Stochastic process in railway traffic flow: Models, methods and implications

摘要

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, doublybounded 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).