@MASTERSTHESIS\{IMM2005-03988,
    author       = "M. A. Hofman and L. F. Madsen",
    title        = "Robustness in train scheduling",
    year         = "2005",
    school       = "Informatics and Mathematical Modelling, Technical University of Denmark, {DTU}",
    address      = "Richard Petersens Plads, Building 321, {DK-}2800 Kgs. Lyngby",
    type         = "",
    note         = "Supervised by Assoc. Prof. Jesper Larsen",
    url          = "http://www2.compute.dtu.dk/pubdb/pubs/3988-full.html",
    abstract     = "In this project robustness in train scheduling is examined. The project is conducted for {DSB} {S-}tog because the current situation is in uenced by a large amount of disturbances which cause delays and low regularity. The aim of this project is to help {DSB} {S-}tog in the development of more robust timetables. The robustness analysis is performed by comparing different already existing and new timetables using simulation. The approach of simulation of timetables is new in connection with {DSB} {S-}tog.

A generic model of the {S-}train network is modelled and implemented using the simulation tool Arena. The model can simulate all arrivals and departures of the trains in the entire network during a day. The model includes an implementation of three different recovery methods where trains are turned at a station prior to the end station, replaced at the central station or entire lines are cancelled in order to eliminate delays.

Distributions of the delays occurring at the stations in the {S-}train network are generated from historical data for the experiments. A number of experiments are conducted and investigated. Experiments include examination of the effect of the different recovery methods, investigation of the consequences of delays and comparison of how different features in the timetables affect the robustness.

The results from the simulation show that generally the robustness decreases as the number of lines in the timetable increases. Furthermore it is proven that the number of lines is not the only important aspect when developing robust timetables. Buffer times at the terminal stations have a significant impact on the robustness and it is also shown that the amount of necessary buffer needed to create a robust timetable is limited. The allocation of buffer times is important since all lines should be able to recover using buffer times. Furthermore line structure also turns out to have an impact on the robustness.

Finally two totally new timetables with new line structures are developed in this project. They both generally achieve an improved robustness."
}