M. Volcic, J. Blieberger, A. Schöbel:

"Kronecker Algebra and its Broad Applications in Railway Systems";

Talk: EURO-ZEL 2013, Zilina; 2013-06-04 - 2013-06-05; in: "EURO-ZEL 2013: Recent Challenges for European Railways", University of Zilina, Zilina (2013), ISBN: 978-80-263-0380-0; 275 - 282.

Kronecker algebra consists of Kronecker product and Kronecker sum. It can be used

to model systems consisting of several actors and a number of limited resources. In particular,

it can be used to model railway systems consisting of trains, their routes in the system, and

track sections building up the railway infrastructure. In this paper we will show several

applications of Kronecker algebra in the railway domain. In particular, we consider: deadlock

analysis [1], travel time analysis [2], and energy analysis. Integrating all three types of analysis

within one single type of Kronecker-based analysis is rather simple and can be done very

efficiently. Our implementation is very efficient both in time and space. Kronecker algebra

operations can easily be parallelized and thus our implementation can fully take advantage of

today's multi-core computer architecture. In addition, our implementation shows that adding

constraints (connections, overtaking ...) to the problem improves execution time. In fact, a

harder problem is easier to solve.

Kronecker algebra, deadlock analysis, travel time analysis, energy analysis

Project Head Johann Blieberger:

Energiebedarfsoptimierung durch Verknüpfung der Betriebsführung des Bahnverkehrs mit der Steuerung des Bahnstromnetzes

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