  This paper introduces a formal method to model the level of demand on control
when executing cognitive processes. The cost of cognitive control is parsed
into an intensity cost which encapsulates how much additional input information
is required so as to get the specified response, and an interaction cost which
encapsulates the level of interference between individual processes in a
network. We develop a formal relationship between the probability of successful
execution of desired processes and the control signals (additive control
biases). This relationship is also used to specify optimal control policies to
achieve a desired probability of activation for processes. We observe that
there are boundary cases when finding such control policies which leads us to
introduce the interaction cost. We show that the interaction cost is influenced
by the relative strengths of individual processes, as well as the
directionality of the underlying competition between processes.
