{"id":"https://openalex.org/W2040807294","doi":"https://doi.org/10.1109/tpds.2014.2361458","title":"Analysis of Random Walk Mobility Models with Location Heterogeneity","display_name":"Analysis of Random Walk Mobility Models with Location Heterogeneity","publication_year":2014,"publication_date":"2014-10-02","ids":{"openalex":"https://openalex.org/W2040807294","doi":"https://doi.org/10.1109/tpds.2014.2361458","mag":"2040807294"},"language":"en","primary_location":{"id":"doi:10.1109/tpds.2014.2361458","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpds.2014.2361458","pdf_url":null,"source":{"id":"https://openalex.org/S97130795","display_name":"IEEE Transactions on Parallel and Distributed Systems","issn_l":"1045-9219","issn":["1045-9219","1558-2183","2161-9883"],"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 Parallel and Distributed Systems","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/A5004595691","display_name":"Jinbei Zhang","orcid":"https://orcid.org/0000-0003-2348-1970"},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jinbei Zhang","raw_affiliation_strings":["Department of Electronic Engineering, Shanghai Jiao Tong University, China","[Department of Electronic Engineering, Shanghai Jiao Tong University, China]"],"affiliations":[{"raw_affiliation_string":"Department of Electronic Engineering, Shanghai Jiao Tong University, China","institution_ids":["https://openalex.org/I183067930"]},{"raw_affiliation_string":"[Department of Electronic Engineering, Shanghai Jiao Tong University, China]","institution_ids":["https://openalex.org/I183067930"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048486573","display_name":"Luoyi Fu","orcid":"https://orcid.org/0000-0001-7796-9168"},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Luoyi Fu","raw_affiliation_strings":["Department of Electronic Engineering, Shanghai Jiao Tong University, China","[Department of Electronic Engineering, Shanghai Jiao Tong University, China]"],"affiliations":[{"raw_affiliation_string":"Department of Electronic Engineering, Shanghai Jiao Tong University, China","institution_ids":["https://openalex.org/I183067930"]},{"raw_affiliation_string":"[Department of Electronic Engineering, Shanghai Jiao Tong University, China]","institution_ids":["https://openalex.org/I183067930"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018442100","display_name":"Xiaohua Tian","orcid":"https://orcid.org/0000-0003-0716-3323"},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaohua Tian","raw_affiliation_strings":["Department of Electronic Engineering, Shanghai Jiao Tong University, China","[Department of Electronic Engineering, Shanghai Jiao Tong University, China]"],"affiliations":[{"raw_affiliation_string":"Department of Electronic Engineering, Shanghai Jiao Tong University, China","institution_ids":["https://openalex.org/I183067930"]},{"raw_affiliation_string":"[Department of Electronic Engineering, Shanghai Jiao Tong University, China]","institution_ids":["https://openalex.org/I183067930"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071987706","display_name":"Ying Cui","orcid":"https://orcid.org/0000-0003-3181-9775"},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ying Cui","raw_affiliation_strings":["Department of Electronic Engineering, Shanghai Jiao Tong University, China","[Department of Electronic Engineering, Shanghai Jiao Tong University, China]"],"affiliations":[{"raw_affiliation_string":"Department of Electronic Engineering, Shanghai Jiao Tong University, China","institution_ids":["https://openalex.org/I183067930"]},{"raw_affiliation_string":"[Department of Electronic Engineering, Shanghai Jiao Tong University, China]","institution_ids":["https://openalex.org/I183067930"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034483183","display_name":"Xinbing Wang","orcid":"https://orcid.org/0000-0002-0357-8356"},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xinbing Wang","raw_affiliation_strings":["Department of Electronic Engineering, Shanghai Jiao Tong University, China","[Department of Electronic Engineering, Shanghai Jiao Tong University, China]"],"affiliations":[{"raw_affiliation_string":"Department of Electronic Engineering, Shanghai Jiao Tong University, China","institution_ids":["https://openalex.org/I183067930"]},{"raw_affiliation_string":"[Department of Electronic Engineering, Shanghai Jiao Tong University, China]","institution_ids":["https://openalex.org/I183067930"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5004595691"],"corresponding_institution_ids":["https://openalex.org/I183067930"],"apc_list":null,"apc_paid":null,"fwci":1.3792,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.83618754,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"26","issue":"10","first_page":"2657","last_page":"2670"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11896","display_name":"Opportunistic