铁路时刻表中的相位同步
Phase Synchronization in Railway Timetables
摘要：
公交时刻表的构建是公交系统中最重要的优化问题之一。在尽量减少旅行时间和其他标准的辅助条件下找到最佳或接近最佳的时间表，是对公共交通运作的有针对性的贡献。除了效率（例如，通过最小平均旅行时间），时间表的一个重要特征是其对延迟传播的鲁棒性。在这里，我们从同步的角度研究长途铁路时刻表（特别是德国当前的长途铁路时刻表）的效率和鲁棒性的平衡，利用大部分火车几乎周期性运行的事实。我们发现，同步是最高的中型站。我们认为，这种同步的角度来看，打开了一个新的途径对铁路时刻表的理解，将它们表示为时空相位模式。然后，鲁棒性和效率可以被视为该相位模式的属性。
英文摘要：
Timetable construction belongs to the most important optimization problems in public transport. Finding optimal or near-optimal timetables under the subsidiary conditions of minimizing travel times and other criteria is a targeted contribution to the functioning of public transport. In addition to efficiency (given, e.g., by minimal average travel times), a significant feature of a timetable is its robustness against delay propagation. Here we study the balance of efficiency and robustness in long-distance railway timetables (in particular the current long-distance railway timetable in Germany) from the perspective of synchronization, exploiting the fact that a major part of the trains run nearly periodically. We find that synchronization is highest at intermediate-sized stations. We argue that this synchronization perspective opens a new avenue towards an understanding of railway timetables by representing them as spatio-temporal phase patterns. Robustness and efficiency can then be viewed as properties of this phase pattern.
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