{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,8]],"date-time":"2026-05-08T16:32:00Z","timestamp":1778257920812,"version":"3.51.4"},"reference-count":31,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2022,7,26]],"date-time":"2022-07-26T00:00:00Z","timestamp":1658793600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["72091513"],"award-info":[{"award-number":["72091513"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["71621001"],"award-info":[{"award-number":["71621001"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The ever-increasing travel demand has brought great challenges to the organization, operation, and management of the subway system. An accurate estimation of passenger flow distribution can help subway operators design corresponding operation plans and strategies scientifically. Although some literature has studied the problem of passenger flow distribution by analyzing the passengers\u2019 path choice behaviors based on AFC (automated fare collection) data, few studies focus on the passenger flow distribution while considering the passenger\u2013train matching probability, which is the key problem of passenger flow distribution. Specifically, the existing methods have not been applied to practical large-scale subway networks due to the computational complexity. To fill this research gap, this paper analyzes the relationship between passenger travel behavior and train operation in the space and time dimension and formulates the passenger\u2013train matching probability by using multi-source data including AFC, train timetables, and network topology. Then, a reverse derivation method, which can reduce the scale of possible train combinations for passengers, is proposed to improve the computational efficiency. Simultaneously, an estimation method of passenger flow distribution is presented based on the passenger\u2013train matching probability. Finally, two sets of experiments, including an accuracy verification experiment based on synthetic data and a comparison experiment based on real data from the Beijing subway, are conducted to verify the effectiveness of the proposed method. The calculation results show that the proposed method has a good accuracy and computational efficiency for a large-scale subway network.<\/jats:p>","DOI":"10.3390\/e24081026","type":"journal-article","created":{"date-parts":[[2022,7,26]],"date-time":"2022-07-26T22:03:42Z","timestamp":1658873022000},"page":"1026","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["A Calculation Method of Passenger Flow Distribution in Large-Scale Subway Network Based on Passenger\u2013Train Matching Probability"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3667-1618","authenticated-orcid":false,"given":"Guanghui","family":"Su","sequence":"first","affiliation":[{"name":"School of Traffic and Transportation, Beijing Jiaotong University, Beijing 100044, China"}]},{"given":"Bingfeng","family":"Si","sequence":"additional","affiliation":[{"name":"School of Traffic and Transportation, Beijing Jiaotong University, Beijing 100044, China"}]},{"given":"Kun","family":"Zhi","sequence":"additional","affiliation":[{"name":"School of Traffic and Transportation, Beijing Jiaotong University, Beijing 100044, China"}]},{"given":"He","family":"Li","sequence":"additional","affiliation":[{"name":"Beijing Metro Network Administration Co., Ltd., Beijing 100101, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,7,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1016\/j.trb.2021.05.009","article-title":"An Exact Method for the Integrated Optimization of Subway Lines Operation Strategies with Asymmetric Passenger Demand and Operating Costs","volume":"149","author":"Mo","year":"2021","journal-title":"Transp. Res. Part B Methodol."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/j.tre.2014.01.002","article-title":"Enhancing Metro Network Resilience via Localized Integration with Bus Services","volume":"63","author":"Jin","year":"2014","journal-title":"Transp. Res. Part E Logist. Transp. Rev."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1016\/S0191-2615(03)00026-2","article-title":"A Dynamic Schedule-Based Model for Congested Transit Networks","volume":"38","author":"Poon","year":"2004","journal-title":"Transp. Res. Part B Methodol."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2890814","DOI":"10.1155\/2017\/2890814","article-title":"Simulation-Based Dynamic Passenger Flow Assignment Modelling for a Schedule-Based Transit Network","volume":"2017","author":"Yao","year":"2017","journal-title":"Discret. Dyn. Nat. Soc."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1177\/0361198120914309","article-title":"Capacity-Constrained Network Performance Model for Urban Rail Systems","volume":"2674","author":"Mo","year":"2020","journal-title":"Transp. Res. Rec."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1016\/j.trc.2011.02.007","article-title":"A Schedule-Based Assignment Model with Explicit Capacity Constraints for Congested Transit Networks","volume":"20","author":"Nuzzolo","year":"2012","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1805","DOI":"10.1016\/j.trb.2011.07.010","article-title":"Schedule-Based Transit Assignment Model with Vehicle Capacity and Seat Availability","volume":"45","author":"Hamdouch","year":"2011","journal-title":"Transp. Res. Part B Methodol."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1016\/j.trb.2017.07.008","article-title":"A Heuristic Method for a Congested Capacitated Transit Assignment Model with Strategies","volume":"106","author":"Codina","year":"2017","journal-title":"Transp. Res. Part B Methodol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1016\/j.trb.2005.05.006","article-title":"A Frequency-Based Assignment Model for Congested Transit Networks with Strict Capacity Constraints: Characterization and Computation of Equilibria","volume":"40","author":"Cepeda","year":"2006","journal-title":"Transp. Res. Part B Methodol."},{"key":"ref_10","unstructured":"Paul, E.C. (2010). Estimating Train Passenger Load from Automated Data Systems: Application to London Underground. [Master\u2019s Thesis, Massachusetts Institute of Technology]."