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

TL;DR

This paper introduces a novel approach using Phase-Type Distributions within a Markov Chain framework to improve the accuracy of railway junction performance assessment, moving beyond exponential assumptions for better infrastructure planning.

Contribution

It extends existing queueing models by incorporating Phase-Type Distributions, allowing more detailed stochastic process modeling for railway junction performance evaluation.

Findings

Enhanced modeling accuracy with Phase-Type Distributions.

Significant differences observed compared to exponential assumptions.

Method aligns well with simulation results for practical applications.

Abstract

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.