{"id":"https://openalex.org/W2965211398","doi":"https://doi.org/10.3390/ijgi8080334","title":"Fleet Size and Rebalancing Analysis of Dockless Bike-Sharing Stations Based on Markov Chain","display_name":"Fleet Size and Rebalancing Analysis of Dockless Bike-Sharing Stations Based on Markov Chain","publication_year":2019,"publication_date":"2019-07-29","ids":{"openalex":"https://openalex.org/W2965211398","doi":"https://doi.org/10.3390/ijgi8080334","mag":"2965211398"},"language":"en","primary_location":{"id":"doi:10.3390/ijgi8080334","is_oa":true,"landing_page_url":"https://doi.org/10.3390/ijgi8080334","pdf_url":"https://www.mdpi.com/2220-9964/8/8/334/pdf?version=1564830375","source":{"id":"https://openalex.org/S2764431341","display_name":"ISPRS International Journal of Geo-Information","issn_l":"2220-9964","issn":["2220-9964"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ISPRS International Journal of Geo-Information","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2220-9964/8/8/334/pdf?version=1564830375","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5103323657","display_name":"Yong Zhai","orcid":null},"institutions":[{"id":"https://openalex.org/I4210141849","display_name":"National Administration of Surveying, Mapping and Geoinformation of China","ror":"https://ror.org/04z3map19","country_code":"CN","type":"government","lineage":["https://openalex.org/I4210141849"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yong Zhai","raw_affiliation_strings":["National Geomatics Center of China, Beijing 100830, China"],"affiliations":[{"raw_affiliation_string":"National Geomatics Center of China, Beijing 100830, China","institution_ids":["https://openalex.org/I4210141849"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110335879","display_name":"Jin Liu","orcid":"https://orcid.org/0009-0003-9543-7642"},"institutions":[{"id":"https://openalex.org/I4210141849","display_name":"National Administration of Surveying, Mapping and Geoinformation of China","ror":"https://ror.org/04z3map19","country_code":"CN","type":"government","lineage":["https://openalex.org/I4210141849"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jin Liu","raw_affiliation_strings":["National Geomatics Center of China, Beijing 100830, China"],"affiliations":[{"raw_affiliation_string":"National Geomatics Center of China, Beijing 100830, China","institution_ids":["https://openalex.org/I4210141849"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100663188","display_name":"Juan Du","orcid":"https://orcid.org/0000-0002-1703-4026"},"institutions":[{"id":"https://openalex.org/I4210141849","display_name":"National Administration of Surveying, Mapping and Geoinformation of China","ror":"https://ror.org/04z3map19","country_code":"CN","type":"government","lineage":["https://openalex.org/I4210141849"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Juan Du","raw_affiliation_strings":["National Geomatics Center of China, Beijing 100830, China"],"affiliations":[{"raw_affiliation_string":"National Geomatics Center of China, Beijing 100830, China","institution_ids":["https://openalex.org/I4210141849"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101926950","display_name":"Hao Wu","orcid":"https://orcid.org/0009-0004-8847-3458"},"institutions":[{"id":"https://openalex.org/I4210141849","display_name":"National Administration of Surveying, Mapping and Geoinformation of China","ror":"https://ror.org/04z3map19","country_code":"CN","type":"government","lineage":["https://openalex.org/I4210141849"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hao Wu","raw_affiliation_strings":["National Geomatics Center of China, Beijing 100830, China"],"affiliations":[{"raw_affiliation_string":"National Geomatics Center of China, Beijing 100830, China","institution_ids":["https://openalex.org/I4210141849"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5110335879"],"corresponding_institution_ids":["https://openalex.org/I4210141849"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":3.0522,"has_fulltext":true,"cited_by_count":23,"citation_normalized_percentile":{"value":0.9017844,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"8","issue":"8","first_page":"334","last_page":"334"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10298","display_name":"Urban Transport and Accessibility","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/3313","display_name":"Transportation"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10298","display_name":"Urban Transport and Accessibility","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/3313","display_name":"Transportation"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11942","display_name":"Transportation and Mobility Innovations","score":0.9941999912261963,"subfield":{"id":"https://openalex.org/subfields/2203","display_name":"Automotive 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/T12306","display_name":"Urban and Freight Transport Logistics","score":0.9915000200271606,"subfield":{"id":"https://openalex.org/subfields/2215","display_name":"Building and Construction"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.7932322025299072},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6753235459327698},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5015785694122314},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.48005354404449463},{"id":"https://openalex.org/keywords/stochastic-matrix","display_name":"Stochastic matrix","score":0.4744221568107605},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4559919536113739},{"id":"https://openalex.org/keywords/continuous-time-markov-chain","display_name":"Continuous-time Markov chain","score":0.4480913281440735},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.4315353035926819},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.42130976915359497},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.4152984917163849},{"id":"https://openalex.org/keywords/markov-model","display_name":"Markov model","score":0.3712029457092285},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3555179238319397},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.18931037187576294},{"id":"https://openalex.org/keywords/variable-order-markov-model","display_name":"Variable-order Markov