While trains travel in a railway network, disturbances may arise and corrective decisions to minimize delay propagation may be necessary to solve conflicting track requests. This problem is known in the literature as the real-time Railway Traffic Management Problem (rtRTMP) and its solutions represent plans of operations that minimize delay propagation due to unexpected disturbances. However, uncertainty may still affect such plans and their expected quality in terms of level of service or risk containment. This article proposes a new approach for the assessment of the risk of onset or worsening of delays associated to an rtRTMP solution when dwell times are uncertain and only an interval representation of them is known to the scheduler. To this aim, the Conditional-Value-at-Risk of the maximum train delay is adopted as risk index. In this study we address both modeling and computational issues, developing and testing a graph-based model to use with an innovative numerical method to obtain a real-time risk evaluation for rtRTMP solutions. The proposed approach is applied on a real case study analyzing the effects of uncertainties of different severity. Promising computational results enable to use the methodology to deal with the rtRTMP taking into account the uncertainty on the involved activities and the risk attitude of the decision-makers at the operational level.

当列车在铁路网络中行驶时，可能会出现干扰，并且可能需要做出最小化延迟传播的纠正决策来解决冲突的轨道请求。这个问题在文献中被称为实时铁路交通管理问题 (rtRTMP)，它的解决方案代表了最小化由于意外干扰引起的延迟传播的操作计划。然而，不确定性仍可能影响此类计划及其在服务水平或风险控制方面的预期质量。本文提出了一种新方法，用于在驻留时间不确定且调度程序只知道它们的间隔表示时，评估与 rtRTMP 解决方案相关的延迟发生或恶化的风险。为此，采用最大列车延误的条件风险价值作为风险指标。在这项研究中，我们解决了建模和计算问题，开发和测试了一个基于图形的模型，以使用创新的数值方法来获得 rtRTMP 解决方案的实时风险评估。所提出的方法应用于分析不同严重性的不确定性影响的真实案例研究。有希望的计算结果使得能够使用该方法来处理 rtRTMP，同时考虑到所涉及活动的不确定性和操作层面决策者的风险态度。