Timetable compression using max-plus automata applied to large railway networks

Demand for railway transportation keeps on growing. Therefore, a thorough understanding of the capacity of railway networks is crucial. In this paper, the well-known compression method based on max-plus algebra is extended. A number of challenges are addressed to apply this compression method to large and complex networks, such as the one considered in this paper. Some trains have to be split artificially, while keeping the parts together during the compression. The trains should also be ordered explicitly, since there is no part of the infrastructure used by all trains. The results in this paper indicate that it is possible to thoroughly analyse the capacity by the adjusted compression method for large and complex networks, but the results should be interpreted with care. The results show, for instance, that the capacity occupation heavily depends on the size of the network that is considered and that it is not easy to give a clear, practical interpretation of the capacity occupation. Nevertheless, the method allowed to determine a number of critical paths and, even more importantly, a number of critical resources in the zones considered.