model","score":0.15769416093826294},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08733421564102173},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.08299455046653748}],"concepts":[{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.7932322025299072},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6753235459327698},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5015785694122314},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.48005354404449463},{"id":"https://openalex.org/C49555168","wikidata":"https://www.wikidata.org/wiki/Q176583","display_name":"Stochastic matrix","level":3,"score":0.4744221568107605},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4559919536113739},{"id":"https://openalex.org/C147080032","wikidata":"https://www.wikidata.org/wiki/Q176720","display_name":"Continuous-time Markov chain","level":5,"score":0.4480913281440735},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.4315353035926819},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.42130976915359497},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.4152984917163849},{"id":"https://openalex.org/C163836022","wikidata":"https://www.wikidata.org/wiki/Q6771326","display_name":"Markov model","level":3,"score":0.3712029457092285},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3555179238319397},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.18931037187576294},{"id":"https://openalex.org/C54907487","wikidata":"https://www.wikidata.org/wiki/Q7915688","display_name":"Variable-order Markov model","level":4,"score":0.15769416093826294},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08733421564102173},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.08299455046653748},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/ijgi8080334","is_oa":true,"landing_page_url":"https://doi.org/10.3390/ijgi8080334","pdf_url":"https://www.mdpi.com/2220-9964/8/8/334/pdf?version=1564830375","source":{"id":"https://openalex.org/S2764431341","display_name":"ISPRS International Journal of Geo-Information","issn_l":"2220-9964","issn":["2220-9964"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ISPRS International Journal of Geo-Information","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:e9357683800747f39e05b3d09f36649e","is_oa":true,"landing_page_url":"https://doaj.org/article/e9357683800747f39e05b3d09f36649e","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":"ISPRS International Journal of Geo-Information, Vol 8, Iss 8, p 334 (2019)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2220-9964/8/8/334/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/ijgi8080334","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"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":"ISPRS International Journal of Geo-Information","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/ijgi8080334","is_oa":true,"landing_page_url":"https://doi.org/10.3390/ijgi8080334","pdf_url":"https://www.mdpi.com/2220-9964/8/8/334/pdf?version=1564830375","source":{"id":"https://openalex.org/S2764431341","display_name":"ISPRS International Journal of Geo-Information","issn_l":"2220-9964","issn":["2220-9964"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ISPRS International Journal of Geo-Information","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2965211398.pdf","grobid_xml":"https://content.openalex.org/works/W2965211398.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W1514324734","https://openalex.org/W1523742540","https://openalex.org/W1608412409","https://openalex.org/W1921393379","https://openalex.org/W1979411729","https://openalex.org/W2032251915","https://openalex.org/W2035563511","https://openalex.org/W2053109393","https://openalex.org/W2054274567","https://openalex.org/W2062147841","https://openalex.org/W2062763974","https://openalex.org/W2074069971","https://openalex.org/W2118382442","https://openalex.org/W2151828736","https://openalex.org/W2213147230","https://openalex.org/W2509231098","https://openalex.org/W2769171548","https://openalex.org/W2889218713","https://openalex.org/W2890694404","https://openalex.org/W2903552754","https://openalex.org/W2917247293","https://openalex.org/W2949830935","https://openalex.org/W3123777455","https://openalex.org/W6666244527","https://openalex.org/W6817700284"],"related_works":["https://openalex.org/W2800044850","https://openalex.org/W2146188408","https://openalex.org/W2734551807","https://openalex.org/W2149353983","https://openalex.org/W2994944459","https://openalex.org/W2884768918","https://openalex.org/W1520319263","https://openalex.org/W4288346508","https://openalex.org/W2947067312","https://openalex.org/W3123502079"],"abstract_inverted_index":{"In":[0],"order":[1],"to":[2,29,112,155,193],"improve":[3],"the":[4,21,31,41,56,59,72,95,98,106,114,126,134,138,145,149,156,162,165,169,176,188,195],"dynamic":[5,146],"optimization":[6],"of":[7,13,33,43,45,62,71,97,137,148,164,171,198],"fleet":[8,35,83,152],"size":[9,36,84,153],"and":[10,25,37,51,68,133],"standardized":[11],"management":[12],"dockless":[14,81,199],"bike-sharing,":[15,46],"this":[16,172],"paper":[17],"focuses":[18],"on":[19,40],"using":[20],"Markov":[22,64],"stochastic":[23],"process":[24,90],"linear":[26,177],"programming":[27,178],"method":[28,109,123,139,179],"solve":[30,194],"problem":[32],"bike-sharing":[34,63,82,99,150],"rebalancing.":[38],"Based":[39],"analysis":[42],"characters":[44],"which":[47],"are":[48],"irreducible,":[49],"aperiodic":[50],"positive-recurrence,":[52],"we":[53,143,174],"prove":[54],"that":[55,187],"probability":[57,74,101,116,128],"limits":[58],"state":[60],"(steady-state)":[61],"chain":[65,80],"only":[66],"exists":[67],"is":[69,87,103,110,130,140],"independent":[70],"initial":[73],"distribution.":[75],"Then":[76],"a":[77],"new":[78],"\u201cMarkov":[79],"solution\u201d":[85],"algorithm":[86,189],"proposed.":[88],"The":[89],"includes":[91],"three":[92],"parts.":[93],"Firstly,":[94],"irreducibility":[96],"transition":[100,115],"matrix":[102],"analyzed.":[104,141],"Secondly,":[105],"rank-one":[107],"updating":[108],"used":[111,192],"construct":[113],"random":[117],"prime":[118],"matrix.":[119],"Finally,":[120],"an":[121],"iterative":[122],"for":[124,180],"solving":[125],"steady-state":[127,151],"vector":[129],"therefore":[131],"given":[132],"convergence":[135],"speed":[136],"Furthermore,":[142],"discuss":[144],"solution":[147],"according":[154],"time":[157],"period,":[158],"so":[159],"as":[160],"improving":[161],"practicality":[163],"algorithm.":[166],"To":[167],"verify":[168],"efficiency":[170],"algorithm,":[173],"adopt":[175],"bicycle":[181],"rebalancing":[182],"analysis.":[183],"Experiment":[184],"results":[185],"show":[186],"could":[190],"be":[191],"disordered":[196],"deployment":[197],"bike-sharing.":[200]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
