Towards Equitable Rail Service Allocation Through Fairness-Oriented Timetabling in Liberalized Markets

TL;DR

This paper tackles fair allocation of scarce rail infrastructure capacity in liberalized European markets. It proposes a fairness-oriented timetabling framework that adapts Jain's index, the Gini coefficient, and the Atkinson index to per-RU service importances and couples them with a genetic algorithm (MEALPY) to generate conflict-free schedules, with a fitness function $fitness = revenue \cdot fairness$. The study shows that equity-based allocations dramatically reduce inequity across balanced, semi-balanced, and unbalanced capacity scenarios, but incur substantial revenue penalties compared with pure profit maximization. Tuning the sensitivity parameter $α$ (e.g., $α=25$ for Jain and Atkinson, $α=10$ for Gini) enhances discrimination of unfair allocations and improves equity outcomes. This work provides a practical, decision-support approach for regulators and infrastructure managers in liberalized rail markets.

Abstract

Over the last few decades, European rail transport has undergone major changes as part of the process of liberalization set out in European regulations. In this context of liberalization, railway undertakings compete with each other for the limited infrastructure capacity available to offer their rail services. The infrastructure manager is responsible for the equitable allocation of infrastructure between all companies in the market, which is essential to ensure the efficiency and sustainability of this competitive ecosystem. In this paper, a methodology based on Jain, Gini and Atkinson equity metrics is used to solve the rail service allocation problem in a liberalized railway market, analyzing the solutions obtained. The results show that the proposed methodology and the equity metrics used allow for equitable planning in different competitiveness scenarios. These results contrast with solutions where the objective of the infrastructure manager is to maximize its own profit, without regard for the equitable allocation of infrastructure. Therefore, the computational tests support the methodology and metrics used as a planning and decision support tool in a liberalized railway market.

Figures (7)

• Figure 1: Calculation of the Gini coefficient.
• Figure 2: Generation of a Fairness-oriented Timetabling
• Figure 3: Inequity (%) evolution over training epochs.
• Figure 4: Evolution of inequity values for the three fairness indices (Jain, Gini, and Atkinson) over training epochs.
• Figure 5: Evolution of fairness index values for the three fairness indices (Jain, Gini, and Atkinson) over training epochs.