{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T17:27:18Z","timestamp":1773682038203,"version":"3.50.1"},"reference-count":15,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2019,4,1]],"date-time":"2019-04-01T00:00:00Z","timestamp":1554076800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the National Key R&amp;D Program of China","award":["2018YFB1201403"],"award-info":[{"award-number":["2018YFB1201403"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Track allocation optimization in railway stations is one of the most fundamental problems for scheduling trains, especially in multi-direction high-speed railway stations. With the construction of high-speed rail networks, this kind of station has become increasingly common. However, the track allocation depends not only on the station tracks, train timetable, and rolling stock plan, but also on the resources in the station throat area. As a result, an effective track allocation plan becomes significant but also difficult. In this paper, we consider all these factors to make the results more practicable and an integer linear model that minimizes the total occupation time of resources in the throat area is presented. A flexible track utilization rule is also adopted to this model to fit the characteristics of the multi-direction station. Meanwhile, a detailed explanation of resources\u2019 occupation time is illustrated to facilitate the representation of the conflicting constraints. To resolve these issues, we use a commercial solver with its default parameters. A computational experiment of a station is conducted to verify the effectiveness of the proposed model. The resources utilization plan indicates that the capacity of a station is limited by the throat area, rather than by the station tracks.<\/jats:p>","DOI":"10.3390\/sym11040459","type":"journal-article","created":{"date-parts":[[2019,4,2]],"date-time":"2019-04-02T03:21:26Z","timestamp":1554175286000},"page":"459","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Track Allocation Optimization in Multi-Direction High-Speed Railway Stations"],"prefix":"10.3390","volume":"11","author":[{"given":"Qin","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Traffic and Transportation, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaoning","family":"Zhu","sequence":"additional","affiliation":[{"name":"School of Traffic and Transportation, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Li","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Traffic and Transportation, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,4,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"4","DOI":"10.32783\/csid-jid.v1i1.4","article-title":"A rail capacity framework: Making the case for rail freight evaluation in Indonesia","volume":"1","author":"Woroniuk","year":"2015","journal-title":"CSID J. Infrastruct. Dev."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1016\/j.retrec.2012.10.003","article-title":"Railway operations, time-tabling and control","volume":"41","author":"Marinov","year":"2013","journal-title":"Res. Transp. Econ."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"208","DOI":"10.1016\/j.trb.2014.05.005","article-title":"Simultaneous train rerouting and rescheduling on an N-track network: A model reformulation with network-based cumulative flow variables","volume":"67","author":"Meng","year":"2014","journal-title":"Transp. Res. Part B Methodol."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1016\/j.omega.2017.08.018","article-title":"Three-stage optimization method for the problem of scheduling additional trains on a high-speed rail corridor","volume":"80","author":"Gao","year":"2017","journal-title":"Omega"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"160","DOI":"10.1016\/S0377-2217(98)00299-9","article-title":"K L-list \u03bb colouring of graphs","volume":"106","author":"Cardillo","year":"1998","journal-title":"Eur. J. Oper. Res."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1287\/trsc.37.2.213.15250","article-title":"Using integer programming to solve the train-platforming problem","volume":"37","author":"Billionnet","year":"2003","journal-title":"Transp. Sci."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1016\/S0377-2217(00)00087-4","article-title":"Routing trains through a railway station based on a node packing model","volume":"128","author":"Zwaneveld","year":"2001","journal-title":"Eur. J. Oper. Res."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"228","DOI":"10.1287\/trsc.1100.0362","article-title":"Routing trains through railway junctions: A new set-packing approach","volume":"45","author":"Lusby","year":"2011","journal-title":"Transp. Sci."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1016\/S0965-8564(02)00012-5","article-title":"Scheduling and platforming trains at busy complex stations","volume":"37","author":"Carey","year":"2003","journal-title":"Transp. Res. Part A Policy Pract."},{"key":"ref_10","unstructured":"Qiao, R. (2012). Research on Selection and Adjustment of Receiving Routes and Dispatching Routes in Passenger Dedicated Line Station. [Ph.D. Thesis, Beijing Jiaotong University]. (In Chinese)."},{"key":"ref_11","unstructured":"Liu, W. (2017). Optimizing the Bottleneck Sections and Track Allocation Problems for Large Railway Passenger Stations under Abnormal Conditions. [Ph.D. Thesis, Beijing Jiaotong University]. (In Chinese)."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"540","DOI":"10.1061\/(ASCE)TE.1943-5436.0000530","article-title":"Track allocation optimization in railway station: Mean-variance model and case study","volume":"139","author":"Wu","year":"2013","journal-title":"J. Transp. Eng."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1016\/j.trb.2014.01.004","article-title":"The train platforming problem: The infrastructure management company perspective","volume":"61","author":"Sels","year":"2014","journal-title":"Transp. Res. Part B Methodol."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1016\/j.trc.2016.05.020","article-title":"Integrated multi-track station layout design and train scheduling models on railway corridors","volume":"69","author":"Qi","year":"2016","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1177\/0020294018785187","article-title":"Track allocation optimization in high-speed railway stations from infrastructure management and service perspectives","volume":"51","author":"Zhang","year":"2018","journal-title":"Meas. Control"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/4\/459\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:42:08Z","timestamp":1760186528000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/4\/459"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,4,1]]},"references-count":15,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2019,4]]}},"alternative-id":["sym11040459"],"URL":"https:\/\/doi.org\/10.3390\/sym11040459","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,4,1]]}}}