An Integrated Model of Train Timetable and Speed Profile for Single Bi-directional Track

Wenxing Wu; Jing Xun; Xiaoyu Liu; Minxue Fu

doi:10.1007/978-981-96-3977-9_27

An Integrated Model of Train Timetable and Speed Profile for Single Bi-directional Track

Wenxing Wu, Jing Xun^*, Xiaoyu Liu, Minxue Fu

^*Corresponding author for this work

Team Bart De Schutter

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

Abstract

In this paper, we consider the integrated model of train timetable and speed profile for a single bi-directional track. This problem aims to schedule train passes along single track from opposite directions to avoid conflicts. It is assumed that there are different types of stations along the track, and trains can only pass each other simultaneously at stations that have sidings. Focusing on the operation scenario, we propose an integrated model of train timetable and speed profile optimization. To address the nonlinear constraints generated by the meeting conflicts in the single bi-directional operation, the Big-M method is used to transform the constraints into linear constraints incorporating binary integer variables such as meeting and train priority. Thus, a mixed integer linear programming (MILP) model is constructed, which can be solved using the Gurobi solver. The model is formulated with two objective functions: one aims to minimize the time deviation of trains running in pairs considering passenger satisfaction, and the other is to minimize the total train travel time. The proposed model is applied to solve the problem based on a single-line urban railway and the feasibility of the model is verified. The results show that the total train travel time is effectively reduced by 29.8%.

Original language	English
Title of host publication	The Proceedings of 2024 International Conference on Artificial Intelligence and Autonomous Transportation - Volume VI
Editors	Jun Liu, Wang Li, Xiongfei Geng, Ke Zhang, Honghai Ji, Kailong Li
Publisher	Springer
Pages	244-251
Number of pages	8
ISBN (Electronic)	978-981-96-3977-9
ISBN (Print)	978-981-96-3976-2
DOIs	https://doi.org/10.1007/978-981-96-3977-9_27
Publication status	Published - 2025
Event	International Conference on Artificial Intelligence and Autonomous Transportation, AIAT 2024 - Beijing, China Duration: 6 Dec 2024 → 8 Dec 2024

Publication series

Name	Lecture Notes in Electrical Engineering
Volume	1394
ISSN (Print)	1876-1100
ISSN (Electronic)	1876-1119

Conference

Conference	International Conference on Artificial Intelligence and Autonomous Transportation, AIAT 2024
Country/Territory	China
City	Beijing
Period	6/12/24 → 8/12/24

Bibliographical note

Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Keywords

Bi-directional Track
Integrated Model
Timetable Scheduling

Access to Document

10.1007/978-981-96-3977-9_27

Cite this

Wu, W., Xun, J., Liu, X., & Fu, M. (2025). An Integrated Model of Train Timetable and Speed Profile for Single Bi-directional Track. In J. Liu, W. Li, X. Geng, K. Zhang, H. Ji, & K. Li (Eds.), The Proceedings of 2024 International Conference on Artificial Intelligence and Autonomous Transportation - Volume VI (pp. 244-251). (Lecture Notes in Electrical Engineering; Vol. 1394). Springer. https://doi.org/10.1007/978-981-96-3977-9_27

Wu, Wenxing ; Xun, Jing ; Liu, Xiaoyu et al. / An Integrated Model of Train Timetable and Speed Profile for Single Bi-directional Track. The Proceedings of 2024 International Conference on Artificial Intelligence and Autonomous Transportation - Volume VI. editor / Jun Liu ; Wang Li ; Xiongfei Geng ; Ke Zhang ; Honghai Ji ; Kailong Li. Springer, 2025. pp. 244-251 (Lecture Notes in Electrical Engineering).

@inproceedings{d3987d9e2c0c4176b5457cba27965151,

title = "An Integrated Model of Train Timetable and Speed Profile for Single Bi-directional Track",

abstract = "In this paper, we consider the integrated model of train timetable and speed profile for a single bi-directional track. This problem aims to schedule train passes along single track from opposite directions to avoid conflicts. It is assumed that there are different types of stations along the track, and trains can only pass each other simultaneously at stations that have sidings. Focusing on the operation scenario, we propose an integrated model of train timetable and speed profile optimization. To address the nonlinear constraints generated by the meeting conflicts in the single bi-directional operation, the Big-M method is used to transform the constraints into linear constraints incorporating binary integer variables such as meeting and train priority. Thus, a mixed integer linear programming (MILP) model is constructed, which can be solved using the Gurobi solver. The model is formulated with two objective functions: one aims to minimize the time deviation of trains running in pairs considering passenger satisfaction, and the other is to minimize the total train travel time. The proposed model is applied to solve the problem based on a single-line urban railway and the feasibility of the model is verified. The results show that the total train travel time is effectively reduced by 29.8%.",

keywords = "Bi-directional Track, Integrated Model, Timetable Scheduling",

author = "Wenxing Wu and Jing Xun and Xiaoyu Liu and Minxue Fu",

note = "Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.; International Conference on Artificial Intelligence and Autonomous Transportation, AIAT 2024 ; Conference date: 06-12-2024 Through 08-12-2024",

