Let us further assume that 
denotes a small set of basic states, for each of which we have a demand matrix 
, where 
denotes the set of origin destination pairs. It is important to note that these basic states need not correspond to a precise period of the day, nor do they necessarily represent the complete demand. Each state s, however, should be associated with a typical and different travel pattern and the set S should be such that the entire demand during the entire day is represented.
For each of the basic states, an assignment is carried out to obtain the corresponding link flows 
, 
, for which we will use the shorthand
Each hour of the day is assumed to be composed of a mix of the basic states. The contribution of each basic state s to each hour of the day h is denoted by 
