Seminar on stochastic max-plus algebra by Prof. Rob Goverde (TU Delft, Holland)

Welcome to this talk by Prof. Rob Goverde from Delft University of Technology!Railway infrastructure capacity analysis using stochastic max-plus algebra

Abstract:Max-plus algebra is a very efficient tool to model and analyse periodic railway timetables and their infrastructure consumption, both in a microscopic and a macroscopic way. In particular, the eigenvalue problem in max-plus algebra relates to the UIC timetable compression method of capacity consumption calculations when the timetable is modelled microscopically with blocking times. In a max-plus setting this capacity method is easily generalized to networks including connections at stations. This presentation shows how these max-plus models can be analysed efficiently in the general-order form, without first having to translate the model to a pure first-order model x(k)=Ax(k-1). The max-plus models can be generalized to stochastic systems, where the process times follow arbitrary stochastic distributions. In this case, the mean cycle time can be computed as a measure of capacity consumption showing the effect of variations in the process times over deterministic values. The algorithms apply to large-scale systems using a sparse matrix representation of the max-plus models.

Bio of the speaker:

Rob Goverde is Assistant Professor at Delft University of Technology. He received an MSc in Mathematics from Utrecht University, a Master of Technological Design (MTD) in Mathematical Modelling and Decision Support from Delft University of Technology, and a PhD from Delft University of Technology for his PhD thesis 'Punctuality of railway operations and timetable stability analysis'. He has 16 years of experience in modelling, analysis, planning, and control of railway operations, and was responsible for the development of the PETER tool for stability analysis of railway timetables, and several tools for process mining of train detection data. Rob has published over 70 articles in refereed journals, books, and conference proceedings.

Date/time: 
Tuesday, May 8, 2012, 17:00