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Railway interlocking systems and Gröbner bases

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  • Roanes-Lozano, Eugenio
  • Roanes-Macías, Eugenio
  • Laita, Luis M.

Abstract

Railway interlocking systems are designed to prevent conflicting actions (related to the position of switches and signals) during everyday railway exploitation. A decision model (independent from the topology of the station) based on the use of polynomial ideals and Gröbner bases is presented. This decision model can also be used to check whether a given section is accessible by a train located in another section or not. The fact that trains could occupy more than one section does not affect the model.

Suggested Citation

  • Roanes-Lozano, Eugenio & Roanes-Macías, Eugenio & Laita, Luis M., 2000. "Railway interlocking systems and Gröbner bases," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 51(5), pages 473-481.
    • Handle: RePEc:eee:matcom:v:51:y:2000:i:5:p:473-481
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    References listed on IDEAS

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    1. Roanes-Lozano, Eugenio & M. Laita, Luis, 1998. "An applicable topology-independent model for railway interlocking systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 45(1), pages 175-183.
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    Cited by:

    1. Roanes-Lozano, Eugenio & Laita, Luis M. & Roanes-Macías, Eugenio & Wester, Michael J. & Ruiz-Lozano, José Luis & Roncero, Carlos, 2009. "Evolution of railway network flexibility: The Spanish broad gauge case," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(8), pages 2317-2332.
    2. Zhou, Yonghua & Tao, Xin & Luan, Lei & Ning, Jingjie, 2018. "Revisiting the 7/23 train accident using computer reconstruction simulation for causation and prevention analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 148(C), pages 1-15.
    3. Roanes-Lozano, Eugenio & Roanes-Macı́as, Eugenio & Laita, Luis M., 2002. "A computer algebra approach to the design of routes and the study of their compatibility in a railway interlocking," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 58(3), pages 203-214.
    4. María Villalba-Orero & Eugenio Roanes-Lozano, 2021. "A Prototype of a Decision Support System for Equine Cardiovascular Diseases Diagnosis and Management," Mathematics, MDPI, vol. 9(20), pages 1-15, October.
    5. Xiangxian, Chen & Yulin, He & hai, Huang, 2011. "A component-based topology model for railway interlocking systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(9), pages 1892-1900.
    6. Roanes-Lozano, Eugenio & Hernando, Antonio & Alonso, Jose Antonio & Laita, Luis M., 2011. "A logic approach to decision taking in a railway interlocking system using Maple," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(1), pages 15-28.

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    1. Xiangxian, Chen & Yulin, He & hai, Huang, 2011. "A component-based topology model for railway interlocking systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(9), pages 1892-1900.
    2. Roanes-Lozano, Eugenio & Laita, Luis M. & Roanes-Macías, Eugenio & Wester, Michael J. & Ruiz-Lozano, José Luis & Roncero, Carlos, 2009. "Evolution of railway network flexibility: The Spanish broad gauge case," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(8), pages 2317-2332.
    3. Zhou, Yonghua & Tao, Xin & Luan, Lei & Ning, Jingjie, 2018. "Revisiting the 7/23 train accident using computer reconstruction simulation for causation and prevention analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 148(C), pages 1-15.
    4. Roanes-Lozano, Eugenio & Roanes-Macı́as, Eugenio & Laita, Luis M., 2002. "A computer algebra approach to the design of routes and the study of their compatibility in a railway interlocking," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 58(3), pages 203-214.
    5. Roanes-Lozano, Eugenio & Hernando, Antonio & Alonso, Jose Antonio & Laita, Luis M., 2011. "A logic approach to decision taking in a railway interlocking system using Maple," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(1), pages 15-28.

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