institution_ids":["https://openalex.org/I129604602"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036000787","display_name":"Guoqiang Mao","orcid":"https://orcid.org/0000-0002-3598-4949"},"institutions":[{"id":"https://openalex.org/I129604602","display_name":"University of Sydney","ror":"https://ror.org/0384j8v12","country_code":"AU","type":"education","lineage":["https://openalex.org/I129604602"]},{"id":"https://openalex.org/I42894916","display_name":"Data61","ror":"https://ror.org/03q397159","country_code":"AU","type":"other","lineage":["https://openalex.org/I1292875679","https://openalex.org/I2801453606","https://openalex.org/I42894916","https://openalex.org/I4387156119"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Guoqiang Mao","raw_affiliation_strings":["NICTA, Sydney, Australia","School of Electrical and Information Engineering, University of Sydney, Australia"],"affiliations":[{"raw_affiliation_string":"NICTA, Sydney, Australia","institution_ids":["https://openalex.org/I42894916"]},{"raw_affiliation_string":"School of Electrical and Information Engineering, University of Sydney, Australia","institution_ids":["https://openalex.org/I129604602"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015736743","display_name":"Brian D. O. Anderson","orcid":"https://orcid.org/0000-0002-1493-4774"},"institutions":[{"id":"https://openalex.org/I42894916","display_name":"Data61","ror":"https://ror.org/03q397159","country_code":"AU","type":"other","lineage":["https://openalex.org/I1292875679","https://openalex.org/I2801453606","https://openalex.org/I42894916","https://openalex.org/I4387156119"]},{"id":"https://openalex.org/I118347636","display_name":"Australian National University","ror":"https://ror.org/019wvm592","country_code":"AU","type":"education","lineage":["https://openalex.org/I118347636"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Brian D. O. Anderson","raw_affiliation_strings":["NICTA, Canberra, Australia","Research School of Information Sciences and Engineering, Australian National University, Australia"],"affiliations":[{"raw_affiliation_string":"NICTA, Canberra, Australia","institution_ids":["https://openalex.org/I42894916"]},{"raw_affiliation_string":"Research School of Information Sciences and Engineering, Australian National University, Australia","institution_ids":["https://openalex.org/I118347636"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5001758927"],"corresponding_institution_ids":["https://openalex.org/I129604602","https://openalex.org/I42894916"],"apc_list":null,"apc_paid":null,"fwci":0.7251,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.76719613,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"13","issue":null,"first_page":"1","last_page":"6"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10246","display_name":"Mobile Ad Hoc Networks","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/T10246","display_name":"Mobile Ad Hoc Networks","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/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9991999864578247,"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/T11896","display_name":"Opportunistic and Delay-Tolerant Networks","score":0.9979000091552734,"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/wireless-network","display_name":"Wireless network","score":0.6189871430397034},{"id":"https://openalex.org/keywords/hop","display_name":"Hop (telecommunications)","score":0.5944579243659973},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5849388837814331},{"id":"https://openalex.org/keywords/wireless","display_name":"Wireless","score":0.5694617629051208},{"id":"https://openalex.org/keywords/node","display_name":"Node (physics)","score":0.5688209533691406},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.5141475796699524},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.4852850139141083},{"id":"https://openalex.org/keywords/phase-transition","display_name":"Phase transition","score":0.44003918766975403},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.41094374656677246},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32057344913482666},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.289869487285614},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.28913429379463196},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2836269438266754},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.15800374746322632}],"concepts":[{"id":"https://openalex.org/C108037233","wikidata":"https://www.wikidata.org/wiki/Q11375","display_name":"Wireless network","level":3,"score":0.6189871430397034},{"id":"https://openalex.org/C25906391","wikidata":"https://www.wikidata.org/wiki/Q1432381","display_name":"Hop (telecommunications)","level":2,"score":0.5944579243659973},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5849388837814331},{"id":"https://openalex.org/C555944384","wikidata":"https://www.wikidata.org/wiki/Q249","display_name":"Wireless","level":2,"score":0.5694617629051208},{"id":"https://openalex.org/C62611344","wikidata":"https://www.wikidata.org/wiki/Q1062658","display_name":"Node (physics)","level":2,"score":0.5688209533691406},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.5141475796699524},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4852850139141083},{"id":"https://openalex.org/C149288129","wikidata":"https://www.wikidata.org/wiki/Q185357","display_name":"Phase