Scientific paper ID 842 : 2013/3

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.