{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,21]],"date-time":"2026-03-21T00:03:54Z","timestamp":1774051434439,"version":"3.50.1"},"reference-count":29,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2019,3,1]],"date-time":"2019-03-01T00:00:00Z","timestamp":1551398400000},"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":["No. U1434207 and U1734204"],"award-info":[{"award-number":["No. U1434207 and U1734204"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Rescheduling is often needed when trains stay in segments or stations longer than specified in the timetable due to disturbances. Under crowded situations, it is more challenging to return to normal with heavy passenger flow. Considering making a trade-off between passenger loss and operating costs, we present a train regulation combined with a passenger control model by analyzing the interactive relationship between passenger behaviors and train operation. In this paper, we convert the problem into a Markov decision process and then propose the management strategy of regulating the running time and controlling the number of boarding passengers. Owing to the high dimensions of the large-scale problem, we applied the Approximate Dynamic Programming (ADP) approach, which approximates the value function with state features to improve computational efficiency. Finally, we designed three experimental scenarios to verify the effectiveness of our proposed model and approach. The results show that both the proposed model and the approach have a good performance in the cases with different passenger flows and different disturbances.<\/jats:p>","DOI":"10.3390\/sym11030303","type":"journal-article","created":{"date-parts":[[2019,3,4]],"date-time":"2019-03-04T05:45:36Z","timestamp":1551678336000},"page":"303","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Train Regulation Combined with Passenger Control Model Based on Approximate Dynamic Programming"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3063-6117","authenticated-orcid":false,"given":"Sijia","family":"Hao","sequence":"first","affiliation":[{"name":"Key Laboratory of Transport Industry of Big Data Application Technologies for Comprehensive Transport, Ministry of Transport, Beijing Jiaotong University, Beijing 100044, China"}]},{"given":"Rui","family":"Song","sequence":"additional","affiliation":[{"name":"Key Laboratory of Transport Industry of Big Data Application Technologies for Comprehensive Transport, Ministry of Transport, Beijing Jiaotong University, Beijing 100044, China"}]},{"given":"Shiwei","family":"He","sequence":"additional","affiliation":[{"name":"Key Laboratory of Transport Industry of Big Data Application Technologies for Comprehensive Transport, Ministry of Transport, Beijing Jiaotong University, Beijing 100044, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6600-6948","authenticated-orcid":false,"given":"Zekang","family":"Lan","sequence":"additional","affiliation":[{"name":"Key Laboratory of Transport Industry of Big Data Application Technologies for Comprehensive Transport, Ministry of Transport, Beijing Jiaotong University, Beijing 100044, China"}]}],"member":"1968","published-online":{"date-parts":[[2019,3,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1016\/j.trb.2014.01.009","article-title":"An overview of recovery models and algorithms for real-time railway rescheduling","volume":"63","author":"Cacchiani","year":"2014","journal-title":"Transp. 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