The real-time railway traffic management problem occurs when the trains get off schedule due to different traffic perturbations. In this case, they must be rerouted, reordered, and rescheduled to resolve the possible conflicts. Nowadays, this problem is usually handled by human dispatchers. There are lots of algorithms aiming to support human dispatchers in making an optimal decision that minimizes delays. However, due to the real-time nature of the problem, the response time of these algorithms is crucial. In this paper, the runtime performance of a state-of-the-art mixed-integer linear programming model is analyzed in different solvers. The analysis is performed via Monte Carlo simulation, generating various realistic scenarios in an infrastructure model of a Hungarian railway control area.