Estimating collision probabilities for trains on railroad stations based on a Poisson model

We consider the problem of estimating the probability of collision between shunting trains and passenger trains on a railroad station. We assume that the flow of shunting trains is Poisson for every turnout switch on which side collisions are possible. The data for computations include the station's topology, timetable of passenger trains, and possible routes of their passing through the station together with the intensities of shunting trains moving through nonisolated turnout switches where collisions are possible, and also mean values of train lengths and their velocities. The proposed mathematical model of train motion can be regarded as a first approximation in modeling the collision process for trains on a railroad station. We also consider a real life example.