Macroscopic traffic flow in railway systems — A discussion of the applicability of fundamental diagrams

Macroscopic traffic flow theory is widely used to analyze the performance and congestion in transportation systems and urban traffic. Currently, the main area of application is road traffic, where fundamental diagrams depicting the relationship between performance parameters such as traffic density, traffic flow and vehicle speed are used to represent traffic regimes and system settings. Research on the applicability for rail traffic systems is only starting to emerge and has mainly focused on mass transit systems and moving block signaling systems, so far. The current paper provides a theoretical analysis of traffic flow properties on unidirectional railway lines. Macroscopic fundamental diagrams are established and used to analyze similarities and differences of traffic flow behavior in railway systems. It is shown how fundamental diagrams allow to pinpoint flow regimes and different phases in train traffic, which can be useful information for system design and operation planning. Railway systems are studied both in a deterministic setting allowing to analyze peak efficiency and in a stochastic setting with perturbations.