SWZ  >  
Research Projects  >  
Delays in public transport networks

Analysis of source delays and their propagation in public transport networks - modeling, simulation and optimization of a stochastic network

The goal of this project is to develop and analyze models describing the origin and propagation of delays in networks. We furthermore will discuss which measures are suitable for increasing the punctuality and reliability of public transport, identify weak points of a public transport system and develop methods for robust and delay-resistant planning.

To this end we will use analytical tools and simulation approaches. As application we focus on railway transportation; however, the methods to be developed will be general enough to be applied also in other public transport domains such as bus or air transportation.

Motivation and technical background

The (economic) impacts of delays are, among others, dissatisfaction of the passengers, decrease of productivity due to bottlenecks and scarce resources, increased energy consumption and negative effects on the environment.

Reasons for source delays can be weather conditions, technical failures, time consuming boarding or de-boarding, accidents or maintenance. Transfer activities of the passengers and limited capacity of the track system are the main reasons why source delays propagate through the network. (Note that in  our project we do not deal with large disruptions and disaster management.)


The goal of our project is to study source delays and their propagation and to develop measures to make public transportation delay-resistant. These may be additional buffer times in the timetable, development of  appropriate delay management strategies (e.g. fixed waiting time rules or new rules of thumb), considering limited capacity already at the stage of line planning and increasing the capacity through an extension of the infrastructure. This means we will look at the strategic planning phase (when designing line plans), at the tactical planning phase (when designing timetables) and at the operational phase (in delay management).

For studying these questions there are different approaches possible. One possibility is to use methods of integer programming as it is already done for timetabling. Existing models have to be extended to make the resulting timetables more robust and reliable, and to include delay management aspects already in the planning phase. Such approaches will be developed in the working group of Prof. Schöbel at the University of Göttingen.

In the working groups of Prof. Hanschke and Prof. Kolonko at the Clausthal University of Technology the focus will be on a stochastic modelling. Suitable families of probability distributions will be used to model the source delays and their propagation and accumulation. This analytical approach will be compared to a purely simulative model of the network. Genetic algorithms will be used to obtain robust timetables.

Within the project, the strengths of both approaches should be analyzed and used in a combined method which will bring new theoretical insight and lead to tools which can help improving real-world public transportation systems.

Involved Scientists

Prof. Dr. Anita Schöbel (Stellvertretende Vorstandsvorsitzende)

Research group Optimization
Institute for Numerical and Applied Mathematics
University of Göttingen

Room 114, Lotzestraße 16-18, 37083 Göttingen
E-Mail: schoebel@math.uni-goettingen.de
Phone: +49 551 39-12237
Fax: +49 551 39-33944

Prof. Dr. Michael Kolonko

Research group Stochastische Optimierung
Institute of Mathematics
Clausthal University of Technology

Room 114, Erzstraße 1, 38678 Clausthal-Zellerfeld
E-Mail: michael.kolonko@tu-clausthal.de
Phone: +49 5323 72-2410
Fax: +49 5323 72-4876

Prof. Dr. Thomas Hanschke

Research group Stochastische Modelle in den Ingenieurwissenschaften
Institute of Mathematics
Clausthal University of Technology

Raum 325, Arnold-Sommerfeld-Straße 6, 38678 Clausthal-Zellerfeld
E-Mail: hanschke@math.tu-clausthal.de
Phone: +49 5323 72-5210
Fax: +49 5323 72-2304

Publication list