Quantifying periodic railway network capacity using petri nets and macroscopic fundamental diagram

Research output: Contribution to journalResearch articleContributedpeer-review



The infrastructure occupation of many European railway networks appears to be at its limits, whilst recent public discussions aim to shift even more traffic towards the railway system. Thus, the question of the railway network's capacity is gaining increasing attention. In this paper, we assess the capacity of periodic railway networks on the strategic level, using a newly developed petri net (PN) based approach: the railway network utilization model (RNUM). The model builds upon individual lines which are connected to more complex networks. The network's emerging elementary circuits are then used for utilization analysis. To assess the networks capacity, the model is applied in the enumeration-based railway network capacity (RNC) framework. By evaluating the maximum utilization of different scenarios, the capacity of the periodic network is identified. This framework provides the minimal operable frequency of the network and corresponding train flows, as well as the average scheduled waiting times per train. It thereby assesses the capacity and the corresponding network effects, which are quantified in a network-specific macroscopic fundamental diagram for the railway network (MFD-R). Experiments on different generic networks demonstrate the RNC framework's applicability and reveal additional insights into the connections between train flow, waiting times and the total number of trains. The results show sensitivity between the networks throughput performance and the networks saturation. The evaluation also shows that the maximum utilization just emerges under very specific conditions and might result in unstable operations. Additionally, the results illustrate dependencies between network capacity and the network's structure. Furthermore, a case study performed at a real life railway network in the Netherlands proves the realism of the results. It is thus shown, that the presented model can contribute to prepare railway networks for tomorrows traffic and thus support the recent ambitions for eco-friendly transport.


Original languageEnglish
Article number104436
JournalTransportation Research Part C: Emerging Technologies
Publication statusPublished - Jan 2024

External IDs

ORCID /0000-0003-4111-2255/work/151437423
ORCID /0000-0002-1424-5741/work/151437441



  • Capacity assessment, Macroscopic fundamental diagram, Petri nets, Railway networks