Unexpected events may perturb operations and generate conflicts that must be addressed promptly to limit delay propagation and other negative impacts on the network. The real-time railway traffic management problem deals with disruptions in railway networks, including tracks, junctions and stations. When they happen in station areas, new decisions involving train platforming, rerouting, ordering and timing must be made in real time. This paper explores a mesoscopic approach to deal with disruptions at rail stations. A mathematical programming-based model is proposed to determine re-routing and re-scheduling decisions for railway traffic in a station area. The key steps of the approach, which simulate what happens in real-time traffic management, are: i) an initial off-line preprocessing stage of the set of feasible routes originally planned, ii) a second preprocessing stage which analyses the disruption and sets the necessary parameters for the last step iii), which consists of an integer programming model that seeks solutions which minimise deviations from planned train schedules and assigns new and appropriate platforms (if necessary). Computational experiments show that realistic instances can be solved near to optimality using CPLEX in very short times. This allows to consider this methodology for solving real time traffic management problems.