transition","level":2,"score":0.44003918766975403},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.41094374656677246},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32057344913482666},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.289869487285614},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.28913429379463196},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2836269438266754},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.15800374746322632},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/glocom.2009.5425885","is_oa":false,"landing_page_url":"https://doi.org/10.1109/glocom.2009.5425885","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"GLOBECOM 2009 - 2009 IEEE Global Telecommunications Conference","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.594.5398","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.594.5398","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://nicta.com.au/research/research_publications?sq_content_src=%2BdXJsPWh0dHBzJTNBJTJGJTJGcHVibGljYXRpb25zLmluc2lkZS5uaWN0YS5jb20uYXUlMkZzZWFyY2glMkZmdWxsdGV4dCUzRmlkJTNEMzE2OCZhbGw9MQ%3D%3D","raw_type":"text"},{"id":"pmh:oai:openresearch-repository.anu.edu.au:1885/53690","is_oa":false,"landing_page_url":"http://hdl.handle.net/1885/53690","pdf_url":null,"source":{"id":"https://openalex.org/S4306402539","display_name":"ANU Open Research (Australian National University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I118347636","host_organization_name":"Australian National University","host_organization_lineage":["https://openalex.org/I118347636"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Proceedings of IEEE Global Communications Conference, Exhibition &amp; Industry Forum (GLOBECOM 2009)","raw_type":"Conference paper"},{"id":"pmh:oai:opus.lib.uts.edu.au:10453/29411","is_oa":false,"landing_page_url":"http://hdl.handle.net/10453/29411","pdf_url":null,"source":{"id":"https://openalex.org/S4306401357","display_name":"UTS ePRESS (University of Technology Sydney)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I114017466","host_organization_name":"University of Technology Sydney","host_organization_lineage":["https://openalex.org/I114017466"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Conference Proceeding"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W587813246","https://openalex.org/W630423399","https://openalex.org/W1967533244","https://openalex.org/W2004289858","https://openalex.org/W2004644628","https://openalex.org/W2007662129","https://openalex.org/W2018438786","https://openalex.org/W2097174445","https://openalex.org/W2106334285","https://openalex.org/W2108327942","https://openalex.org/W2110862165","https://openalex.org/W2112754208","https://openalex.org/W2115162303","https://openalex.org/W2119221712","https://openalex.org/W2124178852","https://openalex.org/W2126610763","https://openalex.org/W2139924859","https://openalex.org/W2145417574","https://openalex.org/W2242479605","https://openalex.org/W2478722229","https://openalex.org/W3144881883","https://openalex.org/W4256020710","https://openalex.org/W6676548508"],"related_works":["https://openalex.org/W2117210722","https://openalex.org/W2589759689","https://openalex.org/W1978191894","https://openalex.org/W2018045843","https://openalex.org/W3125668480","https://openalex.org/W2032875422","https://openalex.org/W1999406711","https://openalex.org/W1989661137","https://openalex.org/W2896124450","https://openalex.org/W4243319602"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"study":[4],"the":[5,69,76,82,97,101,110,122],"well-known":[6],"phase":[7,123],"transition":[8,124],"behavior":[9],"of":[10,32,126],"connectivity":[11,127],"in":[12,18,23,45,106],"a":[13,24,30,42,54,92],"wireless":[14],"multi-hop":[15],"network,":[16],"but,":[17],"contrast":[19],"to":[20,91,109,140,145],"other":[21,77,146],"studies,":[22],"shadowing":[25,84,114],"environment.":[26],"We":[27,95,131],"consider":[28],"that":[29],"total":[31],"n":[33],"nodes":[34,61],"are":[35,62],"randomly,":[36],"independently":[37],"and":[38,58,66,116,144],"uniformly":[39],"distributed":[40],"on":[41],"unit":[43,102],"square":[44],"R":[46],"<sup":[47],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[48],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sup>":[49],",":[50],"each":[51],"node":[52,74],"has":[53],"uniform":[55],"transmission":[56],"power":[57,70],"any":[59],"two":[60],"directly":[63],"connected":[64],"if":[65,68],"only":[67],"received":[71],"by":[72,81],"one":[73],"from":[75],"node,":[78],"as":[79],"determined":[80],"log-normal":[83,113],"model,":[85,115],"is":[86],"larger":[87],"than":[88],"or":[89],"equal":[90],"given":[93],"threshold.":[94],"extend":[96],"results":[98,136],"obtained":[99],"under":[100],"disk":[103],"communication":[104],"model":[105],"previous":[107],"work":[108],"more":[111],"realistic":[112],"derive":[117],"an":[118],"analytical":[119],"formula":[120],"for":[121,128],"width":[125],"large":[129],"n.":[130],"also":[132],"demonstrate":[133],"how":[134],"our":[135],"can":[137],"be":[138],"extended":[139],"higher":[141],"dimensional":[142],"networks":[143],"channel":[147],"models.":[148]},"counts_by_year":[{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
