Scheduling trains on a single railway line is an issue in it own right, and is a building block for scheduling trains in railway networks. A local, state dependent, travel advance strategy combined with a discrete event model of a railway line represent a more efficient way of approaching the scheduling problem than nonlinear programming approaches used in the past. The approach also eliminates a deficiency of nonlinear programming formulations, which produce a programmed schedule that cannot be applied if any perturbation in train operations occurs.