A Formulation of MIP Train Rescheduling at Terminals in Bidirectional Double-Track Lines with a Moving Block and ATO

Authors Kosuke Kawazoe, Takuto Yamauchi, Kenji Tei

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Author Details

Kosuke Kawazoe
  • Faculty of Science and Engineering, Waseda University, Shinjuku, Tokyo, Japan
Takuto Yamauchi
  • Faculty of Science and Engineering, Waseda University, Shinjuku, Tokyo, Japan
Kenji Tei
  • Faculty of Science and Engineering, Waseda University, Shinjuku, Tokyo, Japan

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Kosuke Kawazoe, Takuto Yamauchi, and Kenji Tei. A Formulation of MIP Train Rescheduling at Terminals in Bidirectional Double-Track Lines with a Moving Block and ATO. In 22nd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2022). Open Access Series in Informatics (OASIcs), Volume 106, pp. 10:1-10:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


When delays in trains occur, train schedules are rescheduled to reduce the impact. Despite many existing studies of automated train rescheduling, this study focuses on automated rescheduling considering a moving block and Automatic Train Operation (ATO). This study enables such automated rescheduling by formalizing this problem as a mixed integer programming (MIP) model. In previous work, the formulation was achieved for unidirectional single-track railway lines. In this paper, we aim to achieve the formulation for bidirectional double-track lines. Specifically, we propose a formulation of constraints about trains’ running terminal stations. To evaluate our automated rescheduling approach, we implemented an MIP model consisting of a combination of the new constraints with the previous MIP model. We demonstrated the feasibility of our approach by applying it to a bidirectional double-track line with eight delay scenarios. We also evaluate the delay reduction and computation overhead of our approach by comparing it with a baseline with these eight scenarios. The results show that the total delay of all trains from our approach reduced from 20% to 30% than one from the baseline. On the other hand, the computation time increased from less than 1 second to a minimum of about 20 seconds and a maximum of about 1600 seconds.

Subject Classification

ACM Subject Classification
  • Applied computing → Transportation
  • Train rescheduling
  • Mixed integer programming
  • ATO
  • Moving block


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