Railways are increasingly investing in their infrastructure to achieve sustainability objectives and meet expected growth in demand for rail transport services. Since building new physical infrastructure requires large-scale investments and long lead times, many infrastructure managers (IMs) are prioritizing upgrades to their signalling systems to optimize use of their existing networks. By migrating from legacy multi-aspect to distance-to-go (DTG) signalling, IMs gain the ability to safely run trains closer together, better manage disruptions occurring in normal operations, and implement other compatible technologies that can increase capacity and enhance service.
The key advantages of DTG systems are derived from their ability to provide more precise brake and speed supervision relative to multi-aspect signalling. Existing multi-aspect signalling systems rely on lineside signals to display braking indications to trains and do not consider train braking capabilities when determining the minimum separation between trains. As a result, minimum train separation is based on the worst-case braking distance of any train that could operate on the line. In contrast, brake supervision in DTG signalling systems is performed by the train’s onboard computer which calculates a train’s braking distance based on that specific train’s current speed and braking capability. The ability to determine braking distance based on a train’s own characteristics allows more delayed braking relative to multi-aspect signalling. Moreover, migrating the brake supervision from track to train eliminates the need for lineside signalling and related restrictions on block lengths, thereby permitting layouts with shorter blocks than would otherwise be possible with multi-aspect signalling.
To further increase network capacity, IMs are also looking to implement Connected Driver Advisory Systems (C-DAS) and Automatic Train Operation (ATO) systems. These systems permit greater coordination of train paths at the operational level through the provision of timing windows to trains (referred to as a Train Path Envelope or TPE) in real time. This timing information, in turn, helps trains avoid conflicts at the operational level when recovering from small departure delays at stations.
In practice, the benefits of DTG signalling and C-DAS/ATO systems can best be realized if timetabling algorithms consider the actual capabilities of those digital technologies to operate trains closer together in regular operations. It is therefore necessary to align tactical and operational scheduling rules, and to update train planning rules to reflect the capabilities of DTG signalling and C-DAS/ATO systems. However, state-of-the-art-methods for tactical scheduling could result in suboptimal network use as they do not accurately represent operational processes occurring on the railway network, and rely on different levels of detail than those used for real-time traffic management. Furthermore, the abstraction of signalling constraints at the tactical level necessitates additional and more detailed assessments using microscopic methods to achieve a target service plan and timetable feasibility.

To help maximize utilization of its existing infrastructure, the railway industry requires train service optimization models with headway constraints for state-of-the-art distance-to-go signalling systems. To this end, this paper introduces an approach for assessing train path feasibility in ETCS Level 2, Moving Block, and Virtual Coupling, that could be used to construct alternative graphs for timetable optimization. The methodology is the first for distance-to-go signalling systems that accounts for the impact of train acceleration and braking on the braking curve, guaranteeing a feasible and optimal timetable. The alternative graph models are specifically adapted to the train and signalling systems used, with the models for Moving Block and Virtual Coupling being the first with continuous representation of open track. The methodology is used to assess the capacity of Virtual Coupling and Moving Block, respectively, on the South West Main Line in the United Kingdom. The results show that Virtual Coupling can increase railway capacity compared to plain Moving Block, but this may depend on network topology.