Queueing Modelling is proposed in the domain of Intelligent User Interfaces and, more generally, in the field of Human-Computer Interaction. It is argued that Queueing Modelling can facilitate assessment of the current state and prediction of the future behaviour of user-computer interaction. This assessment can be used as the basis for adaptations either at design-time or at run-time, and can benefit the development and evaluation of adaptable or adaptive user interfaces. In order to illustrate our approach, we present specific queueing systems which model the sensory load of the user in the context of Intelligent Multimedia User Interfaces. Indicative adaptation policies that build on this analysis are also exemplified.