An Integrated Mathematical Model for Ensuring Train Traffic Safety in a Centralised Dispatching System Based on Control Theory, Based on Finite-State Automata

This paper presents an integrated mathematical model to improve the safety and operational efficiency of train traffic in centralised railway dispatching systems. The proposed approach combines the alternative graph model with a Mealy automaton to synchronously address route planning, delay minimisation, and strict compliance with safety requirements. Formal control theory based on finite-state automata is employed to describe routing logic and signal control through state transitions, while the alternative graph model represents scheduling constraints and resource conflicts. To enhance real-time adaptability, a tabu search algorithm is implemented for train schedule optimisation, enabling dynamic rescheduling under changing operational conditions. The mathematical formulation incorporates blocking time parameters, a system of discrete constraints, and automaton-based safety conditions governing train movements and route authorisation. The integrated model explicitly formalises the processes of block section occupation and release, ensuring consistency between control logic and scheduling decisions. Practical testing and computational experiments demonstrate that the proposed approach effectively reduces train delays, improves the reliability of dispatch control, and increases system resilience to dynamic disturbances. The results confirm that the developed model can be implemented within existing centralised dispatching infrastructures without requiring a complete system overhaul. Overall, the proposed framework expands the functional capabilities of centralised dispatch systems by enabling efficient schedule generation, minimising the propagation of delays, and ensuring reliable command exchange between central control posts and field-level railway infrastructure.

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