Planning and optimization of passenger railway services with virtually coupled trains

This paper proposes a model for designing a passenger railway service in the framework of a virtual coupling scenario, where automated trains can be grouped to form a convoy. In particular the proposed model considers automated carriages that can virtually split and merge together to form a train with a time-varying composition and capacity. Moreover, each carriage is associated to a destination, so that a train can be composed by different carriages, each of them capable of independently taking a different direction at a junction. This work describes a novel optimization model, based on an integer mathematical programming formulation, aimed to determine the optimal paths and departure times of the carriages in a urban railway network, and thus the optimal time-variant capacity along the path between each pair origin-destination, according to transport demand and in particular minimizing the necessity for the passengers to change train in order to reach their destination. In order to allow trains to change their composition, some maneuvers at the stations are assumed to be possible, like the parking of unused carriages on a side track and the change of track allowed by appropriate switches. The paper presents also some results of the implementation of the model on an example case study, with the aim of testing the model and discussing some features of the solution.