An improved equation model for the train movement

In this paper, a new term is introduced into the equation of train movement, which is about the influences of the safety stopping distance and stations on the motion of train, when there are many trains on the line. The aim is that the improved equation can well describe the motion of train under the moving block condition. In order to test the improved model, we use a simulation analysis approach to solve a simplified form of the improved equation model. In the simulations, we investigate the space–time diagram for the railway traffic flow and the trajectories of the train movement. The numerical simulation results demonstrate that the improved model can well describe the dynamic behaviour of the train movement under the moving block condition. Some complex phenomena of train movement can be well reproduced but more work is required for a full simulation of the general model.