Stochastic Modeling of Train Delays Formation

Two stochastic models of train interaction are considered in the paper. These models are designed to study the process of calculation the arrival deviation probability density function. The stochastic models allow you to receive an adequate forecast the development of traffic situation taking random fluctuations of the train run trajectory into account. The paper proves the equivalence of two train traffic models that reflect the mechanism of formation the arrival time distribution. Both models take the scattering of train departure deviations into account. The first type model describes the result of the run time random nature, while the second model reflects the impact of short-term unplanned train stops. The study also makes an attempt to outline the regularity of formation the standard and the abnormal arrival deviation distributions. The proposed models are verified by using the results of the historical data analysis obtained at the main railway line.