Railway networks have become increasingly important in recent times, especially to move freight and public transportation from road traffic and planes to more environmentally friendly trains. Since expanding the global railway network is time and resource consuming, maximizing the rail capacity on the existing infrastructure is desirable. However, simply running more trains is infeasible as certain constraints enforced by the train control system must be satisfied. The capacity of a network depends (amongst others) on the distance between trains allowed by this safety system. While most signaling systems rely on fixed blocks defined by costly hardware, new specifications provided by the ETCS Hybrid Level 3 (since recently also known as ETCS Level 2 with Hybrid Train Detection) allow the usage of virtual subsections. This additional degree of freedom allows for shorter train following times and, thus, more trains on existing railway tracks. On the other hand, new design tasks arise on which automated methods might be helpful for designers of modern railway networks. However, although first approaches exist that solve design problems arising within ETCS Hybrid Level 3, neither formal descriptions nor results on the computational complexity of the corresponding design tasks exist. In this paper, we fill this gap by providing a formal description of design tasks for the Hybrid Level 3 of the European Train Control System and proofs that these tasks are NP-complete or NP-hard, respectively. By that, we are providing a solid basis for the future development of methods to solve those tasks, which will be integrated into the Munich Train Control Toolkit available at https://github.com/cda-tum/mtct.

翻译：近年来，铁路网络的重要性日益凸显，尤其是在将货运和公共交通从道路交通和飞机转向更环保的列车方面。由于扩建全球铁路网络既耗时又耗资源，因此最大化现有基础设施上的铁路容量是可取的。然而，简单地增加列车运行数量并不可行，因为必须满足列车控制系统施加的某些约束。铁路网络的容量（除其他因素外）取决于该安全系统所允许的列车间距。虽然大多数信号系统依赖于由昂贵硬件定义的固定闭塞分区，但ETCS混合等级3（最近也被称为采用混合列车检测的ETCS等级2）提供的新规范允许使用虚拟子区段。这一额外的自由度使得列车追踪间隔更短，从而能在现有铁路轨道上运行更多列车。另一方面，新的设计任务应运而生，自动化方法可能对现代铁路网络的设计者有所帮助。然而，尽管已有初步方法解决ETCS混合等级3中出现的部分设计问题，但相应的设计任务既缺乏形式化描述，也缺乏计算复杂度的结果。本文填补了这一空白，提供了欧洲列车控制系统混合等级3设计任务的形式化描述，并证明了这些任务分别为NP完全或NP困难问题。由此，我们为未来开发解决这些任务的方法奠定了坚实基础，这些方法将集成到慕尼黑列车控制工具包（可从https://github.com/cda-tum/mtct获取）中。