2. Literature review

A substantial volume of literature is devoted to study of the train delays effect on the railway functioning. Deterministic models for primary and knock-on delays description were proposed in [1, 2]. These models based on the application of graph theory allow adjust the train traffic schedule. However, such approach considering the different characteristics of train traffic (e.g., travel and dwell times, headways, etc.) as deterministic values does not take into account the uncertainties that arise in reality.

Stochastic modeling takes the influence of random factors (e.g., see [3–8]) into account. Authors of [7] determine a probabilistic distribution of the arrival times. The problem of finding a distribution of arrival train delays is examined in [8]. It should be noted that in these papers, special cases of primary delay distribution are considered. It is supposed in [8] that the random duration of the primary delay corresponds to some generalization of the exponential law. The paper [7] employs discretization of the delay distribution.

Some of the researchers have analyzed statistical data on deviations of the train arrival times from the planned ones. In particular, the papers [9–11] show that scattering of these deviations correspond to the exponential distribution.
