Risk of delay evaluation in real-time train scheduling with uncertain dwell times

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.