# Optimisation and analysis of railway timetables under consideration of uncertainties

• Optimierung und Analyse von Eisenbahnfahrplänen unter Berücksichtigung von Unsicherheiten

Haehn, Rebecca; Ábrahám, Erika (Thesis advisor); Nießen, Nils (Thesis advisor); Remke, Anne (Thesis advisor)

Aachen : RWTH Aachen University (2022)
Dissertation / PhD Thesis

Dissertation, RWTH Aachen University, 2022

Abstract

Railway systems are complex systems that are strongly affected by uncertainties like weather, technical problems, or demand. Despite these uncertainties, railway systems need to function efficiently. In general this thesis aims to advance the consideration of uncertainty in the railway planning process to optimally utilise the existing railway network capacity. The focus in this thesis is on the delays that result from the uncertain environmental conditions. To consider these in the railway planning process, a symbolic simulation algorithm is proposed to examine the delay propagation in a railway network for a given timetable. This allows to estimate the timetable robustness and the network capacity. Several performance indicators for railway timetables that can be evaluated using the symbolic simulation are discussed. To optimally utilise the network capacity also an algorithm to schedule additional freight trains is presented. The main contributions of this thesis are the following: 1. An algorithm to schedule additional freight trains is presented, to utilise the remaining network capacity without disturbing an existing timetable. 2. A novel symbolic simulation algorithm for railway timetables is proposed. The algorithm receives as input a railway infrastructure model, a corresponding timetable, and discrete primary delay distributions. It computes iteratively over time the delay propagation in the given railway system. Symbolic expressions are used to represent multiple possible values for the primary delays. This enables to simulate all discrete primary delay combinations at once. 3. An implementation of these algorithms is provided in C++ and evaluated on some real-world railway infrastructure networks and timetables based on the German railway system. The applicability and functionality of the algorithms is demonstrated. The proposed symbolic simulation algorithm is aimed to be a helpful addition to existing railway timetable simulations, which are mostly based on Monte Carlo simulation. In contrast to those, the symbolic approach stores the history of specific train states, which can be used to explain the occurring delays. In addition, the results of the symbolic simulation are exact with respect to the input model and the discrete primary delay distributions.