and Delay-Tolerant Networks","score":0.9997000098228455,"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/T11896","display_name":"Opportunistic and Delay-Tolerant Networks","score":0.9997000098228455,"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/T10246","display_name":"Mobile Ad Hoc Networks","score":0.9995999932289124,"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":0.9954000115394592,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/random-walk","display_name":"Random walk","score":0.789955735206604},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.6450452208518982},{"id":"https://openalex.org/keywords/independent-and-identically-distributed-random-variables","display_name":"Independent and identically distributed random variables","score":0.5974429845809937},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5904667377471924},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5704689621925354},{"id":"https://openalex.org/keywords/cover","display_name":"Cover (algebra)","score":0.41268038749694824},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.4117794632911682},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4046289920806885},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3566405177116394},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.2565959692001343},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.18654891848564148}],"concepts":[{"id":"https://openalex.org/C121194460","wikidata":"https://www.wikidata.org/wiki/Q856741","display_name":"Random walk","level":2,"score":0.789955735206604},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.6450452208518982},{"id":"https://openalex.org/C141513077","wikidata":"https://www.wikidata.org/wiki/Q378542","display_name":"Independent and identically distributed random variables","level":3,"score":0.5974429845809937},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5904667377471924},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5704689621925354},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.41268038749694824},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.4117794632911682},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4046289920806885},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3566405177116394},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.2565959692001343},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.18654891848564148},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tpds.2014.2361458","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpds.2014.2361458","pdf_url":null,"source":{"id":"https://openalex.org/S97130795","display_name":"IEEE Transactions on Parallel and Distributed Systems","issn_l":"1045-9219","issn":["1045-9219","1558-2183","2161-9883"],"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 Parallel and Distributed Systems","raw_type":"journal-article"},{"id":"pmh:oai:repository.hkust.edu.hk:1783.1-158638","is_oa":false,"landing_page_url":"http://repository.hkust.edu.hk/ir/Record/1783.1-158638","pdf_url":null,"source":{"id":"https://openalex.org/S4306401796","display_name":"Rare & Special e-Zone (The Hong Kong University of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I200769079","host_organization_name":"Hong Kong University of Science and Technology","host_organization_lineage":["https://openalex.org/I200769079"],"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"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","score":0.550000011920929,"display_name":"Sustainable cities and communities"}],"awards":[{"id":"https://openalex.org/G178677581","display_name":null,"funder_award_id":"61271219","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3584224770","display_name":null,"funder_award_id":"61325012","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3733007272","display_name":null,"funder_award_id":"61202373","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6801275059","display_name":null,"funder_award_id":"20130073110025","funder_id":"https://openalex.org/F4320321106","funder_display_name":"Ministry of Education of the People's Republic of China"},{"id":"https://openalex.org/G7378474545","display_name":null,"funder_award_id":"61221001","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8124223923","display_name":null,"funder_award_id":"61428205","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"},{"id":"https://openalex.org/F4320321106","display_name":"Ministry of Education of the People's Republic of