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Worst-case execution time analysis of multi-threaded software is still a challenge. This comes mainly from the fact that the number of thread interleavings grows exponentially in the number of threads and that synchronization has to be taken into account. In particular, a suitable graph based model has been missing. The idea that thread interleavings can be studied with a matrix calculus is a novel approach in this research area. Our sparse matrix representations of the program are manipulated using Kronecker algebra. The resulting graph represents the multi-threaded program and plays a similar role for concurrent systems as control flow graphs do for sequential programs. Thus a suitable graph model for timing analysis of multi-threaded software has been set up. Due to synchronization it turns out that often only very small parts of the resulting graph are actually needed, whereas the rest is unreachable. A lazy implementation of the matrix operations ensures that the unreachable parts are never calculated. This speeds up processing significantly and shows that our approach is very promising.