For years, formal methods have been successfully applied in the railway domain to formally demonstrate safety of railway systems. Despite that, little has been done in the field of formal methods to address the cyber-physical nature of modern railway signalling systems. In this article, we present an approach for a formal development of cyber-physical railway signalling systems that is based on a refinement-based modelling and proof-based verification. Our approach utilises the Event-B formal specification language together with a hybrid system and communication modelling patterns to developing a generic hybrid railway signalling system model that can be further refined to capture a specific railway signalling system. The main technical contribution of this article is the refinement of the hybrid train Event-B model with other railway signalling sub-systems. The complete model of the cyber-physical railway signalling system was formally proved to ensure a safe rolling stock separation and prevent their derailment. Furthermore, the article demonstrates the advantage of the refinement-based development approach of cyber-physical systems, which enables a problem decomposition and in turn reduction in the verification and modelling effort.

Abstract The decentralised railway signalling systems have a potential to increase capacity, availability and reduce maintenance costs of railway networks. However, given the safety-critical nature of railway signalling and the complexity of novel distributed signalling solutions, their safety should be guaranteed by using thorough system validation methods. To achieve such a high-level of safety assurance of these complex signalling systems, scenario-based testing methods are far from being sufficient despite that they are still widely used in the industry. Formal verification is an alternative approach which provides a rigorous approach to verifying complex systems and has been successfully used in the railway domain. Despite the successes, little work has been done in applying formal methods for distributed railway systems. In our research we are working towards a multifaceted formal development methodology of complex railway signalling systems. The methodology is based on the Event-B modelling language which provides an expressive modelling language, a stepwise development and a proof-based model verification. In this paper, we present the application of the methodology for the development and verification of a distributed protocol for reservation of railway sections. The main challenge of this work is developing a distributed protocol which ensures safety and liveness of the distributed railway system when message delays are allowed in the model.

The modern radio-based railway signalling systems aim to increase network's capacity by enabling trains to run closer to each other. At the core of such systems is train's on-board computer (discrete) responsible for computing and controlling the speed (continuous) of the train. Such systems are best captured by hybrid models, which capture discrete and continuous system's aspects. Hybrid models are notoriously difficult to model and verify, in our research we address this problem by applying hybrid systems' modelling patterns and stepwise refinement for developing hybrid train speed controller model.