China","ror":"https://ror.org/01mv9t934"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W755194005","https://openalex.org/W1514107797","https://openalex.org/W1541172283","https://openalex.org/W1586184796","https://openalex.org/W1986507557","https://openalex.org/W1987175624","https://openalex.org/W1987752153","https://openalex.org/W1988434354","https://openalex.org/W1991242126","https://openalex.org/W2016850222","https://openalex.org/W2045619381","https://openalex.org/W2055696952","https://openalex.org/W2059561772","https://openalex.org/W2069488474","https://openalex.org/W2113607286","https://openalex.org/W2115227517","https://openalex.org/W2119370781","https://openalex.org/W2120204400","https://openalex.org/W2122659814","https://openalex.org/W2127066052","https://openalex.org/W2142468746","https://openalex.org/W2146369691","https://openalex.org/W2149071511","https://openalex.org/W2149959815","https://openalex.org/W2167167562","https://openalex.org/W2171471095","https://openalex.org/W2172002381","https://openalex.org/W3098255066","https://openalex.org/W3105329945","https://openalex.org/W6630727257","https://openalex.org/W6680886856","https://openalex.org/W6685315540"],"related_works":["https://openalex.org/W1597743604","https://openalex.org/W3004218185","https://openalex.org/W2038723108","https://openalex.org/W4390241083","https://openalex.org/W4245457074","https://openalex.org/W4232403550","https://openalex.org/W623607250","https://openalex.org/W2323735050","https://openalex.org/W2347733609","https://openalex.org/W4253472526"],"abstract_inverted_index":{"This":[0],"paper":[1],"investigates":[2],"random":[3,83,118,170],"walk":[4,119],"mobility":[5,115],"models":[6],"with":[7,64,167,188],"location":[8,71,189,217,252],"heterogeneity,":[9],"where":[10,33,47],"different":[11,15,96,210],"locations":[12,21],"may":[13],"have":[14,36],"neighboring":[16,153],"regions.":[17],"We":[18,219],"consider":[19],"<inline-formula><tex-math>$n$</tex-math></inline-formula>":[20],"in":[22,254],"a":[23,57,74,214],"one-dimension":[24],"network":[25,43,237],"and":[26,44,111,116,140,161,181,229],"investigate":[27,248],"two":[28,104],"cases,":[29,106],"i.e.,":[30],"<i>full-range":[31],"locations</i>":[32,46],"nodes":[34,48,200],"situated":[35],"the":[37,42,61,65,78,108,122,128,136,150,173,182,196,203,231,234,241,249],"capability":[38],"to":[39,51,53,91,95,149,209,225,247],"shuffle":[40],"throughout":[41],"<i>long-range":[45],"are":[49,146],"allowed":[50],"move":[52,245],"positions":[54],"nearby":[55],"within":[56],"certain":[58],"range.":[59],"In":[60,127,191],"former":[62],"situation,":[63],"exact":[66],"expressions":[67],"derived,":[68],"we":[69,244],"find":[70],"heterogeneity":[72,253],"has":[73],"critical":[75],"impact":[76,235,250],"on":[77,134,233,240],"first":[79,137,174],"hitting":[80,175],"time":[81,139,142,176],"of":[82,98,124,152,199,216,236,251],"walk,":[84],"varying":[85,121],"from":[86],"<inline-formula>":[87],"<tex-math>$\\Theta":[88],"(n)$</tex-math>":[89],"</inline-formula>":[90,160],"<inline-formula><tex-math>$\\Theta":[92],"\\left(n^3\\right)$</tex-math></inline-formula>":[93],"according":[94],"extent":[97],"heterogeneity.":[99,190,218],"The":[100],"result":[101,215],"covers,":[102],"as":[103,213],"special":[105],"both":[107,135],"classic":[109],"independent":[110],"identically":[112],"distributed":[113],"(i.i.d)":[114],"traditional":[117],"when":[120],"number":[123],"full-range":[125],"locations.":[126],"latter":[129],"one,":[130],"our":[131,193,227],"asymptotic":[132],"results":[133,224],"crossing":[138],"cover":[141],"suggest":[143],"that":[144,202],"they":[145],"inversely":[147],"proportional":[148],"range":[151],"region":[154],"<inline-formula><tex-math>$r$</tex-math></inline-formula>":[155],"(":[156],"<inline-formula><tex-math>":[157],"$\\propto":[158],"r^{-2}$</tex-math>":[159],"<inline-formula><tex-math>$\\propto":[162],"r^{-1}$</tex-math></inline-formula>":[163],",":[164],"respectively).":[165],"Furthermore,":[166],"multiple":[168],"concurrent":[169],"walks":[171],"introduced,":[172],"can":[177],"be":[178],"drastically":[179],"decreased":[180],"effect":[183],"is":[184],"strengthened":[185],"if":[186],"combined":[187],"addition,":[192],"investigation":[194],"into":[195],"stationary":[197],"distribution":[198],"indicates":[201],"uniformity":[204],"no":[205],"longer":[206],"holds":[207],"due":[208],"transition":[211],"probabilities,":[212],"also":[220],"conduct":[221],"extensive":[222],"simulation":[223],"verify":[226],"observations":[228],"enhance":[230],"understanding":[232],"parameters.":[238],"Based":[239],"insights":[242],"obtained,":[243],"forward":[246],"two-dimension":[255],"networks.":[256]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
