We model railway traffic dynamics based on microscopic behavior of vehicles, i.e. speed and distance between vehicles. We consider domain dynamics (e.g. signalling system, kinematic equations) and additional components which are modelled as stochastic factors, affecting speed. Those latter model well the trajectories of railway vehicles observed in real life, representing the combined effect of human actions, track variations, resistances, control systems and actions. We propose multiple stochastic process models (i.e. Brownian motion, Ornstein-Uhlenbeck, doubly-bounded Cox-Ingersoll-Ross, and doubly mean-reverting Langevin equation) which extend the existing traffic flow theory models for cars towards railway traffic and its specific requirements and constraints. To the best of authors’ knowledge, this paper is the first work which considers stochastic components in order to model mathematically realistic railway traffic dynamics in line with the findings in roadway microscopic traffic behaviour modelling. Closed expressions of relevant characteristics for some stochastic process models have been derived. The behavior of the system has been simulated to derive macroscopic performance indicators and later compared with a deterministic model performance as a benchmark. The models can be useful to estimate the benefits introduced by automation in railways, including Automated Train Operation (ATO).

我们基于车辆的微观行为（即 车辆之间的速度和距离）对铁路交通动力学进行建模。我们考虑域动力学（例如 信号系统，运动学方程）和被建模为随机因素的其他组件，从而影响速度。后一种模型很好地模拟了现实生活中观察到的铁路车辆的轨迹，代表了人类行为，轨道变化，阻力，控制系统和行为的综合影响。我们提出了多种随机过程模型（即 布朗运动，Ornstein-Uhlenbeck，双重有界Cox-Ingersoll-Ross和双重均值回复Langevin方程）将现有的汽车交通流理论模型扩展到铁路交通及其特定要求和约束。据作者所知，本文是第一篇考虑随机因素的工作，目的是根据道路微观交通行为建模的发现，对数学上现实的铁路交通动力学进行建模。已经推导出了一些随机过程模型的相关特征的封闭表达式。已对系统的行为进行了仿真，以得出宏观性能指标，随后将其与确定性模型性能进行比较，以此作为基准。这些模型可用于估算铁路自动化带来的收益，