The real time railway traffic management seeks for the train routing and scheduling that minimize delays after an unexpected event perturbs the operations. In this paper, we propose a mixed integer linear programming formulation for tackling this problem, modeling the infrastructure in terms of track-circuits, which are the basic components for train detection. This formulation considers all possible alternatives for train rerouting in the infrastructure and all rescheduling alternatives for trains along these routes. To the best of our knowledge, we present the first formulation that solves this problem to optimality. We tested the proposed formulation on real perturbation instances representing traffic in a control area including the Lille Flandres station (France), achieving very good performance in terms of computation time.