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doi = "10.1007/978-981-96-3977-9_27",

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Wu, W, Xun, J, Liu, X & Fu, M 2025, An Integrated Model of Train Timetable and Speed Profile for Single Bi-directional Track. in J Liu, W Li, X Geng, K Zhang, H Ji & K Li (eds), The Proceedings of 2024 International Conference on Artificial Intelligence and Autonomous Transportation - Volume VI. Lecture Notes in Electrical Engineering, vol. 1394, Springer, pp. 244-251, International Conference on Artificial Intelligence and Autonomous Transportation, AIAT 2024, Beijing, China, 6/12/24. https://doi.org/10.1007/978-981-96-3977-9_27

An Integrated Model of Train Timetable and Speed Profile for Single Bi-directional Track. / Wu, Wenxing; Xun, Jing; Liu, Xiaoyu et al.
The Proceedings of 2024 International Conference on Artificial Intelligence and Autonomous Transportation - Volume VI. ed. / Jun Liu; Wang Li; Xiongfei Geng; Ke Zhang; Honghai Ji; Kailong Li. Springer, 2025. p. 244-251 (Lecture Notes in Electrical Engineering; Vol. 1394).

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

TY - GEN

T1 - An Integrated Model of Train Timetable and Speed Profile for Single Bi-directional Track

AU - Wu, Wenxing

AU - Xun, Jing

AU - Liu, Xiaoyu

AU - Fu, Minxue

N1 - Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

PY - 2025

Y1 - 2025

N2 - In this paper, we consider the integrated model of train timetable and speed profile for a single bi-directional track. This problem aims to schedule train passes along single track from opposite directions to avoid conflicts. It is assumed that there are different types of stations along the track, and trains can only pass each other simultaneously at stations that have sidings. Focusing on the operation scenario, we propose an integrated model of train timetable and speed profile optimization. To address the nonlinear constraints generated by the meeting conflicts in the single bi-directional operation, the Big-M method is used to transform the constraints into linear constraints incorporating binary integer variables such as meeting and train priority. Thus, a mixed integer linear programming (MILP) model is constructed, which can be solved using the Gurobi solver. The model is formulated with two objective functions: one aims to minimize the time deviation of trains running in pairs considering passenger satisfaction, and the other is to minimize the total train travel time. The proposed model is applied to solve the problem based on a single-line urban railway and the feasibility of the model is verified. The results show that the total train travel time is effectively reduced by 29.8%.

AB - In this paper, we consider the integrated model of train timetable and speed profile for a single bi-directional track. This problem aims to schedule train passes along single track from opposite directions to avoid conflicts. It is assumed that there are different types of stations along the track, and trains can only pass each other simultaneously at stations that have sidings. Focusing on the operation scenario, we propose an integrated model of train timetable and speed profile optimization. To address the nonlinear constraints generated by the meeting conflicts in the single bi-directional operation, the Big-M method is used to transform the constraints into linear constraints incorporating binary integer variables such as meeting and train priority. Thus, a mixed integer linear programming (MILP) model is constructed, which can be solved using the Gurobi solver. The model is formulated with two objective functions: one aims to minimize the time deviation of trains running in pairs considering passenger satisfaction, and the other is to minimize the total train travel time. The proposed model is applied to solve the problem based on a single-line urban railway and the feasibility of the model is verified. The results show that the total train travel time is effectively reduced by 29.8%.

KW - Bi-directional Track

KW - Integrated Model

KW - Timetable Scheduling

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DO - 10.1007/978-981-96-3977-9_27

M3 - Conference contribution

AN - SCOPUS:105002556490

SN - 978-981-96-3976-2

T3 - Lecture Notes in Electrical Engineering

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BT - The Proceedings of 2024 International Conference on Artificial Intelligence and Autonomous Transportation - Volume VI

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A2 - Li, Wang

A2 - Geng, Xiongfei

A2 - Zhang, Ke

A2 - Ji, Honghai

A2 - Li, Kailong

PB - Springer

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ER -

Wu W, Xun J, Liu X, Fu M. An Integrated Model of Train Timetable and Speed Profile for Single Bi-directional Track. In Liu J, Li W, Geng X, Zhang K, Ji H, Li K, editors, The Proceedings of 2024 International Conference on Artificial Intelligence and Autonomous Transportation - Volume VI. Springer. 2025. p. 244-251. (Lecture Notes in Electrical Engineering). doi: 10.1007/978-981-96-3977-9_27

An Integrated Model of Train Timetable and Speed Profile for Single Bi-directional Track

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Keywords

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