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"392","DOI":"10.1016\/j.trb.2010.07.002","article-title":"Frequency-Based Transit Assignment Considering Seat Capacities","volume":"45","author":"Fonzone","year":"2011","journal-title":"Transp. Res. Part B Methodol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"511","DOI":"10.1016\/j.trb.2016.06.011","article-title":"Understanding Urban Mobility Patterns with a Probabilistic Tensor Factorization Framework","volume":"91","author":"Sun","year":"2016","journal-title":"Transp. Res. Part B Methodol."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1016\/j.trb.2016.10.015","article-title":"Crowding Cost Estimation with Large Scale Smart Card and Vehicle Location Data","volume":"95","author":"Graham","year":"2017","journal-title":"Transp. Res. Part B Methodol."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1016\/j.trb.2016.04.005","article-title":"Willingness to Board: A Novel Concept for Modeling Queuing up Passengers","volume":"90","author":"Liu","year":"2016","journal-title":"Transp. Res. Part B Methodol."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"6657486","DOI":"10.1155\/2022\/6657486","article-title":"Exploring for Route Preferences of Subway Passengers Using Smart Card and Train Log Data","volume":"2022","author":"Lee","year":"2022","journal-title":"J. Adv. Transp."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"557","DOI":"10.1016\/j.trc.2010.12.003","article-title":"Smart Card Data Use in Public Transit: A Literature Review","volume":"19","author":"Pelletier","year":"2011","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"5597130","DOI":"10.1155\/2021\/5597130","article-title":"Calibrating Path Choices and Train Capacities for Urban Rail Transit Simulation Models Using Smart Card and Train Movement Data","volume":"2021","author":"Mo","year":"2021","journal-title":"J. Adv. Transp."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Zhang, J., Chen, F., Yang, L., Ma, W., Jin, G., and Gao, Z. (2022). Network-Wide Link Travel Time and Station Waiting Time Estimation Using Automatic Fare Collection Data: A Computational Graph Approach. IEEE Trans. Intell. Transp. Syst., 1\u201316.","DOI":"10.1109\/TITS.2022.3181381"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"6830450","DOI":"10.1155\/2019\/6830450","article-title":"Data-Driven Approaches to Mining Passenger Travel Patterns: \u201cLeft-Behinds\u201d in a Congested Urban Rail Transit Network","volume":"2019","author":"Chen","year":"2019","journal-title":"J. Adv. Transp."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"102037","DOI":"10.1016\/j.tre.2020.102037","article-title":"Data-Driven Approach for Solving the Route Choice Problem with Traveling Backward Behavior in Congested Metro Systems","volume":"142","author":"Yu","year":"2020","journal-title":"Transp. Res. Part E Logist. Transp. Rev."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"5451017","DOI":"10.1155\/2022\/5451017","article-title":"Data-Driven Method for Passenger Path Choice Inference in Congested Subway Network","volume":"2022","author":"Su","year":"2022","journal-title":"Complexity"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"731","DOI":"10.1007\/s11116-010-9290-0","article-title":"Estimation Method for Railway Passengers\u2019 Train Choice Behavior with Smart Card Transaction Data","volume":"37","author":"Kusakabe","year":"2010","journal-title":"Transportation"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"57","DOI":"10.3141\/2284-07","article-title":"Model of Passenger Flow Assignment for Urban Rail Transit Based on Entry and Exit Time Constraints","volume":"2284","author":"Zhou","year":"2012","journal-title":"Transp. Res. Rec."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"790","DOI":"10.1109\/TITS.2016.2587864","article-title":"Estimation of Passenger Route Choice Pattern Using Smart Card Data for Complex Metro Systems","volume":"18","author":"Zhao","year":"2017","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"522","DOI":"10.1016\/j.trb.2017.04.012","article-title":"A Probabilistic Passenger-to-Train Assignment Model Based on Automated Data","volume":"104","author":"Zhu","year":"2017","journal-title":"Transp. Res. Part B Methodol."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"102896","DOI":"10.1016\/j.trc.2020.102896","article-title":"Passenger Itinerary Inference Model for Congested Urban Rail Networks","volume":"123","author":"Zhu","year":"2021","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1","DOI":"10.3141\/2649-01","article-title":"Train Overcrowding: Investigation of the Provision of Better Information to Mitigate the Issues","volume":"2649","author":"Preston","year":"2017","journal-title":"Transp. Res. Rec."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1002\/atr.1203","article-title":"Development of a Transfer-Cost-Based Logit Assignment Model for the Beijing Rail Transit Network Using Automated Fare Collection Data","volume":"47","author":"Si","year":"2013","journal-title":"J. Adv. Transp."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"124","DOI":"10.1016\/j.trc.2015.08.010","article-title":"Assessment of Antenna Characteristic Effects on Pedestrian and Cyclists Travel-Time Estimation Based on Bluetooth and WiFi MAC Addresses","volume":"60","author":"Abedi","year":"2015","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"106528","DOI":"10.1016\/j.knosys.2020.106528","article-title":"Spatio-Temporal Trajectory Estimation Based on Incomplete Wi-Fi Probe Data in Urban Rail Transit Network","volume":"211","author":"Gu","year":"2021","journal-title":"Knowledge-Based Syst."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"103260","DOI":"10.1016\/j.trc.2021.103260","article-title":"A Radar-Nearest-Neighbor Based Data-Driven Approach for Crowd Simulation","volume":"129","author":"Zhao","year":"2021","journal-title":"Transp. Res. Part C Emerg. Technol."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/8\/1026\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:56:44Z","timestamp":1760140604000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/8\/1026"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,7,26]]},"references-count":31,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2022,8]]}},"alternative-id":["e24081026"],"URL":"https:\/\/doi.org\/10.3390\/e24081026","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,7,26]]}}}