Dynamic cost functions and freight transport modal split evolution

•Modal split evolves in a sequence of time periods with different characteristics.•The distribution of dynamic cost functions determines the modal split evolution.•Modal split evolution is stable if users react slowly to transport cost changes.•Similarity of the dynamic cost functions fosters a stable modal split evolution.

The paper studies the characteristics of the evolution over time of modal split for a transport system in which various modes compete with each other and face the freight flow increase in different ways. It is shown that the modal split evolution is constituted by a sequence of time periods, in each of which the dynamic characteristics of the system are different. An equilibrium, stable or unstable, is reached after a transition phase, whose length depends on the characteristics of the system, and in some cases exceeds the length of the period, so that an equilibrium is not reached.