At peak hours, railway timetables extensively exploit the infrastructure for accommodating traffic. Hence, the occurrence of unexpected events, even of apparently negligible entity, may cause a relevant deviation with respect to the scheduled timetable. If a train is delayed due to an unexpected event, conflicts may emerge, multiple trains may claim the same track section concurrently : in this case trains may have to stop or slow-down for ensuring safety and delay propagation may emerge. The selection of the train routing and scheduling for minimizing delay propagation has been formalized as the real-time Railway Traffic Management Problem (rtRTMP). In this study, we propose a fixed-speed mixed-integer linear programming formulation for optimally solving the rtRTMP. We model the infrastructure in terms of track-circuits, which are the basic components for train detection. In a thorough experimental analysis we quantify the improvement, in terms of reduction of delay propagation, that can be achieved by allowing the platform assignment to be different from the one defined in the timetable.