  The railway timetables are designed in an optimal manner to maximize the
capacity usage of the infrastructure concerning different objectives besides
avoiding conflicts. The real-time railway traffic management problem occurs
when the pre-planned timetable cannot be fulfilled due to various disturbances;
therefore, the trains must be rerouted, reordered, and rescheduled. Optimizing
the real-time railway traffic management aims to resolve the conflicts
minimizing the delay propagation or even the energy consumption. In this paper,
the existing mixed-integer linear programming optimization models are extended
considering a safety-relevant issue of railway traffic management, the
overlaps. However, solving the resulting model can be time-consuming in complex
control areas and traffic situations involving many trains. Therefore, we
propose different runtime efficient multi-stage heuristic models by decomposing
the original problem. The impact of the model decomposition is investigated
mathematically and experimentally in different rail networks and various
simulated traffic scenarios concerning the objective value and the
computational demand of the optimization. Besides providing a more realistic
solution for the traffic management problem, the proposed multi-stage models
significantly decrease the optimization runtime.
