The dynamics of modal split for freight transport

•Modal split of a freight multimodal transport system evolves over time.•The evolution essentially depends on the dynamic cost functions of the modes.•The knowledge of the past evolution enables estimating the dynamic cost functions.•The model enables forecasting the future evolution of modal split.

The paper presents a dynamic model of modal split in a multimodal freight transport system, which supposes that the evolution over time of transport demand is accompanied by a corresponding evolution of transport modes, and that users react with delay to cost variations. Starting with these hypotheses, and following the paradigm of random utility, a recursive equation is obtained, whose iterated application furnishes the sequence of the demand fractions on the various transport modes in the successive epochs of the time period during which the evolution of the transport system is studied and enables forecasting the future modal split evolution.