A major problem of public transport, and railways in particular, is to improve quality of operations by updating an offline timetable to the ever changing delays situation, in order to improve performance of the transport system. In railway systems, this relates to reduce train delays by reordering retiming or rerouting trains, and/or change connection plans and route advised to passengers, to improve their travel time.

Key point of research is the interaction between the problem (of the infrastructure manager) to reschedule trains and the problem (of the travellers) to find the optimal route in the network. In fact, changing passenger flows, respectively delaying trains and/or dropping passenger connections, varies the setting under which the two decision makers respectively interact. The interaction of the two decisions makers is mediated by the information one decision maker has about the other, and the service which is offered/used. We report different methods to address this dilemma, by agent based simulations, by game-theoretical approaches, and by estimating models of human behavior based on observed actions.