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Railway networks have become increasingly important in recent times,especially to move freight and public transportation from road traffic andplanes to more environmentally friendly trains. Since expanding the globalrailway network is time and resource-consuming, maximizing the rail capacity onthe existing infrastructure is desirable. However, simply running more trainsis infeasible as certain constraints enforced by the train control system mustbe satisfied. The capacity of a network depends (amongst others) on thedistance between trains allowed by this safety system. While most signalingsystems rely on fixed blocks defined by costly hardware, new specificationsprovided by Level 2 with Hybrid Train Detection of the European Train ControlSystem (ETCS L2 HTD), formerly known as ETCS Hybrid Level 3, allow the usage ofvirtual subsections. This additional degree of freedom allows for shorter trainfollowing times and, thus, more trains on existing railway tracks. On the otherhand, new design tasks arise on which automated methods might be helpful fordesigners of modern railway networks. However, although first approaches existthat solve design problems arising within ETCS L2 HTD, neither formaldescriptions nor results on the computational complexity of the correspondingdesign tasks exist. In this paper, we fill this gap by providing a formaldescription of design tasks for ETCS L2 HTD and proof that these tasks areNP-complete or NP-hard, respectively. By that, we are providing a solid basisfor the future development of methods to solve those tasks, which will beintegrated into the Munich Train Control Toolkit available open-source onGitHub at https://github.com/cda-tum/mtct.

Design Tasks and Their Complexity for the European Train Control System with Hybrid Train Detection