correspond to
and the hourly demand 
is
The hourly contribution coefficients 
can be estimated by a multiple linear regression with the observed flows 
as the dependent variables and the assigned flows of the basic states 
as the independent variables
The regressions to obtain the coefficients 
are done once for a given set of states, based on assignments onto the base year network on which the volume were counted. These coefficients are then used to obtain the hourly volumes and demands for the base year. Of course, the same coefficients can also be used to study network changes under the assumption that the demand structure remains unchanged. In this case, the vectors would be obtained by assigning onto the modified network.
A
