State-of-the-Art of Railway Operations Research

The paper discusses the current state of research concerning the modelling of stochastic train operations in order to optimise the use of capacity by means of analytical methods and micro-simulation. Timetable quality is governed by precise running and realistic recovery times, as well as optimal headway and buffer times. Analytic (queueing) models and micro-simulation are used for estimation of waiting times, while combinatorial models and stability analysis by means of max-plus algebra technique are suitable for network timetable optimisation. Operations quality can be modeled by the estimation of (admitted) queue length and micro-simulation. A recently developed probabilistic model for the estimation of delay propagation in stations and junctions based on the stochastic variation of track occupancy times depending on conditional probability distributions of hinder by headway constraints and route conflicts is presented, while stochastic timetable optimisation may help to determine a more efficient distribution of running time margins and to increase punctuality in large networks.