Estimating aggregate railway performance from realized empirical data: Literature review, a test case and a research roadmap

Railway operations are organized according to a complex interplay of resources and according to a rigid time separation of train runs over infrastructure elements. The system dynamics are complex, and span in time and space. We use in this work the concepts of macroscopic fundamental diagrams, or more in general the analysis in a density-flow-speed diagram, to analyse and describe realized railway operations. Specifically, we review the state of the art in aggregated models of railway performance. We illustrate a possible application by means of a test case. We consider realized railway operations, aggregated on a railway line with heterogeneous traffic, as measured in a set of stations. We use a density-flow-speed diagram to represent the recorded operations, similar to the concepts of macroscopic fundamental diagram or network fundamental diagram. In this sense, it is a first try to estimate a macroscopic relationship, from realized data based on heterogeneous railway services with different stopping patterns. The analyses show the challenges of aggregate operations for different railway stretches, from realized data. We report what is the influence of delays, represented in those diagrams by a shift of the operating point. Future promising directions of research are concluded from the analysis.