A fast and general algebraic approach to Railway Interlocking System across all train stations

Antonio Hernando; José Luis Galán-García; Gabriel Aguilera-Venegas; Antonio Hernando; José Luis Galán-García; Gabriel Aguilera-Venegas

doi:10.3934/math.2024373

AIMS Mathematics

2024, Volume 9, Issue 3: 7673-7710. doi: 10.3934/math.2024373

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A fast and general algebraic approach to Railway Interlocking System across all train stations

1.
Depto. de Sistemas Informáticos, E.T.S.I. de Sistemas Informáticos, Universidad Politécnica de Madrid, Madrid, Spain
2.
Departamento de Matemática Aplicada, Escuela de Ingenierías Industriales, Universidad de Málaga, Málaga, Spain

Received: 12 October 2023 Revised: 06 February 2024 Accepted: 19 February 2024 Published: 22 February 2024
MSC : 13P05

Railway interlocking systems are crucial safety components in rail transportation, designed to prevent train collisions by regulating switch positions and signal indications. These systems delineate potential train movements within a railway station by connecting sections into routes, which are further divided into blocks. To ensure safety, the system prohibits the simultaneous allocation of the same block or intersecting routes to multiple trains. In this study, we characterize the 'interlocking problem' as a safety verification task for a single real-time station configuration, rather than a 'command and control' function. This is a matter of verification, not solution, typically managed by an interlocking system that receives movement authority requests. Over the years, we have developed various algebraic models to address this issue, suggesting the potential use of computer algebra systems in implementing interlocking systems. However, some of these models exhibit limitations. In this paper, we propose a novel algebraic model for decision-making in railway interlocking systems that overcomes the limitations of previous approaches, making it suitable for large railway stations. Our primary objective is to offer a mathematical solution to interlocking problems in linear time, which our approach accomplishes.
- railway interlocking system,
- computer algebra,
- decision making,
- commutative algebra
Citation: Antonio Hernando, José Luis Galán-García, Gabriel Aguilera-Venegas. A fast and general algebraic approach to Railway Interlocking System across all train stations[J]. AIMS Mathematics, 2024, 9(3): 7673-7710. doi: 10.3934/math.2024373

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Abstract

Railway interlocking systems are crucial safety components in rail transportation, designed to prevent train collisions by regulating switch positions and signal indications. These systems delineate potential train movements within a railway station by connecting sections into routes, which are further divided into blocks. To ensure safety, the system prohibits the simultaneous allocation of the same block or intersecting routes to multiple trains. In this study, we characterize the 'interlocking problem' as a safety verification task for a single real-time station configuration, rather than a 'command and control' function. This is a matter of verification, not solution, typically managed by an interlocking system that receives movement authority requests. Over the years, we have developed various algebraic models to address this issue, suggesting the potential use of computer algebra systems in implementing interlocking systems. However, some of these models exhibit limitations. In this paper, we propose a novel algebraic model for decision-making in railway interlocking systems that overcomes the limitations of previous approaches, making it suitable for large railway stations. Our primary objective is to offer a mathematical solution to interlocking problems in linear time, which our approach accomplishes.

References

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