Utilizing phase-type distributions for queueing-based railway junction performance determination

To ensure the effective and objective development of transportation networks, it is crucial to identify performance limitations across various subsystems. A timetable-independent assessment of infrastructure capacity at railway junctions is a fundamental aspect of long-term rail network planning. While recent research introduced queueing-based methods to quantify route-based railway junction performance, modelling arrival and service processes has been limited to exponential distributions. This work utilizes Phase-Type Distributions to propose an extension to a previously described Continuous-Time Markov Chain model. In a comparison between assumed distribution combinations, the effect of a more detailed stochastic process modelling is described. Furthermore, an analysis of the differences to a simulation method is conducted for an exemplary railway junction. The introduced method enables infrastructure managers to accurately model stochastic processes for performance determination in the early stages of the strategic planning phase. • Phase-type distributions to enhance railway junction analysis in CTMC models. • Validation of model effectiveness through inter-model comparisons and simulations. • An efficient algorithm to estimate timetable capacity using queue-length thresholds. • A case study to identify bottlenecks in mixed-traffic railway junctions.