Meeting functional requirements for real-time railway traffic management with mathematical models

Abstract

Railway traffic management is the process of executing production plans, supervising traffic, detecting conflicts, and applying dispatching measures to resolve them. The activity space of traffic managers is constrained by infrastructure, rolling stock, and operations related features and rules. These constraints result in functional requirements that mathematical models should satisfy to be useful to support realtime traffic management. First, this paper identifies and describes these requirements. Second, it presents an overview of the most prominent mathematical formulations for timetabling and rescheduling in the literature. Using sample scheduling problems, it highlights how individual train runs and interactions are represented. The similarities and the differences among the formulations are strengthened to distinguish two main categories of models. Finally, the models are analysed with respect to the functional requirements from real-time traffic management. As expected, off-line scheduling models do not satisfy the requirements related to real-time monitoring and intervention. In contrast, on-line models satisfy most requirements. In particular, there are two rescheduling models that satisfy all functional requirements: the Resource Con- flict Graph and an extension of the Alternative Graph.