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Virtual coupling is a novel railway transport concept that allows trains to split and join on-the-fly by switching from mechanical to virtual couplers. One of the main challenges in applying virtual coupling in metro railways is to reduce the tracking distance between trains without compromising safety. This paper proposes a relative operation-based train separation model to reduce the safe distance between trains. This model applies a fault tolerance principle. The principle is that the preceding train normally operates for a time interval from its last-known state before initiating an emergency brake to stop the train. A difficulty in applying the proposed model is to predict the boundary of all possible time-position trajectories of the preceding train, which is the reachability problem of a hybrid system. To solve this problem, we formalise the operation of the preceding train by a parameterized hybrid automaton. A polytope-based algorithm is then developed for computing an over-approximated reachable set of the automaton. We compare our approach with a state-of-the-art relative braking distance-based train separation model for virtual coupling on a concrete metro line in Chengdu, China, and evaluate the method with several benchmarks. The results demonstrate that the relative operation-based model substantially reduces the safe distances between trains. Compared to conventional approaches, the proposed model provides a considerable 90.7&#x0025; decrease in unnecessary waiting time at railway stations for virtually coupled trains and a 4.9&#x0025; increase in the capacity of the given railway lines.

A Relative Operation-Based Separation Model for Safe Distances of Virtually Coupled Trains