Original scientific paper

https://doi.org/10.17559/TV-20131107130926

Application of Kronecker algebra in railway operation

Mark Stefan (Volcic) ; Austrian Institute of Technology GmbH, Giefinggasse 2, A-1210 Vienna, Austria
Johann Blieberger ; TU Wien, Institute of Computer Aided Automation Treitlstraße 1-3, A-1040 Vienna, Austria
Andreas Schöbel ; OpenTrack Railway Technology Ltd., Kaasgrabengasse 19/8, A-1190 Vienna, Austria / Karlsplatz 13, 1040 Vienna, Austria

Abstract

We present a methodology for dispatching trains which prevents deadlocks and includes possible limitation of the available energy provided by the power supply. Our approach applies Kronecker algebra to manipulate matrices. Generally blocking of trains occurs due to a lack of some resource which can be either infrastructure or energy. Our method can also be used to calculate travel times in a rough way. Thereby blocking time is included in the calculated travel time. To model the movements of trains in a railway system we use graphs, which are represented by adjacency matrices. We assume that the edges in a graph are labelled by elements of a semiring. Usually two or more distinct train route graphs refer to the same track section to model synchronization. Our approach can be used to model a complex railway system. For example, if additional trains have to be scheduled, power stations or interconnection lines fail or are not available due to maintenance, our model can be used to calculate the impact on the travel times of the trains in the system.

Keywords

deadlock; dispatching; energy-aware; Kronecker algebra; travel time

Hrčak ID:

174696

URI

https://hrcak.srce.hr/174696

Publication date:

10.2.2017.

Article data in other languages: croatian

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