<span class="word">An <span class="word"><span class="changedDisabled">Integrated <span class="word"><span class="changedDisabled">Mathematical <span class="word"><span class="changedDisabled">Model <span class="word">for <span class="word"><span class="changedDisabled">Ensuring <span class="word"><span class="changedDisabled">Train <span class="word"><span class="changedDisabled">Traffic <span class="word"><span class="changedDisabled">Safety <span class="word">in <span class="word">a <span class="word"><span class="changedDisabled">Centralized <span class="word"><span class="changedDisabled">Dispatching <span class="word"><span class="changedDisabled">System <span class="word"><span class="changedDisabled">Based <span class="word">on <span class="word"><span class="changedDisabled">Automata <span class="word"><span class="changedDisabled">Theory

This paper presents an integrated mathematical model aimed at improving the safety and operational efficiency of train traffic in centralized railway dispatching systems. The proposed approach combines the alternative graph model with a Mealy automaton to synchronously address route planning, delay minimization, and strict compliance with safety requirements. Formal automata theory 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 optimization, 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 authorization. The integrated model explicitly formalizes 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 centralized dispatching infrastructures without requiring a complete system overhaul. Overall, the proposed framework expands the functional capabilities of centralized dispatch systems by enabling efficient schedule generation, minimizing the propagation of delays, and ensuring reliable command exchange between central control posts and field-level railway infrastructure.