Utilizing Bayesian Optimization for Timetable-Independent Railway Junction Performance Determination

TL;DR

The paper addresses determining timetable‑independent junction capacity under dynamic traffic by solving a non‑linear optimization where capacity constraints are expensive CTMC evaluations. It adapts Bayesian optimization to a known objective with unknown, constraint‑driven evaluations, incorporating a GP mean reflecting an exponential constraint trend and a Matérn kernel for flexible surrogate modeling. The approach is demonstrated on a small illustrative junction and a real‑world Parisian junction (Triangle of Gagny), where dynamic traffic distributions outperform fixed timetable baselines, with notable gains in throughput and robust performance under high penalty weights. This framework enables data‑efficient, planning‑oriented capacity assessment for long‑term railway infrastructure, supporting decisions under traffic composition uncertainty.

Abstract

The efficiency of railway infrastructure is significantly influenced by the mix of trains that utilize it, as different service types have competing operational requirements. While freight services might require extended service times, passenger services demand more predictable schedules. Traditional methods for addressing long-term traffic assignment problems often rely on fixed-value capacity limitations, determined based on specific assumptions about traffic composition. This paper introduces a methodology for determining timetable-independent capacity within the traffic rate assignment problem, enabling the calculation of junction capacities under dynamic traffic distributions. We solve the underlying non-linear constrained optimization problem maximizing the traffic throughput using Bayesian optimization (BO). This setting combines a known objective function with expensive- to-compute capacity constraints, motivating an adaption of standard BO problems, where objective functions are usually unknown. We tailor the acquisition process in BO to this specific setting and increase performance by incorporating prior knowledge about the shape of the constraint functions into the Gaussian process surrogate model. Our derived approaches are benchmarked on a railway junction near Paris, significantly outperforming fixed traffic composition models and highlighting the benefits of dynamic capacity allocation.

Figures (7)

• Figure 1: Overview of the proposed method. We aim to maximize the number of trains through a junction by using Bayesian optimization to find globally optimal traffic rate assignments respecting computationally expensive to evaluate capacity constraints that are modeled with continuous-time Markov chains.
• Figure 2: Exemplary plot of a constraint $c_r$ and its components $L_r, L_{r, \text{limit}}$ for different traffic rates $\lambda_{\text{total}}$.
• Figure 3: Iterations of EI-Exp-TR (see Section \ref{['sec:model_select']}) and their corresponding maximal constraint $\max c_r$ and objective value.
• Figure 4: Objective distribution between all methods and experiments for $w_U = 5$.
• Figure 5: Infrastructure layout of the Triangle of Gagny. Adapted from pellegriniOptimalTrainRouting2014emundsEvaluatingRailwayJunction2024