Conflict detection and resolution models typically consider train separation distances based on a number of blocks corresponding to conventional fixed-block signalling systems. However, modern distance-to-go railway signalling systems, such as the European Train Control System (ETCS), use braking curve supervision, resulting in train- and speed-dependent train separation distances. This paper proposes a modelling approach that incorporates train- and speed-dependent brake indication points and the resulting blocking times, enhancing conflict detection and resolution models for distance-to-go signalling. By integrating these enhancements into the state-of-the-art RECIFE-MILP model, a mixed integer linear programming formulation explicitly representing fixed-block distance-to-go signalling is obtained. The enhanced model is evaluated considering the state-of-practice fixed-block distance-to-go signalling system ETCS Level 2, and is compared with the original model for conventional fixed-block signalling in two real-world case studies. Results show that the shorter train separation under distance-to-go signalling leads to different rescheduling decisions, including a significant number of reroutings and some reorderings. With that, reductions in total train delay are achieved for 98% and 55% of the respective case study instances. While the mean reductions are below 1%, reductions of up to 7% are observed. These findings illustrate the operational relevance of incorporating distance-to-go principles into conflict detection and resolution modelling.

To further improve the capacity on the European railway network, next-generation distance-to-go signalling systems are being developed in the context of the European Train Control System (ETCS). This paper investigates the impact of track discretisation granularity on conflict detection and resolution for ETCS with onboard train integrity monitoring. The study enhances a previously developed model for fixed-block distance-to-go signalling introducing a track discretisation procedure and reformulating safe train separation constraints at switches. The assessment is performed on a junction and a corridor case study, using track discretisations with maximum section lengths from 50 to 800 metres. Though finer discretisations potentially improve the model objective, computation times quickly increase. While the results show minimum effects of the track discretisation on the conflict detection and resolution, they suggest that maximum section lengths of 200 or 400 metres may offer a good balance between solution quality and computation complexity, depending on the track layout and traffic density.

For effective railway operations, real-time railway traffic management is crucial. In case of disturbances, traffic management can apply rescheduling and rerouting measures to resolve conflicts while minimising the propagation of delay. To support human dispatchers in taking optimised decisions, conflict detection and resolution (CDR) models are developed. Predominantly based on alternative graphs or mixed integer linear programming (MILP), the existing models mostly refer to conventional signalling systems in which the track is discretised into fixed blocks. Only at block entries, trains can receive a brake indication. Hence, train separation is based on a number of blocks. With the implementation of continuous braking curve supervision in distance-to-go (DTG) signalling systems such as the European Train Control System (ETCS), train separation is based on absolute braking distances. Consequently, an explicit relation between speed and train separation is required in CDR models for DTG signalling. Recently, we proposed enhancements for existing CDR models
to describe DTG operations. The enhancements relate to track discretisation, speed profile options and train separation. We applied these enhancements to RECIFE-MILP, resulting in a tailored CDR model for DTG signalling. In this research, we consider the model for the more advanced DTG signalling systems of ETCS Level 3: Fixed Virtual Block and Moving Block. In these train-centric signalling systems, train position and integrity are monitored onboard
– as opposed to conventional trackside train detection. We update the DTG model accordingly, and we investigate the impact of track discretisation granularity on the model performance. The impact is assessed in terms of delay recovery and rescheduling decisions. The results indicate that, depending on the track and traffic scenario, a finer granularity can lead to different rescheduling and rerouting decisions due to shorter train separation.

In case of disturbed railway operations, traffic management can apply rescheduling measures to resolve conflicts while minimising delay propagation. This can be optimised by conflict detection and resolution (CDR) models. Usually based on alternative graph or mixed integer linear programming (MILP) formulations, existing models mostly refer to conventional signalling systems in which the track is discretised into blocks. Only at block entries, trains can receive a brake indication. Hence, train separation distances are based on a number of blocks. With the implementation of continuous braking curve supervision in distance-to-go (DTG) signalling systems such as the European Train Control System (ETCS), train separation is based on absolute braking distances. Consequently, an explicit relation between speed and train separation is required in CDR models for DTG signalling. Recently, we enhanced the CDR model RECIFE-MILP to DTG operations. The enhancements relate to track discretisation and speed-dependent train separation. In this research, we investigate the effect of track discretisation granularity on the performance of the enhanced model for next-generation DTG signalling systems: ETCS Level 3 Fixed Virtual Block and Moving Block. The performance is assessed regarding total delay and rescheduling decisions. The results indicate that, depending on the track and traffic scenario, a finer granularity can lead to different rescheduling decisions due to shorter train separation.

Conflict detection and resolution models are being developed to support railway traffic management in taking optimised rescheduling decisions in case of disturbances. Existing models mostly concern fixed-block signalling systems, in which minimum train separation distances are determined based on a preset number of blocks representing worst-case braking distances. In a moving-block signalling system, minimum train separation is based on absolute braking distances and hence depends on train speed differently from how fixed-block conflict detection and resolution models. In this paper, we propose a conflict detection and resolution model that approximates moving-block operations. The model enhances the state-of-the-art fixed-block rescheduling model RECIFE-MILP. The enhancements include a reconsideration of the discretisation of the infrastructure, the introduction of a speed profile alternative and a redefinition of the blocking times. We verify the model by comparing the solutions of the moving-block version with the fixed-block version for a specific scenario. The results indicate that the moving-block model can propose different rescheduling decisions than the fixed-block model with a better delay recovery.

Railway industry is developing advanced signalling systems like moving block to improve network capacity. In traditional fixed-block systems, safe train separation is determined based on a fixed number of block sections representing worst-case braking distances. In moving-block systems, the train separation is reduced to absolute braking distances. The introduction of moving-block signalling requires a change in operational rules and hence in real-time conflict detection and resolution methods in case of disturbances. Existing conflict detection and resolution models are mainly based on fixed-block signalling and the available models for moving-block signalling do not sufficiently represent the dynamic relation between safe train separation and actual train speeds.
To address this gap, we propose a conflict detection and resolution model that approximates moving-block operations. The model enhances the state-of-the-art fixed-block model RECIFE-MILP. The enhancements include a reconsideration of the discretisation of the infrastructure, the introduction of a speed profile alternative and a redefinition of blocking times. With this, the model is able to include speed-dependent occupation times, train separation based on absolute braking distances and continuous braking curve supervision.
We present the reformulated MILP (mixed integer linear programming) model and apply it to two French case studies: the Gonesse junction and a part of the Paris-Le Havre line. For various one-hour periods, rescheduling strategies and disturbance scenarios, we compare the optimal solutions of the enhanced and the original RECIFE-MILP model in terms of total train delay and rescheduling decisions. The results show that the enhanced model can propose different rescheduling decisions than the original model, with a better delay recovery exploiting the moving-block system.

Railway traffic management is responsible for the detection and resolution of conflicts in case of disturbed operations. To minimise delay propagation, rescheduling decisions are taken by human dispatchers, possibly supported by mathematical models. Existing conflict detection and resolution (CDR) models mostly refer to conventional fixed-block multi-aspect signalling systems, in which minimum train headways are determined based on a preset number of blocks considering worst-case braking distances and number of signal aspects. In moving-block signalling systems, minimum headways are based on absolute braking distances. This paper reviews literature on CDR with the aim to identify gaps and to propose next steps in the research on CDR under moving-block signalling. A research agenda presents various modelling options, for which modelling approaches are proposed based on a comparative analysis.