Department of Information and Computing Sciences, Utrecht University, Princetonplein 5, 3584 CC, Utrecht, The Netherlands.
Centre for Complex Systems Studies, Utrecht University, Minnaertgebouw, Leuvenlaan 4, 3584 CE, Utrecht, The Netherlands.
Sci Rep. 2021 Oct 21;11(1):20860. doi: 10.1038/s41598-021-00361-z.
Railway systems provide pivotal support to modern societies, making their efficiency and robustness important to ensure. However, these systems are susceptible to disruptions and delays, leading to accumulating economic damage. The large spatial scale of delay spreading typically make it difficult to distinguish which regions will ultimately affected from an initial disruption, creating uncertainty for risk assessment. In this paper, we identify geographical structures that reflect how delay spreads through railway networks. We do so by proposing a graph-based, hybrid schedule and empirical-based model for delay propagation and apply spectral clustering. We apply the model to four European railway systems: the Netherlands, Germany, Switzerland and Italy. We characterize these geographical delay structures in the railway systems of these countries and interpret these regions in terms of delay severity and how dynamically disconnected they are from the rest. The method also allows us to point out important differences between these countries' railway systems. For practitioners, such geographical characterization of railways provides natural boundaries for local decision-making structures and risk assessment.
铁路系统为现代社会提供了至关重要的支持，因此确保其效率和稳健性至关重要。然而，这些系统容易受到干扰和延误，导致经济损失不断累积。延迟传播的大空间尺度通常使得难以区分哪些区域最终会受到初始干扰的影响，这给风险评估带来了不确定性。在本文中，我们确定了反映延迟如何通过铁路网络传播的地理结构。我们通过提出一种基于图的、混合计划和基于经验的延迟传播模型并应用谱聚类来实现这一点。我们将该模型应用于四个欧洲铁路系统：荷兰、德国、瑞士和意大利。我们描述了这些国家铁路系统中的地理延迟结构，并根据延迟严重程度以及与其他部分的动态分离程度来解释这些区域。该方法还使我们能够指出这些国家铁路系统之间的重要差异。对于从业者来说，这种对铁路的地理特征描述为本地决策结构和风险评估提供了自然边界。
