Robust Timetabling for Railway Systems

Academic year2018-2019                                                                
Day(s)Monday and Thursday
Number of meetings        14
Dates of all meetings4, 7, 11, 14, 18, 21, 25, 28 February, 4, 7, 11, 14, 18, 21 March 2019
LocationVrije Universiteit, De Boelelaan 1105, 1081 HV Amsterdam
RoomBV-0H36 (BelleVUe building no 1091 at this map) exception: Thursday14 February HG-02A36 (2nd floor A wing main building)
LecturersLecturer and coordinator
  • Prof. dr. Bernd Heidergott, Dept. Econometrics VU, email:
Guest lecturer on railway planning tool PETER
  • Dr. Rob Goverde, Civiele Techniek en Geowetenschappen, TU Delft, email:

Course description

This course is also open for 1st years students Computer Science, Business Analytics, Mathematics, Econometrics & Operations Research

The railways are an essential part of the Dutch public transportation infrastructure. Despite the effort in time and money invested into the railway systems, the system is perceived as not operating at the desired level of reliability. So, why is it so hard to come up with a reliable timetable for the railways? This course will delve into the problem of designing periodic timetables for railways. Surprisingly enough an exotic algebra from mathematics helps tackling the problem. We will enter the realm of this exotic algebra, where, for instance, it is true that 3+7=7 and 3 x7=10, and we see how this can be turned into a natural language for the analysis trains. Though trains will be the main topic of our lectures we will also present surprising applications of the technique for development of rescue robots.

The course is self-contained as the mathematical theory used in this course is based on an exotic algebra, which levels the advantage students with a (strong) mathematical background may have. While having timetable design as guiding problem, we will have ample opportunity to discuss and understand some of the fundamental philosophical and logical problems of the foundation mathematics: This is a course about mathematics rather than a mathematics course.

Relevance of the course
In a world that is becoming increasingly quantitative, mathematics belongs to the core of our cultural heritage more than ever. Experiencing the full cycle of the use of mathematics (from theoretical and fundamental questions to an application, and from the application to new questions triggering the development of new theory) will provide a deep understanding of the mutual influence between the mathematical/quantitative-academic paradigm and the real world.

Attainment targets/learning outcomes

  1. Ability to work with non-standard concepts (such as "strange" algebras)
  2. Ability to reflect on and discuss formal mathematical concepts ("abstract can be very real")
  3. Developing an understanding on how real life problems influence mathematical theory building
  4. Understanding the process of abstraction in theory building
  5. Ability to communicate an abstract mathematical idea and to present findings of self-study

Practical Information:

This course has the following components

  • 5 x global lectures
  • 6 x interactive group sessions
  • 1 x specific lecture on robotics (and an excursion to the Delft Center for Systems and Control)
  • 1 x specific lecture on actual railway planning
  • 1 x essay (group effort)
  • 1 x exam (individual effort)

Study materials:

  • Francios Baccelli, Guy Cohen, Geert Jan Olsder and Jean-Pierre Quadrat: Synchronization and Linearity. Series in Probability and Mathematical Statistics, Wiley, (1992)
  • Bernd Heidergott: Max-Plus linear Stochastic Systems and Perturbation Analysis
  • The International Series of Discrete Event Systems 15, Springer, (2007).
  • Bernd Heidergott, Geert Jan Olsder and Jacob van der Woude: Max Plus at Work.
  • Princeton Series in Applied Mathematics, Princeton University Press, (2006).
  • D. Huisman, L.G. Kroon, R.M. Lentink and M.J.C.M. Vromans , “Operations Research in passenger railway transportation”, Statistica Neerlandica 59 (2005), pp. 467-497
  • Additional literature depending on the students’ interest and the assignments.

Assessment method(s):

Participation in the preparation, presentation and report on chosen self-study topic (group effort, 50%), and written exam (individual, 50 %).

Remarks: maximum amount of students is 15. Basic knowledge of mathematics is required.